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Assume three mediums with refractive index $a$ , $b$ , $c$ where is $a$ for Air and $b$ and $c$ are some different medium. Relation between them is $a<c<b$. As Light enters Via point $P$ and $Q$ it's velocity changes while travelling through mediums. Then what is rate of change of velocity at $P$ and $Q$ respectively?enter image description here

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  • $\begingroup$ Just as a brief aside, the path of the light should bend towards the axis from a to b, and away from the axis from b to c. $\endgroup$
    – DanDan面
    Commented Sep 30, 2021 at 16:20
  • $\begingroup$ Look up Cherenkov radiation. $\endgroup$
    – my2cts
    Commented Sep 30, 2021 at 18:06

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The speed of light is not differentiable at the interface. On the macro scale, the velocity is discontinuous. If you zoom in to the scale of a single atom looking for a continuous curve, you'll get a superposition of two c-propagating electromagnetic waves: one the original light, the other an induced wave from the atom being displaced by the electromagnetic wave. The interference pattern very near the atom looks like a beam of light which travels at $c/n$. Far from the atom the induced wave is negligible. In the middle distance, it looks like a c-propagating wave with some interference.

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