### Refraction

1. The index of refraction of a medium in which the speed of light v < c is
n ≡ c / v.
Note that the frequency is unchanged as light moves through different mediums.

(For sound, c is usually taken to be the speed of sound in air, so that n for sound is often < 1.)

2. Snell's law for waves refracting at the interface of two media is
n1 sin θ1 = n2 sin θ2,
where θi are measured relative to the normal to the interface between the media:

Note that for refraction from a medium of greater index of refraction into a medium with a lesser index of refraction (n1 > n2), there are angles θ1 > θcritical for which there is no solution:

n1 sin θcritical = n2.
These angles result in total internal reflection back into the original medium.
3. Snell's law includes reflection as a special case (n1 = n2 implies that θ1 = θ2).

Reflection results in a phase change of π when it is off the surface of a medium with a higher index of refraction.

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©2010, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.