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When light travels from an optically denser to a rarer medium, it bends away from the normal and at a specific angle of incidence, the angle of refraction is ${90}^{\circ}$. When the angle of incidence is equal to the Critical angle, the refracted ray grazes the path of separation of the two media. So at this angle, the speed of light would be that of the denser medium or that of the rarer medium?

Qmechanic
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Rishith Raj Raizada
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  • If you read this, it seems it can be much more complicated https://en.wikipedia.org/wiki/Slow_light – anna v Jan 01 '24 at 06:06
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    Related: https://physics.stackexchange.com/q/52555/ – JohnA. Jan 01 '24 at 06:55
  • Thanks for your help – Rishith Raj Raizada Jan 01 '24 at 15:02
  • This is actually a pretty tough question IMO. Post the answer if you find out. – JohnA. Jan 01 '24 at 15:04
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    The question linked by JohnA. has an answer which covers your question as well. Zo the Relativist writes that at the critical angle all the light is reflected, hence there is no physical ray which is transmitted grazing the boundary between the two media. – A. P. Jan 01 '24 at 17:28
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    @JohnA. I'd say the answer you link, also answers this question implicitly. It's the speed of light of medium A in medium A and of medium B in medium B. There is no infinitely thin, perfectly collimated beam – so some light will be transmitted at low angles, and the rest will be reflected. Talking about "exactly at the boundary" is not working out anyway (as the averaged wave equation will break down when you look close enough). – Sebastian Riese Jan 01 '24 at 18:31
  • Agree Sebastian, let me know if you agree with what’s writen below. – JohnA. Jan 01 '24 at 18:49

1 Answers1

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Based on this answer, the transmission coefficients of Frenels equations are $0$ and thus no light is refracted. Therefore any light that exists traveling at the speed of the denser medium because all light got reflected.

However, if light is travelling on a boundary (more generally), the beam has an actual width so anything on the rarer medium will travel at the speed light travels on that medium and vice versa for the denser medium. No light can travel in the $0$ width boundary.

JohnA.
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