http://www.physicsbook.gatech.edu/api.php?action=feedcontributions&feedformat=atom&user=Zhaoxian+ZhangPhysics Book - User contributions [en]2026-05-10T18:44:49ZUser contributionsMediaWiki 1.42.7http://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40789Light Scattering2022-07-25T05:21:44Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[https://en.wikipedia.org/wiki/Rayleigh_scattering]. This is a from of elastic scattering where scattered light does not lose energy. In Rayleigh scattering, the particles are considered to be point dipoles, and scatter light according to molecular polarizability. <br />
<br />
When the particle size is larger, the scattering event is more complicated and characterized by Mie theory[https://en.wikipedia.org/wiki/Mie_scattering] which have analytical solutions for scattering event with spherical scatterers, or discrete dipole approximation[https://en.wikipedia.org/wiki/Discrete_dipole_approximation] which applies to more complicated shapes, both are based on solving Maxwell's equations.<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40788Light Scattering2022-07-25T05:16:17Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[https://en.wikipedia.org/wiki/Rayleigh_scattering]. When the particle size is larger, the scattering event is characterized by Mie theory[https://en.wikipedia.org/wiki/Mie_scattering] or discrete dipole approximation[https://en.wikipedia.org/wiki/Discrete_dipole_approximation] by solving Maxwell's equations.<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40787Light Scattering2022-07-25T05:15:29Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[https://en.wikipedia.org/wiki/Rayleigh_scattering]. When the particle size is larger, the scattering event is characterized by Mie theory[https://en.wikipedia.org/wiki/Mie_scattering] or discrete dipole approximation[https://en.wikipedia.org/wiki/Discrete_dipole_approximation] by solving Maxwell's equations.<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Photons]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40786Light Scattering2022-07-25T05:13:35Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[https://en.wikipedia.org/wiki/Rayleigh_scattering]. When the particle size is larger, the scattering event is characterized by Mie theory[https://en.wikipedia.org/wiki/Mie_scattering] or discrete dipole approximation[https://en.wikipedia.org/wiki/Discrete_dipole_approximation] by solving Maxwell's equations.<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40785Light Scattering2022-07-25T05:12:20Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[https://en.wikipedia.org/wiki/Rayleigh_scattering]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell's equations.<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40784Light Scattering2022-07-25T05:09:53Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving [[Maxwell's equations]].<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40783Light Scattering2022-07-25T05:09:07Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving [[Maxwell's equation]].<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40782Light Scattering2022-07-25T05:08:52Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving [[Maxwell's equations]].<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40781Light Scattering2022-07-25T05:06:52Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of [[Electromagnetic Radiation]], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40780Light Scattering2022-07-25T05:05:11Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with [[Electric Dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
<br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
<br />
==Computational Models of Scattering==<br />
<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40779Light Scattering2022-07-25T05:03:46Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with [[electric dipole]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40778Light Scattering2022-07-25T05:03:37Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with [[electric dipoles]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40777Light Scattering2022-07-25T05:03:16Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with [[dipoles]]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40776Light Scattering2022-07-25T04:59:05Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
[[File:Compton.PNG]]<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=File:Compton.PNG&diff=40775File:Compton.PNG2022-07-25T04:58:15Z<p>Zhaoxian Zhang: </p>
<hr />
<div></div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40774Light Scattering2022-07-25T04:48:08Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Consider a single scattering event from within a volume. Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40773Light Scattering2022-07-25T04:47:00Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
[[File:Rayleigh_diagram.PNG]]<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=File:Rayleigh_diagram.PNG&diff=40772File:Rayleigh diagram.PNG2022-07-25T04:45:51Z<p>Zhaoxian Zhang: </p>
<hr />
<div></div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40771Light Scattering2022-07-25T04:38:40Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
The principle of light scattering not only is an important theory to describe everyday phenomenon and help understand the physical world but is also extremely useful in many fields today. <br />
<br />
In material science, light scattering is used to measure the size of large molecules such as polymers. This technique allows us to make advanced plastics today. Many biological and medical manufacturing processes also require the use of light scattering. The ability to characterize small sizes in nanometers in vast quantities close to the Avogadro’s number is unique to light scattering.<br />
<br />
Light scattering is also useful in astronomy, enabling scientists to characterize interstellar dust and nebulae from the light that passes through.<br />
<br />
The more advanced theories of scattering of electromagnetic waves derived from light scattering is extremely useful today, being applied to radio communication, or even manufacturing of stealth aircraft.<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40770Light Scattering2022-07-25T04:27:06Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
