Light Propagation Through a Medium

This page is going to be about about Light Propagation. A work in progress . Edited by Roshan Konda Fall 2017

The Main Idea

When light travels through anything but a vacuum the speed of light travels at a speed different from c=3.00E8 m/s and the light particles scatter. The highest speed that light can travel though is the universal constant c. Light also refracts, or changes direction when it enters a new medium.

A Mathematical Model

The speed of light through a medium can be given by the formula n=(c/v), where n is the index of refraction, v is the velocity of light through the medium and c is the speed of light through a vacuum. The relationship between the angle of incidence and angle of refraction when light passes through a medium is given by Snell's Law. n1sin(theta1) = n2sin(theta2)

A Computational Model

Examples

Easy

The speed of light is measured to be 2.76E8 m/s, What is the index of refraction for the medium?

Solution

The index of refraction is n=(c/v), n=(3.00E8)/(2.76E8) = 1.09.

Medium

What is the index of refraction of a refractive medium if the angle of incidence in air is 30 degrees and the angle of refraction is 15 degrees?

Solution

solving for n2 in snells law gives (1*sin(30))/sin(15) = 1.93

Difficult

A light ray passes from air into glass at an angle of 20 degrees with respect to the normal. What is the angle of refraction?

Solution

Plugging into Snell's Law gives 1.00sin(20)=1.50sin(theta), solving for theta gives a value of 13.2 degrees.

Connectedness

One extremely important use of Snell's Law and light propagation through a medium is telecommunications. Fiber optics take advantage of Snell's Law to send large amounts of data. Since these fiber optics cables are not laid out in straight lines the light beams refract significantly and index of refraction are used to guide the light beam through the cable.