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Re: Total Internal Reflection

Is there a simple proof of Fermat's principle?


Bob LaMontagne wrote:

To get reflection or refraction, the paths involved must obey Fermat's
principle (see Feynman's delightful book, QED, for the reasons.) The
principle says that the path must be a minimum or maximum to get
constructive interference at a particular angle. The is no minimum path
for refraction when the conditions for total internal reflection are met
- hence no constructive interference to give a unique direction to the
refracted light. The internally reflected light still has the usual
minimum path.

Bob at PC


A point of curiosity, if you can help.

A wave is traveling from a slow to a faster material. At the critical
angle the wave is totally reflected. I know the math. I know the argument
that the exiting wave has a limited finite speed and can play Huygens'
principle to get all the way to the critical angle. One would think a HS
teacher should be happy. We know it happens and we can solve problems
about it happening but I cannot answer the very curious student (me
included) who wants a deeper understanding, a mechanism for this
happening. My assortment of texts did not do it for me. Can any of you?

Actually, I am not sure I can adequately explain why reflection works the
way it does in general.

Happy Friday!

Ken Fox