<br />
Recall the energy equation:<br />
<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
<br />
Since the energy lost by the photon is gained by the electron, <br />
<br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
<br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40769Light Scattering2022-07-25T04:25:55Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{\gamma}}- vec{P_{\gamma’}})*(vec{P_{\gamma}}- vec{P_{\gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{\gamma}^2 + P_{\gamma’}^2 - 2 P_{\gamma} P_{\gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{\gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40768Light Scattering2022-07-25T04:24:47Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis as Lord Rayleigh did is much simpler and reveals how the sky appears blue.<br />
<br />
Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
<br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. <br />
<br />
This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40767Light Scattering2022-07-25T04:20:56Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has intensity <math>I_{s}</math> and electric field <math>E_{s}</math> . The electric field of the scattered light should be proportional to the illuminated volume <math>V</math> or <math>R^3</math>, and the incident electric field <math>E_{i}</math>. <br />
Since Rayleigh scattering is elastic, the energy should be conserved. Therefore, the total energy we observe should be independent of the distance from the scattering event<math>r</math>, which requires the intensity to decay with <math>\frac{1}{r^2}</math> and the electric field to decay with <math>\frac{1}{r}</math>.<br />
Now we have the scattered energy <math>E_{s}</math> proportional to <math>\frac{E_{i}R^3}{r}</math>. This would be dimensionally consistent if we have some term with dimension of length squared in the denominator, and it would make sense for this to be <math>\frac{E_{i}R^3}{r \lambda^2}</math>.<br />
The scattered intensity <math>I_{s}</math> is then going to be proportional to <math>\frac{E_{i}^2 R^6}{r^2 \lambda^4}</math>. This means that the shorter wavelengths are much more intensely scattered in Rayleigh scattering than longer wavelengths. Combined with the fact that human eyes perceive blue better than violet and that the sun is more intense in blue than violet, it makes the sky appear blue from lights scattered off atmospheric molecules. <br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40766Light Scattering2022-07-25T04:02:24Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
<br />
'''Compton Scattering'''<br />
<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40765Light Scattering2022-07-25T04:01:40Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
'''Compton Scattering'''<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
<br />
\delta E_{e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40764Light Scattering2022-07-25T04:00:35Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
'''Compton Scattering'''<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{\electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
<br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
<br />
Alternatively, the square of the change in energy of the electron is:<br />
<br />
<math><br />
\delta E_{\e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
\delta E_{\e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
<br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
<br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40763Light Scattering2022-07-25T03:59:06Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
'''Compton Scattering'''<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{\electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
Alternatively, the square of the change in energy of the electron is:<br />
<math><br />
\delta E_{\e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
\delta E_{\e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
==Connectedness==<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40762Light Scattering2022-07-25T03:58:30Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
'''Compton Scattering'''<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{\electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
Alternatively, the square of the change in energy of the electron is:<br />
<math><br />
\delta E_{\e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
\delta E_{\e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
==Connectedness<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering&diff=40761Light Scattering2022-07-25T03:56:23Z<p>Zhaoxian Zhang: Created page with " Claimed by Zhaoxian Zhang (Summer 2022) Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomen..."</p>
<hr />
<div> Claimed by Zhaoxian Zhang (Summer 2022)<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
[[File:Blue_sky.PNG]]<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
Compton Scattering<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{\electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
Alternatively, the square of the change in energy of the electron is:<br />
<math><br />
\delta E_{\e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
\delta E_{\e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
The Blue Sky<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
==Connectedness<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
[[File:Rayleigh.PNG]]<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Main_Page&diff=40760Main Page2022-07-25T03:55:36Z<p>Zhaoxian Zhang: /* Photons */</p>
<hr />
<div>__NOTOC__<br />
= '''Georgia Tech Student Wiki for Introductory Physics.''' =<br />
<br />
This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!<br />
<br />
Looking to make a contribution?<br />
#Pick one of the topics from intro physics listed below<br />
#Add content to that topic or improve the quality of what is already there.<br />
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.<br />
<br />
Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.<br />
<br />
== Source Material ==<br />
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).<br />
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]<br />
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]<br />
