How Does Snell's Law Change in Curved Spacetime?

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SUMMARY

Snell's Law, which states that n1 sin[x1] = n2 sin[x2], remains applicable in curved spacetime, with the index of refraction being observer-dependent due to variations in optical density. The discussion highlights the need for a derivation of Snell's Law within the framework of General Relativity (GR), particularly in strong gravitational fields. References to relevant literature, including "Ray Optics, Fermat's Principle, and Applications to General Relativity" by Volker Perlick, provide foundational insights into this topic.

PREREQUISITES
  • Understanding of General Relativity (GR)
  • Familiarity with Snell's Law in classical optics
  • Knowledge of optical density and its implications
  • Basic principles of ray optics and Fermat's Principle
NEXT STEPS
  • Research the derivation of Snell's Law in General Relativity
  • Explore the implications of observer-dependent indices of refraction
  • Study the applications of Fermat's Principle in curved spacetime
  • Review the literature on strong field relativistic effects in optics
USEFUL FOR

Physicists, optical engineers, and students of General Relativity interested in the intersection of optics and gravitational theory.

blumfeld0
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Ever since I took GR I have always been interested in how snell's law changes, if it changes at all, in curved spacetime.
The index of refraction depends on the optical density of the medium and this would be observer dependent? am i right on that?
i would love to see a paper or other online reference where snells law is derived in GR. i.e in the strong field relativistic limit.

or maybe it doesn't change at all? it just stays n1 sin[x1 ] = n2 sin[x2]

like P = number density* boltzmann's constant *Temperature holds relativistically and non-relativistically as I recall.

thanks!
 
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