Speed of light in a moving medium

[jobyts]

Let's say the speed of light in a medium is c'. Assume that the medium itself is moving at a very high speed v (close to c). What is the speed of light in the moving medium if
a. light and medium are moving in the same direction.
b. opposite direction (can the speed be zero or negative?)
c. in perpendicular.

 

[sylas]

Assuming an isotropic medium, the speed of light in the medium is less than c. The question states that it is c'.

If the medium is moving in same direction as the light, from the perspective of some external observer, then the corresponding speed of the light for that observer is given by the SR formula for adding velocities.

$$\frac{v+c'}{1+vc'/c^2}$$​

I think that the transverse velocity of the medium is irrelevant, but I am checking that to see if my hunch is correct.

If v is greater than c' and in the opposite direction, then indeed the light in the isotropic refractive medium is moving backwards, respective to the external observer.

Cheers -- sylas