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*From*: Bernard Cleyet <anngeorg@PACBELL.NET>*Date*: Mon, 2 Feb 2004 23:32:45 -0800

Is there a simple proof of Fermat's principle?

bc

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

SSHS KPHOX wrote:

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

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