The speed of light is the same in all frames of reference. But imagine a scenario in which you passed by a ship which had (B=.78), while your ship had (B=.94). While somehow being able to look through the window of the ship you were passing, you see someone pointing a green laser into a fish tank, and of course the light refracts. Solving for the new angle is simple,(a bit of linear algebra, using the Lorentz matrix with angular components), but we all know that the speed of that light changes after it was refracted. So, would I measure the same velocity of that light as someone who is in the rest frame of the refraction incidence? I mean it is light, so all observers should measure it moving the same speed, correct? But, my gut tells me that I would clearly have to add the velocities using the velocity component Lorentz matrix. Where is the kicker?
2 Answers
You need to distinguish between being able to see and/or measure what happens in different frames and using the Lorentz transformations to tell you what happens in different frames. If you use the Lorentz transformations you'll find that the speed of light in the fish tank is not the same for both sets of observers. In effect the refractive index will be different in the two frames.
A closely related question is How does wind speed affect the velocity of light?. Substitute water for air and it's the same as your question. Another related question is Does the speed of medium affect the path of light?.
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All these dilemmas with different speed of light as observed by different observers are not real. They never occur in reality. They are only imaginary and can never be tested experimentally.
Observers in two different inertial frames cannot see/measure the same ray of light. This is physically impossible, for in order for you to see the light it must come exactly to your eye (measuring device). Light "exists" only for the one to whom it comes directly. If light is "passing you by", you cannot see it.
Therefore, two different observers will never actually measure different speeds of the same light. If one will measure it, the other will not be able to.
If I understand your set-up correctly, the person being in the other spaceship (not the one where the tank is located) will see only the light sent to him from the tank through vacuum separating the two spaceships. Therefore, as the speed of light in vacuum is $c$, than that's exactly what he will measure. (And yet, the person in the spaceship with the tank in it will never see light sent to the other rocket, so he will not be able to make any direct comparisons.)
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