Well, I thought I landed up with some good idea this time. Sadly, nothing new and this is resolved very easily. In Special Theory of Relativity, we have the postutate about the speed of light being the maximum speed of transmission. Now, with this postutate and a few other postulates about measurement of position,time and $$c$$ being same in all interntial frames, we can get nice results. One of them being the Invariance equation.

Question: Now what would happen if I use a similar signal in a medium? We know the "effective velocity" of light that we observe in a medium is $$v < c$$. (If this wasn't the case, then when it exists the medium it would be $$v > c$$ which isn't possible.Does it imply I can make measurements only using this upper bound of velocity on the medium?

Answer: It's fairly straight forward. There are two ways of looking at it this. Either, I can remove the medium entirely and make the measurements of events the same as in vacuum and then replace the medium back. This is more of a frame by frame approach. If you want a more convincing answer then you could argue that, we send signals of light even before any interaction with the molecules of the medium. We consider such a scale and hence in that scale, it is effectively the same concepts of SPR we use. We can extend this throughout the whole of the medium as this through bits.

Had this doubt while reading GR.

Kudos!