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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?

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  • $\begingroup$ If you read this, it seems it can be much more complicated en.wikipedia.org/wiki/Slow_light $\endgroup$
    – anna v
    Jan 1 at 6:06
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    $\begingroup$ Related: physics.stackexchange.com/q/52555 $\endgroup$
    – JohnA.
    Jan 1 at 6:55
  • $\begingroup$ Thanks for your help $\endgroup$ Jan 1 at 15:02
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    $\begingroup$ 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. $\endgroup$
    – A. P.
    Jan 1 at 17:28
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    $\begingroup$ @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). $\endgroup$ Jan 1 at 18:31

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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.

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