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]<br />
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]<br />
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]<br />
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]<br />
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]<br />
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]<br />
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]<br />
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]<br />
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]<br />
<br />
== Resources ==<br />
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]<br />
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]<br />
* A page to keep track of all the physics [[Constants]]<br />
* A listing of [[Notable Scientist]] with links to their individual pages <br />
<br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 1==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====GlowScript 101====<br />
<div class="mw-collapsible-content"><br />
*[[Python Syntax]]<br />
*[[GlowScript]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====VPython====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[VPython]]<br />
*[[VPython basics]]<br />
*[[VPython Common Errors and Troubleshooting]]<br />
*[[VPython Functions]]<br />
*[[VPython Lists]]<br />
*[[VPython Loops]]<br />
*[[VPython Multithreading]]<br />
*[[VPython Animation]]<br />
*[[VPython Objects]]<br />
*[[VPython 3D Objects]]<br />
*[[VPython Reference]]<br />
*[[VPython MapReduceFilter]]<br />
*[[VPython GUIs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Vectors and Units====<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[SI Units]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Types of Interactions and How to Detect Them]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Velocity and Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's First Law of Motion]]<br />
*[[Mass]]<br />
*[[Velocity]]<br />
*[[Speed]]<br />
*[[Speed vs Velocity]]<br />
*[[Relative Velocity]]<br />
*[[Derivation of Average Velocity]]<br />
*[[2-Dimensional Motion]]<br />
*[[3-Dimensional Position and Motion]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Momentum and the Momentum Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Linear Momentum]]<br />
*[[Newton's Second Law: the Momentum Principle]]<br />
*[[Impulse and Momentum]]<br />
*[[Net Force]]<br />
*[[Inertia]]<br />
*[[Acceleration]]<br />
*[[Relativistic Momentum]]<br />
<!-- Kinematics and Projectile Motion relocated to Week 3 per advice of Dr. Greco --><br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
*[[Iterative Prediction]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Analytic Prediction with a Constant Force====<br />
<div class="mw-collapsible-content"><br />
<!-- *[[Analytical Prediction]] Deprecated --><br />
*[[Kinematics]]<br />
*[[Projectile Motion]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Iterative Prediction with a Varying Force====<br />
<div class="mw-collapsible-content"><br />
*[[Fundamentals of Iterative Prediction with Varying Force]]<br />
*[[Spring_Force]]<br />
*[[Simple Harmonic Motion]]<br />
<!--*[[Hooke's Law]] folded into simple harmonic motion--><br />
<!--*[[Spring Force]] folded into simple harmonic motion--><br />
*[[Iterative Prediction of Spring-Mass System]]<br />
*[[Terminal Speed]]<br />
*[[Predicting Change in multiple dimensions]]<br />
*[[Two Dimensional Harmonic Motion]]<br />
*[[Determinism]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Fundamental Interactions====<br />
<div class="mw-collapsible-content"><br />
*[[Gravitational Force]]<br />
*[[Gravitational Force Near Earth]]<br />
*[[Gravitational Force in Space and Other Applications]]<br />
*[[3 or More Body Interactions]]<br />
<!--[[Fluid Mechanics]]--><br />
*[[Electric Force]]<br />
*[[Introduction to Magnetic Force]]<br />
*[[Strong and Weak Force]]<br />
*[[Reciprocity]]<br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Properties of Matter====<br />
<div class="mw-collapsible-content"><br />
*[[Kinds of Matter]]<br />
*[[Ball and Spring Model of Matter]]<br />
*[[Density]]<br />
*[[Length and Stiffness of an Interatomic Bond]]<br />
*[[Young's Modulus]]<br />
*[[Speed of Sound in Solids]]<br />
*[[Malleability]]<br />
*[[Ductility]]<br />
*[[Weight]]<br />
*[[Hardness]]<br />
*[[Boiling Point]]<br />
*[[Melting Point]]<br />
*[[Change of State]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Identifying Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Free Body Diagram]]<br />
*[[Inclined Plane]]<br />
*[[Compression or Normal Force]]<br />
*[[Tension]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Curving Motion====<br />
<div class="mw-collapsible-content"><br />
*[[Curving Motion]]<br />
*[[Centripetal Force and Curving Motion]]<br />
*[[Perpetual Freefall (Orbit)]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Energy Principle====<br />
<div class="mw-collapsible-content"><br />
*[[Energy of a Single Particle]]<br />
*[[Kinetic Energy]]<br />
*[[Work/Energy]]<br />
*[[The Energy Principle]]<br />
*[[Conservation of Energy]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Work by Non-Constant Forces====<br />
<div class="mw-collapsible-content"><br />
*[[Work Done By A Nonconstant Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
*[[Potential Energy of Macroscopic Springs]]<br />
*[[Spring Potential Energy]]<br />
*[[Ball and Spring Model]]<br />
*[[Gravitational Potential Energy]]<br />
*[[Energy Graphs]]<br />
*[[Escape Velocity]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Multiparticle Systems====<br />
<div class="mw-collapsible-content"><br />
*[[Center of Mass]]<br />
*[[Multi-particle analysis of Momentum]]<br />
*[[Potential Energy of a Multiparticle System]]<br />
*[[Work and Energy for an Extended System]]<br />
*[[Internal Energy]]<br />
**[[Potential Energy of a Pair of Neutral Atoms]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Choice of System====<br />
<div class="mw-collapsible-content"><br />
*[[System & Surroundings]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Thermal Energy, Dissipation, and Transfer of Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Thermal Energy]]<br />
*[[Specific Heat]]<br />
*[[Calorific Value(Heat of combustion)]]<br />
*[[First Law of Thermodynamics]]<br />
