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

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SUMMARY

This discussion focuses on proving Snell's Law using Fermat's Principle, emphasizing the need to express the sine of the relevant angles in terms of the variables used. Participants recommend applying Fermat's Principle to the time expression derived from the angles and then performing algebraic manipulations to match the sine expressions. Additionally, it is crucial to express the velocities c1 and c2 in terms of the indices of refraction to complete the proof effectively.

PREREQUISITES
  • Understanding of Fermat's Principle
  • Knowledge of Snell's Law
  • Basic algebra skills for manipulation of expressions
  • Familiarity with indices of refraction
NEXT STEPS
  • Study the derivation of Snell's Law from Fermat's Principle
  • Practice algebraic manipulation of trigonometric functions
  • Explore the concept of indices of refraction in different media
  • Review examples of light refraction scenarios
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Students and educators in physics, particularly those interested in optics and the mathematical foundations of light behavior.

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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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