Doppler shift from moving thick medium

Question:

A light source inside a thick medium (low speed of light) is moving at a speed v towards a receiver outside in free space. What is the frequency shift of the light seen by an observer in free space?

Answer:

In this situation, the frequency of the light will shift due to the Doppler effect and the speed of light will change due to the change of medium. A useful equation to deal with the transition between two media would be v = c/n where c is the speed of light in free space, v the speed of light in a medium and n the index of refraction of the medium.

The source emits light in the heavy medium that will be frequency shifted. When the light crosses the boundary, the light will travel faster while maintaining the same Doppler-shifted frequency.

In calculations, one should use the speed of light in the heavy medium for the moving source and the speed of light in free space for the receiver.

-Jeff Tessein