*[[Second Law of Thermodynamics and Entropy]]<br />
*[[Temperature]]<br />
*[[Transformation of Energy]]<br />
*[[The Maxwell-Boltzmann Distribution]]<br />
*[[Air Resistance]]<br />
*[[The Third Law of Thermodynamics]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Rotational and Vibrational Energy====<br />
<div class="mw-collapsible-content"><br />
*[[Translational, Rotational and Vibrational Energy]]<br />
*[[Rolling Motion]]<br />
</div><br />
</div><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Different Models of a System====<br />
<div class="mw-collapsible-content"><br />
*[[Point Particle Systems]]<br />
*[[Real Systems]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Friction====<br />
<div class="mw-collapsible-content"><br />
*[[Friction]]<br />
*[[Static Friction]]<br />
*[[Kinetic Friction]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conservation of Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Conservation of Momentum]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Collisions====<br />
<div class="mw-collapsible-content"><br />
*[[Newton's Third Law of Motion]]<br />
*[[Collisions]]<br />
*[[Elastic Collisions]]<br />
*[[Inelastic Collisions]]<br />
*[[Maximally Inelastic Collision]]<br />
*[[Head-on Collision of Equal Masses]]<br />
*[[Head-on Collision of Unequal Masses]]<br />
*[[Scattering: Collisions in 2D and 3D]]<br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Coefficient of Restitution]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rotations====<br />
<div class="mw-collapsible-content"><br />
*[[Rotational Kinematics]]<br />
*[[Eulerian Angles]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Angular Momentum====<br />
<div class="mw-collapsible-content"><br />
*[[Total Angular Momentum]]<br />
*[[Translational Angular Momentum]]<br />
*[[Rotational Angular Momentum]]<br />
*[[The Angular Momentum Principle]]<br />
*[[Angular Impulse]]<br />
*[[Predicting the Position of a Rotating System]]<br />
*[[The Moments of Inertia]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Analyzing Motion with and without Torque====<br />
<div class="mw-collapsible-content"><br />
*[[Torque]]<br />
*[[Torque 2]]<br />
*[[Systems with Zero Torque]]<br />
*[[Systems with Nonzero Torque]]<br />
*[[Torque vs Work]]<br />
*[[Gyroscopes]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Introduction to Quantum Concepts====<br />
<div class="mw-collapsible-content"><br />
*[[Bohr Model]]<br />
*[[Energy graphs and the Bohr model]]<br />
*[[Quantized energy levels]]<br />
*[[Electron transitions]]<br />
*[[Entropy]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 2==<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====3D Vectors====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Vectors]]<br />
*[[Right-Hand Rule]]<br />
*[[Right Hand Rule]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Field and Electric Potential]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric force====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric field of a point particle====<br />
<div class="mw-collapsible-content"><br />
*[[Point Charge]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Superposition====<br />
<div class="mw-collapsible-content"><br />
*[[Superposition Principle]]<br />
*[[Superposition principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Dipole]]<br />
*[[Magnetic Dipole]]<br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Interactions of charged objects====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Field]]<br />
*[[Electric Potential]]<br />
*[[Electric Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Tape experiments====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Polarization====<br />
<div class="mw-collapsible-content"><br />
*[[Polarization]]<br />
*[[Electric Polarization]]<br />
*[[Polarization of an Atom]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Conductors and Insulators====<br />
<div class="mw-collapsible-content"><br />
*[[Conductivity and Resistivity]]<br />
*[[Insulators]]<br />
*[[Potential Difference in an Insulator]]<br />
*[[Conductors]]<br />
*[[Polarization of a conductor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Charging and Discharging====<br />
<div class="mw-collapsible-content"><br />
*[[Charge Transfer]]<br />
*[[Electrostatic Discharge]]<br />
*[[Charged Conductor and Charged Insulator]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged rod====<br />
<div class="mw-collapsible-content"><br />
*[[Field of a Charged Rod|Charged Rod]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Field of a charged ring/disk/capacitor====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Ring]]<br />
*[[Charged Disk]]<br />
*[[Charged Capacitor]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Field of a charged sphere====<br />
<div class="mw-collapsible-content"><br />
*[[Charged Spherical Shell]]<br />
*[[Field of a Charged Ball]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential energy====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Energy]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric potential====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]] <br />
*[[Potential Difference in a Uniform Field]]<br />
*[[Potential Difference of Point Charge in a Non-Uniform Field]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sign of a potential difference====<br />
<div class="mw-collapsible-content"><br />
*[[Sign of a Potential Difference]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Potential at a single location====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential]]<br />
*[[Potential Difference at One Location]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Path independence and round trip potential====<br />
<div class="mw-collapsible-content"><br />
*[[Path Independence of Electric Potential]]<br />
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in an insulator====<br />
<div class="mw-collapsible-content"><br />
*[[Potential Difference in an Insulator]]<br />
*[[Electric Field in an Insulator]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Moving charges in a magnetic field====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Biot-Savart Law====<br />
<div class="mw-collapsible-content"><br />
*[[Biot-Savart Law]]<br />
