Is the speed of light constant in a medium?

[lmoh]

One of the main postulates of relativity is that the speed of light is always constant. However, light does not always travel at c, it only travels at that speed in a vacuum (supposedly). When it is in a medium such as water or air, it moves at a noticably slower rate, where even other objects are capable of moving faster than light (not as eye-popping as it sounds). But do the same rules of relativity apply in this case? If not, how should light be treated in this case?

 

[jtbell]

One of the main postulates of relativity is that the speed of light is always constant.

No, the postulate says that the speed of light is constant in vacuum.

However, light does not always travel at c, it only travels at that speed in a vacuum (supposedly). When it is in a medium such as water or air, it moves at a noticably slower rate, where even other objects are capable of moving faster than light (not as eye-popping as it sounds). But do the same rules of relativity apply in this case? If not, how should light be treated in this case?

The speed of light in a moving medium equals the speed of light in a stationary medium (of the same material, of course) "plus" the speed of the medium relative to the observer. Here "plus" means not ordinary arithmetic addition, but instead the relativistic "velocity addition" rule, with which I hope you're acquainted.

The effects of this were actually measured by Fizeau in 1851, long before Einstein came along. Not knowing anything about Einstein's relativity (of course!), Fizeau interpreted his results in terms of "partial dragging" of the luminiferous aether by the moving medium (water in his experiments).

http://en.wikipedia.org/wiki/Fizeau_experiment

 

[harrylin]

[..] light does not always travel at c, it only travels at that speed in a vacuum (supposedly). When it is in a medium such as water or air, it moves at a noticably slower rate, where even other objects are capable of moving faster than light (not as eye-popping as it sounds). But do the same rules of relativity apply in this case? If not, how should light be treated in this case?

Roughly that same question was asked last month:
www.physicsforums.com/showthread.php?t=628996