Speed of light in a different medium

[uq_civediv]

a lot of transformation laws have c in them. the speed of light, however, depends on the medium ( $$c'$$ ) and is different from the $$c$$ in vaccuum.

so my question is, which one should i use in relativistic laws if the medium is , say, water with $$c' = \frac{c}{1.33}$$

of course one would say $$c$$, but in the $$w=\frac{u+v}{1+\frac{u v}{c^2}}$$ the speeds can get up to $$c$$, whereas in that medium they should never go faster than $$c'$$

or how should i apply relativistic laws in a specific medium ?

and the momentum of light $$\frac{E}{c}$$?

 

[granpa]

whereas in that medium they should never go faster than c'.
http://en.wikipedia.org/wiki/Cherenkov_radiation

Čerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle (such as a proton) passes through an insulator at a speed greater than the speed of light in that medium. The characteristic "blue glow" of nuclear reactors is due to Čerenkov radiation.