*[[Biot-Savart Law for Currents]]<br />
</div><br />
</div><br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Moving charges, electron current, and conventional current====<br />
<div class="mw-collapsible-content"><br />
*[[Moving Point Charge]]<br />
*[[Current]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a wire====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Long Straight Wire]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Magnetic field of a current-carrying loop====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Loop]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic field of a Charged Disk====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Field of a Disk]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic dipoles====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Dipole Moment]]<br />
*[[Bar Magnet]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Atomic structure of magnets====<br />
<div class="mw-collapsible-content"><br />
*[[Atomic Structure of Magnets]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Steady state current====<br />
<div class="mw-collapsible-content"><br />
*[[Steady State]]<br />
*[[Non Steady State]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Kirchoff's Laws====<br />
<div class="mw-collapsible-content"><br />
*[[Kirchoff's Laws]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric fields and energy in circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Potential Difference]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Macroscopic analysis of circuits====<br />
<div class="mw-collapsible-content"><br />
*[[Series Circuits]]<br />
*[[Parallel Circuits]]<br />
*[[Parallel Circuits vs. Series Circuits*]]<br />
*[[Loop Rule]]<br />
*[[Node Rule]]<br />
*[[Fundamentals of Resistance]]<br />
*[[Problem Solving]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Electric field and potential in circuits with capacitors====<br />
<div class="mw-collapsible-content"><br />
*[[Charging and Discharging a Capacitor]]<br />
*[[RC Circuit]] <br />
*[[R Circuit]]<br />
*[[AC and DC]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic forces on charges and currents====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[Motors and Generators]]<br />
*[[Applying Magnetic Force to Currents]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
*[[Right-Hand Rule]]<br />
*[[Analysis of Railgun vs Coil gun technologies]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Electric and magnetic forces====<br />
<div class="mw-collapsible-content"><br />
*[[Electric Force]]<br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
*[[VPython Modelling of Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Velocity selector====<br />
<div class="mw-collapsible-content"><br />
*[[Lorentz Force]]<br />
*[[Combining Electric and Magnetic Forces]]<br />
</div><br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Hall Effect====<br />
<div class="mw-collapsible-content"><br />
*[[Hall Effect]]<br />
<h1><strong>Alayna Baker Spring 2020</strong></h1><br />
[[File:Hall Effect 1.jpg]]<br />
[[File:Hall Effect 2.jpg]]<br />
<br />
*[[Right-Hand Rule]]<br />
*[[Motional Emf]]<br />
*[[Magnetic Force]]<br />
*[[Magnetic Torque]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
]]]====Motional EMF====<br />
<br />
<div class="mw-collapsible-content"><br />
*[[Motional Emf]]<br />
<h1><strong>Adeline Boswell Fall 2019</strong></h1><br />
[[File:Motional EMF Example.jpg]]<br />
<br />
*[[Motional Emf using Faraday's Law]]<br />
</div><br />
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"<br />
<br />
[[File:MotEMFCR.jpg]]<br />
<br />
====Magnetic force====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Force]]<br />
*[[Lorentz Force]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Magnetic torque====<br />
<div class="mw-collapsible-content"><br />
*[[Magnetic Torque]]<br />
*[[Right-Hand Rule]]<br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Gauss's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Flux Theorem]]<br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Ampere's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Ampere's Law]]<br />
*[[Ampere-Maxwell Law]]<br />
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]<br />
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]<br />
*[[Magnetic Field of a Toroid Using Ampere's Law]]<br />
*[[Magnetic Field of a Solenoid Using Ampere's Law]]<br />
*[[The Differential Form of Ampere's Law]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Semiconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Semiconductor Devices]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Faraday's Law====<br />
<div class="mw-collapsible-content"><br />
*[[Faraday's Law]]<br />
*[[Motional Emf using Faraday's Law]]<br />
*[[Lenz's Law]]<br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Maxwell's equations====<br />
<div class="mw-collapsible-content"><br />
*[[Gauss's Law]]<br />
*[[Magnetic Flux]]<br />
*[[Ampere's Law]]<br />
*[[Faraday's Law]]<br />
*[[Maxwell's Electromagnetic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Circuits revisited====<br />
<div class="mw-collapsible-content"><br />
<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Inductors====<br />
<div class="mw-collapsible-content"><br />
*[[Inductors]]<br />
*[[Current in an LC Circuit]]<br />
*[[Current in an RL Circuit]]<br />
</div><br />
</div><br />
<br />
===Week 15===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
==== Electromagnetic Radiation ====<br />
<div class="mw-collapsible-content"><br />
*[[Electromagnetic Radiation]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Sparks in the air====<br />
<div class="mw-collapsible-content"><br />
*[[Sparks in Air]]<br />
*[[Spark Plugs]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Superconductors====<br />
<div class="mw-collapsible-content"><br />
*[[Superconducters]]<br />
*[[Superconductors]]<br />
*[[Meissner effect]]<br />
</div><br />
</div><br />
</div><br />
<br />
<div style="float:left; width:30%; padding:1%;"><br />
<br />
==Physics 3==<br />
<br />
===Week 1===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Classical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 2===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Special Relativity====<br />
