# Acceleration of Light when it moves through different medium

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 $$a. As Light enters Via point $$P$$ and $$Q$$ it's velocity changes while travelling through mediums. Then what is rate of change of velocity at $$P$$ and $$Q$$ respectively?

• 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. Commented Sep 30, 2021 at 16:20
• Look up Cherenkov radiation. Commented Sep 30, 2021 at 18:06

## 1 Answer

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.