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 θ_i 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 > θ_critical for which there is no solution:

   n₁ sin θ_critical = 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.