Proof of Fermat's principle of least time?

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SUMMARY

The proof of Fermat's principle of least time is not a conventional proof but rather a derivation from established physical laws. It is fundamentally linked to Huygen's principle and the Variation principle in classical mechanics. This principle asserts that light follows the path that requires the least time, aligning with natural laws rather than being subject to proof in the traditional sense.

PREREQUISITES
  • Understanding of Huygen's principle
  • Familiarity with the Variation principle in classical mechanics
  • Basic knowledge of optics and light behavior
  • Concepts of natural laws in physics
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Physicists, optics researchers, and students studying classical mechanics and the principles of light behavior will benefit from this discussion.

Nick Jackson
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I've been looking for this proof for months but I wasn't able to find something...
 
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It is not something that you prove. It is (part of) a Law of Nature.
You can derive it from Huygen's principle, and it follows from the Variation principle in classical mechanics.
 

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