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Kinematics and Snell's Law

The phase factors of all three waves must be equal on the actual boundary itself, hence:

 (9.54)

as a kinematic constraint for the wave to be consistent. That is, this has nothing to do with physics'' per se, it is just a mathematical requirement for the wave description to work. Consequently it is generally covered even in kiddy-physics classes, where one can derive Snell's law just from pictures of incident waves and triangles and a knowledge of the wavelength shift associated with the speed shift with a fixed frequency wave.

At , the three 's must lie in a plane and we obtain:

 (9.55)

which is both Snell's Law and the Law of Reflection, where we use to put it in terms of the index of refraction, defined by . Note that we cancel , using the fact that the frequency is the same in both media.

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Robert G. Brown 2007-12-28