<div class="mw-collapsible-content"><br />
*[[Frame of Reference]]<br />
<br />
*[[Einstein's Theory of Special Relativity]]<br />
*[[Time Dilation]]<br />
*[[Einstein's Theory of General Relativity]]<br />
*[[Albert A. Micheleson & Edward W. Morley]]<br />
*[[Magnetic Force in a Moving Reference Frame]]<br />
</div><br />
</div><br />
<br />
===Week 3===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Photons====<br />
<div class="mw-collapsible-content"><br />
*[[Spontaneous Photon Emission]]<br />
*[[Light Scattering]]<br />
*[[Lasers]]<br />
*[[Electronic Energy Levels and Photons]]<br />
*[[Quantum Properties of Light]]<br />
*[[The Photoelectric Effect]]<br />
</div><br />
</div><br />
<br />
===Week 4===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Matter Waves====<br />
<div class="mw-collapsible-content"><br />
*[[Wave-Particle Duality]]<br />
*[[Particle in a 1-Dimensional box]]<br />
*[[Heisenberg Uncertainty Principle]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
<br />
====Schrödinger Equation====<br />
<div class="mw-collapsible-content"><br />
*[[Solution for a Single Free Particle]]<br />
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]<br />
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]<br />
*[[Solution for Simple Harmonic Oscillator]]<br />
</div><br />
</div><br />
<br />
===Week 5===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Wave Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Standing Waves]]<br />
*[[Wavelength]]<br />
*[[Wavelength and Frequency]]<br />
*[[Mechanical Waves]]<br />
*[[Transverse and Longitudinal Waves]]<br />
</div><br />
</div><br />
<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Quantum Mechanics====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Tunneling through Potential Barriers]]<br />
</div><br />
</div><br />
<br />
===Week 6===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Rutherford-Bohr Model====<br />
<div class="mw-collapsible-content"><br />
*[[Rutherford Experiment and Atomic Collisions]]<br />
*[[Bohr Model]]<br />
*[[Quantized energy levels]]<br />
*[[Energy graphs and the Bohr model]]<br />
</div><br />
</div><br />
<br />
===Week 7===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Hydrogen Atom====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
</div><br />
</div><br />
<br />
===Week 8===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Many-Electron Atoms====<br />
<div class="mw-collapsible-content"><br />
*[[Quantum Theory]]<br />
*[[Atomic Theory]]<br />
*[[Pauli exclusion principle]]<br />
</div><br />
</div><br />
<br />
===Week 9===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Molecules====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Molecules]]<br />
*[[Covalent Bonds]]<br />
</div><br />
<br />
===Week 10===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Statistical Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
*[[Application of Statistics in Physics]]<br />
*[[Temperature & Entropy]]<br />
</div><br />
<div class="mw-collapsible-content"><br />
<br />
===Week 11===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Condensed Matter Physics====<br />
<div class="mw-collapsible-content"><br />
</div><br />
</div><br />
<br />
===Week 12===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====The Nucleus====<br />
<div class="mw-collapsible-content"><br />
*[[Nucleus]]<br />
</div><br />
</div><br />
<br />
===Week 13===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Nuclear Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Nuclear Fission]]<br />
*[[Nuclear Energy from Fission and Fusion]]<br />
</div><br />
</div><br />
<br />
===Week 14===<br />
<div class="toccolours mw-collapsible mw-collapsed"><br />
====Particle Physics====<br />
<div class="mw-collapsible-content"><br />
*[[Elementary Particles and Particle Physics Theory]]<br />
*[[String Theory]]<br />
</div><br />
</div><br />
</div></div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Light_Scattering:_Why_is_the_Sky_Blue&diff=40759Light Scattering: Why is the Sky Blue2022-07-25T03:54:25Z<p>Zhaoxian Zhang: </p>
<hr />
<div>'''Claimed by Zhaoxian Zhang (Summer 2022)'''<br />
<br />
Light scattering is the change in momentum and energy of light when it passes through an object. Light scattering occurs because light, as a form of electromagnetic wave[link], interacts with charge. This often happens with light interacting with dipoles[link]. dusts in the air, molecules in the air, particles in solutions, water droplets, and many other common things can form dipoles. These interactions lead to everyday phenomena like whiteness of cloud or the redness of sunset, and even governs the color of the sky.<br />
<br />
[[File:Blue_sky.PNG]]<br />
<br />
Light scattering can be characterized into elastic or inelastic scattering, depending on how energy is exchanged during the interaction. In elastic scattering, the scattered particle conserves its original kinetic energy.<br />
==Mathematical Models of Scattering==<br />
In modeling scattering effects, a dimensionless parameter <math>x</math> is often used to characterize the size of the scattering particle in relation to the scattered wavelength. It is calculated with the following relation:<br />
<math><br />
x = \frac{2 \pi r}{\lambda}<br />
</math><br />
When <math>x<<1</math>, or when the scattering particle is much smaller than the wavelength of scattered light, the scattering event can be characterized by Rayleigh Scattering[link]. When the particle size is larger, the scattering event is characterized by Mie theory[link] or discrete dipole approximation[link] by solving Maxwell equations[link].<br />
==Computational Models of Scattering==<br />
==Examples of Scattering==<br />
Compton Scattering<br />
Compton scattering is an example of an inelastic scattering event, in which a photon gives a part of its momentum to an electron when it collides with it and scatters off at an angle. Because the transfer in momentum, the photon changes its wavelength after collision. The amount of change in wavelength can be derived from conservation of energy and momentum. <br />
Recall the energy equation:<br />
<math>E^2 = (\rho c)^2 + (mc)^2</math><br />
Since the energy lost by the photon is gained by the electron, <br />
<math>\delta E_{photon} = -\delta E_{\electron}</math><br />
