Speed of light in a different medium

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Main Question or Discussion Point

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

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

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

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

and the momentum of light [tex] \frac{E}{c} [/tex]?
 
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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.
 

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