Snell's Law: Origins and Applications

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SUMMARY

Snell's Law, which describes the relationship between the angles of incidence and refraction when light passes through different media, is fundamentally derived from Fermat's principle of least time. Additionally, it can be established through Maxwell's equations under specific boundary conditions. An alternative derivation involves the interference of light waves, where constructive interference occurs at extrema of phase, determining the actual paths of light. These derivations highlight the mathematical and physical principles underlying Snell's Law.

PREREQUISITES
  • Fermat's principle of least time
  • Maxwell's equations
  • Wave interference concepts
  • Basic optics terminology
NEXT STEPS
  • Study the derivation of Snell's Law using Fermat's principle
  • Explore Maxwell's equations in the context of optics
  • Investigate wave interference and its applications in optics
  • Learn about the practical applications of Snell's Law in various fields
USEFUL FOR

Physicists, optics researchers, and students studying wave phenomena will benefit from this discussion, particularly those interested in the theoretical foundations and applications of Snell's Law.

Ernestazik
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From what physical concept is Snell's law derived?
 
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It can be quite easily derived using Fermat's principle that light rays will travel in the shortest path (time-wise). It can also be derived by applying Maxwell's equations with the proper boundary conditions. And according to wikipedia, although I'm not familiar with this derivation:

"Snell's law can be derived using interference of all possible paths of light wave from source to observer—it results in destructive interference everywhere except extrema of phase (where interference is constructive)—which become actual paths."
 

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