Consider the change in momentum of the photon, as it flies off at a different angle, is simply the vector difference of the momentums. When squared in energy calculation, this difference can be simplified using scalar product:<br />
<math><br />
\delta E_{\gamma} = (vec{P_{gamma}}- vec{P_{gamma’}})*(vec{P_{gamma}}- vec{P_{gamma’}})c^2<br />
\delta E_{\gamma} = (P_{gamma}^2 + P_{gamma’}^2 - 2 P_{gamma} P_{gamma’} cos \theta )c^2<br />
</math><br />
For momentum of a photon <math> P = hf/c </math>, the above expression becomes:<br />
<math><br />
\delta E_{\gamma} = ((\frac{hf}{c})^2 + (\frac{hf’}{c})^2 - \frac{hf}{c} \frac{hf’}{c} cos \theta )c^2<br />
</math><br />
Alternatively, the square of the change in energy of the electron is:<br />
<math><br />
\delta E_{\e} = (mc^2)^2 +(\delta P_{gamma} c)^2<br />
\delta E_{\e} = (mc^2)^2 =(\frac{hf}{c} - \frac{hf’}{c})^2 c^2<br />
</math><br />
Equate these expressions in energy and simplifying, we eventually get to the equation describing Compton scattering:<br />
<math><br />
(\lambda - \lambda’) = \frac{h}{m_{e}c} (1-cos \theta)<br />
</math><br />
Which describes how the frequency of the photon changes when scattering from an electron.<br />
<br />
'''The Blue Sky'''<br />
While the derivation of original Rayleigh scattering equations is much more complicated, a simple dimensional analysis, as Lord Rayleigh did in his first analysis, is much simpler and reveals how the sky appears blue.<br />
Say the scattered light has electric field <math>E_{s}</math> . The intensity of the scattered light<br />
==Connectedness<br />
<br />
<br />
==History==<br />
John William Strutt (Lord Rayleigh) (1842-1919) was born in the United Kingdom. He made fundamental discoveries in the fields of acoustics and optics that are basic to the theory of wave propagation in fluids. He was also responsible for much of the early discoveries in scattering. <br />
<br />
[[File:Rayleigh.PNG]]<br />
<br />
His work on scattering began with the question of the color of the sky. John Tyndall[link] first discovered that light scattered from small particles appeared blue from the famous Tyndall effect. But it was Lord Rayleigh who worked out the math and solved the mystery of the color of the sky. <br />
= See also =<br />
<br />
===Further reading===<br />
<br />
Read more about:<br />
<br />
- Lord Rayleigh (John Strutt): http://micro.magnet.fsu.edu/optics/timeline/people/rayleigh.html<br />
<br />
- Isaac Newton: http://www.biography.com/people/isaac-newton-9422656<br />
<br />
- Electromagnetic and Visible Spectra: http://www.physicsclassroom.com/class/light/Lesson-2/The-Electromagnetic-and-Visible-Spectra<br />
<br />
- Dispersion of Light by Prisms: http://www.physicsclassroom.com/class/refrn/Lesson-4/Dispersion-of-Light-by-Prisms<br />
<br />
===External links===<br />
<br />
http://science.hq.nasa.gov/kids/imagers/ems/visible.html<br />
<br />
http://www.sciencekids.co.nz/sciencefacts/light.html<br />
<br />
==References==<br />
<br />
http://www.sciencemadesimple.com/space_black_sunset_red.html<br />
<br />
http://missionscience.nasa.gov/ems/09_visiblelight.html<br />
<br />
http://www.livescience.com/50678-visible-light.html<br />
<br />
http://www.livescience.com/32559-why-do-we-see-in-color.html<br />
<br />
http://www.webexhibits.org/colorart/bh.html<br />
<br />
http://www.edmundoptics.com/technical-resources-center/optics/introduction-to-optical-prisms/<br />
<br />
http://www.britannica.com/biography/John-William-Strutt-3rd-Baron-Rayleigh<br />
<br />
https://en.wikipedia.org/wiki/Light_scattering<br />
<br />
[[Category:Radiation]]</div>Zhaoxian Zhanghttp://www.physicsbook.gatech.edu/index.php?title=Mechanical_Waves&diff=40703Mechanical Waves2022-07-24T19:17:02Z<p>Zhaoxian Zhang: </p>
<hr />
<div>Claimed by Snehil Mathur (Spring 2022)<br />
<br />
Mechanical Waves are waves that propagate through a medium, one that is either solid, liquid, or gas. The speed at which a wave travels depends on the mediums' properties, both elastic and inertial.<br />
<br />
==The Main Idea==<br />
<br />
Waves can be described as disturbances that travel through space and can transport energy from its source to another location. These are often represented in an oscillating manner.<br />
<br />
Mechanical waves are waves that propagate through matter (gas, liquid, or solid) and require a medium in order to transport energy. Inherently, these waves cannot travel through a vacuum.<br />
<br />
There are three main types of mechanical waves:<br />
<br />
<br />
'''Transverse Waves:'''<br />
<br />
Waves in which the particles oscillate back and forth in the direction perpendicular to the motion of the wave. The particle travels the length of the amplitude of the and completes its oscillation corresponding to when the wave moves over one wavelength. Some examples of transverse waves are ripples in the water and a vibrating string.<br />
<br />
[[File:Twave.gif]]<br />
[https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html]<br />
<br />
<br />
'''Longitudinal Waves:'''<br />
<br />
Waves in which the particles move in the same direction as the wave motion. While still in an oscillating motion, they move "back-and-forth" with respect to the direction the wave is propagating in. Some examples of longitudinal waves include sound waves and the motion of compressing and stretching a spring.<br />
<br />
[[File:Lwave.gif]]<br />
[https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html]<br />
<br />
<br />
'''Surface Waves:'''<br />
<br />
Waves in which the particles within the medium move both parallel and perpendicular to the propagation direction of the wave. They're called surface waves due to their nature of travelling along the surface of a medium. This gives the particles on the wave a circular-like motion. The surface of a wave in the water is the most direct example of a surface wave; other examples include seismic waves and gravity waves along the surface of liquids.<br />
<br />
[[File:Swave.gif]]<br />
[https://www.acs.psu.edu/drussell/demos/waves/wavemotion.html]<br />
<br />
===A Mathematical Model===<br />
<br />
Mechanical waves implement a variety of equations that can be used to solve for different characteristics of a wave.<br />
The wave equation is used to find the speed of propagation of a transverse wave:<br />
<br />
