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.

 

[Entropia]

The speed of light in different mediums is a fundamental concept in physics and is a result of the interaction between light and matter. In a vacuum, the speed of light is constant and is represented by the symbol c. However, when light travels through a medium such as water, its speed is reduced and is represented by c'. This is because the particles in the medium interact with the light, causing it to slow down.

In relativistic laws, the speed of light plays a crucial role and is typically represented by c. This is because these laws were developed based on the behavior of light in a vacuum. However, when dealing with a specific medium, such as water with c' = c/1.33, it is important to use the appropriate value for the speed of light in that medium.

For example, in the equation w=(u+v)/(1+uv/c^2), the speeds of the objects u and v should be measured relative to the speed of light in that specific medium, which is c'. This means that the equation would be modified to w=(u'+v')/(1+u'v'/c'^2), where u' and v' are the speeds of the objects relative to the speed of light in that medium.

Similarly, when dealing with the momentum of light, it is important to use the appropriate value for the speed of light in that medium. The momentum of light is typically represented by E/c, where E is the energy of the light. In a specific medium, this would be modified to E'/c', where E' is the energy of the light relative to the speed of light in that medium.

In summary, when applying relativistic laws in a specific medium, it is important to use the appropriate value for the speed of light in that medium. This ensures that the laws accurately reflect the behavior of objects and light in that specific medium.