Does the light speed change in media? [duplicate]

Does the light speed change? The Theory of Relativity says that the speed of light in vacuum is the same and unchangeable, while I read that the speed of light in glass is lower than in air, and that it's the maximum in vacuum.

If so that the speed of light in media changes, then we can conduct the following suppose a media as air, and a body is moving through it in a uniform velocity, we get that time relative to this body dilates because of it's motion, $t = \dfrac{t'}{ \sqrt{1- \dfrac{v^2}{ c^2}}}$

Now suppose another media as $CO_2$ gas, and the same body is moving through it with the same regular velocity, time also dilates relative to it. So, since the velocity is the same, Time must dilate with the same value, but the speed of light is different, So time dilation has to be different. So which one is correct? Does this dilation of time change or no? I'm really confused.

• Relativity says that the speed of light in vacuum is invariant. That's all. Commented Mar 14, 2014 at 18:17
• Also related: physics.stackexchange.com/q/44115 Commented Mar 14, 2014 at 18:43

• Actually, relativity does say that massless particles can't travel slower than $c$. Commented Mar 14, 2014 at 18:54