Proving Snell's Law with Fermat's Principle: A Beginner's Guide

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To prove Snell's Law using Fermat's principle, start by expressing the sines of the relevant angles in terms of your chosen variables. Apply Fermat's principle to the time expression you've created, which involves calculating the path taken by light. It is essential to express the velocities in terms of the indices of refraction for the two media involved. The proof will involve significant algebraic manipulation to match the sine expressions. Following these steps will lead to a successful demonstration of Snell's Law.
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Can someone help me on how to prove Snell's Law using Fermat's principle? I'm not so good with topics about light, so I don't how to start.
 

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MissP.25_5 said:
Can someone help me on how to prove Snell's Law using Fermat's principle? I'm not so good with topics about light, so I don't how to start.

Looks like you've made a start...

It also looks like you might want to write out expressions for sines of the relevant angles in terms of the variables you're using so that you'll be able to recognize them later. Then apply Fermat's principle to the time expression you've written. After that it'll be a lot of banging away at the algebra in order to pattern-match the sine expressions...

Remember to express your velocities c1 and c2 in terms of the indexes of refraction.
 
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I got it! Thanks :)
 

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