<math>v = \lambda f</math><br />
<br />
Where <math>v</math> is the velocity, <math>\lambda</math> is the wavelength, and <math>v</math> is the frequency. Another form of this equation specific to mechanical waves is the formula:<br />
<br />
<math>v = \sqrt{Stiffness/Inertia}</math><br />
<br />
Another common form of this equation is the wave speed for a stretched string, <math>v = \sqrt{T/\mu}</math>, where <math>T</math> is the string tension and <math>\mu</math> is the mass per unit length of string. This equation allows for the calculation of the speed of a wave in different forms of matter. To find the equation of a wave that falls under two different mediums, we can apply superposition to find the new wave equation by adding the functions the two different functions that describe possible waves in the medium:<br />
<br />
<math>y(x,t)=y_{1}+y_{2}</math><br />
<br />
Where <math>y_{1}</math> and <math>y_{2}</math> are the two possible wave functions for different mediums.<br />
<br />
===A Computational Model===<br />
<br />
How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]<br />
<br />
==Examples==<br />
<br />
<br />
===Simple===<br />
<br />
Q1) What kind of wave is a stadium wave?<br />
<br />
<br />
A1) Transverse Wave<br />
<br />
===Middling===<br />
<br />
Q2)<br />
A wave travels with a period of 5 ns. The wave can be seen in the image below:<br />
[[File:SimpleWave.png]]<br />
<br />
(The units of both of axis of this graph are in nm)<br />
<br />
<br />
Find the speed of the wave described above:<br />
<br />
<br />
<br />
A2)<br />
The wave equation to find the speed of this function is: <math>v = \lambda f</math>. To find the frequency, we apply the conversion from period to frequency: <math>f=1/T</math><br />
<br />
<math>f=\frac{1}{5*10^{-9}} = 2*10^8</math><br />
<br />
To find the wavelength <math>\lambda</math>, we find the length it takes for the wave to complete on cycle. Based on the graph, we can visually verify that the wavelength is 10 nm. With both the wavelength and the frequency, we can calculate the speed:<br />
<br />
<math>v = (2*10^9)(10*10^9) = \textbf{2*10^19}</math><br />
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===Difficult===<br />
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Q3) A transverse wave moves across a string. The wave can be represented with the equation <math>y(x,t)=0.5*sin(7x-3t)</math> with respect to it's position <math>x</math> in meters and time <math>t</math> in seconds. Find the amplitude, wavelength, period, and speed of the wave.<br />
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A3) For this question, we can use a lot of the wave functions we've learned from the past in order to convert the constants in this equation to the characteristics needed. First, we can write this equation as a form of its parent function:<br />
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<math>y(x,t)=Asin(kx-\omega t)</math><br />
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Where <math>A</math> is the amplitude, <math>k</math> is the wave number, and <math>\omega</math> is the angular frequency. From reading the given equation, we can find:<br />
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<math>\textbf{Amplitude = 0.5 m}</math><br />
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<math>k = 7</math><br />
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<math>\omega =3</math><br />
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We can use the wave number <math>k</math> to find the wavelength:<br />
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<math>k=\frac{2\pi}{\lambda}</math><br />
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<math>\textbf{Wavelength = λ}=\frac{2\pi}{k}≈\textbf{0.898 m}</math><br />
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To find the period <math>T</math>, we convert from the angular frequency with this equation:<br />
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<math>\omega =\frac{2\pi}{T}</math><br />
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<math>\textbf{Period = T = }=\frac{2\pi}{\omega}≈\textbf{2.094 s}</math><br />
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Finally, to find the speed, we can an altered version of the wave equation to substitute in <math>k</math> in order to make it easier:<br />
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<math>v=\frac{\omega}{k}</math><br />
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<math>=\frac{3}{7}≈0.429</math><br />
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<math>\textbf{Speed = v ≈ 0.429}</math><br />
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==Connectedness==<br />
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* This topic is connected to the way sound moves. They're created by an object vibrating and generating pulses of pressure waves that travel through the air and carry energy over distances.<br />
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==History==<br />
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*Wasn't able to find directly related information to mechanical waves<br />
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== See also ==<br />
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Connected topics include Electromagnetic Waves and Spring Motion.<br />
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===Further reading===<br />
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From cK-12.org: [https://www.ck12.org/physics/mechanical-wave/lesson/Mechanical-Wave-MS-PS/?referrer=concept_details]<br />
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From Texas A&M University: [http://people.tamu.edu/~mahapatra/teaching/ch15.pdf]<br />
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===External links===<br />
[https://flexbooks.ck12.org/cbook/ck-12-middle-school-physical-science-flexbook-2.0/section/16.4/primary/lesson/surface-wave-ms-ps/]<br />
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[https://webhome.phy.duke.edu/~lee/P142/Ref_Waves.pdf]<br />
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==References==<br />
<br />
This section contains the the references you used while writing this page<br />
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[[Category:Which Category did you place this in?]]</div>Zhaoxian Zhang