Understanding the Frame Dependence of the Speed of Light in a Medium

[madness]

The speed of light in a vacuum is c in all inertial frames. What about in a medium? Light in a superfluid can be slowed to a few miles per hour, so if this speed was the same for all inertial observers, relativistic effects would be very noticeable on an everyday speed-scale. This doesn't happen, so the speed of light must be frame dependent in a medium. Is there a relation that describes this, or some explanation of why this is the case?
Another thing that is confusing me is this: the Lorentz transformation for time is
t' = gamma(v)[t-vx/c^2], rearranging gives
t = t'/gamma(v)+vx/c^2
which is not what i get from the lorentz transform in reverse
t = gamma(-v)[t'+vx/c^2], where gamma(v) = gamma(-v)
Hopefully someone can point out my mistake. Thanks.

 

[ZapperZ]

Hint1: That "speed of light" that is being measured is the group velocity.

Hint2: You may want to read one of the entries in the FAQ sticky located in the General Physics forum.

Zz.

 

[Ich]

t = gamma(-v)[t'+vx/c^2]

should be
t = gamma(-v)[t'+vx'/c^2]