I am running at $5 \text{ ms}^{-1}$ and holding a torch pointing in the direction of motion. This torch has a large block of glass attached to the end. Would a stationary observer see the light as moving at the speed of light in glass ($2 \ 10^8 \text{ ms}^{-1}$) or as $5 \text{ ms}^{-1}$ faster? What if I was moving at $1 \ 10^8 \text{ ms}^{-1}$ or $2 \ 10^8 \text{ ms}^{-1}$?
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$\begingroup$ This might help. How can a red light photon be different from a blue light photon? $\endgroup$– mmesser314Commented Oct 7, 2021 at 14:38
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$\begingroup$ Possible duplicate: Is the speed of light in all media independent of reference frame? $\endgroup$– Qmechanic ♦Commented Oct 7, 2021 at 14:54
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$\begingroup$ How could light traveling at velocity $v<c$ in one frame appear to travel at velocity $v$ to an observer running along beside it? $\endgroup$– WillOCommented Oct 7, 2021 at 14:56
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2 Answers
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The short answer is "no". There is only one speed that is invariant (the same for all observers). That particular special speed $c$ is often called the "speed of light" because light travels at that speed in vacuum. But it's the speed that's important, not the light -- that is, if light is slowed down by a medium, it's no longer traveling at the special speed $c$ and hence its speed is determined just the same as the speed of anything else (using the usual relativistic formula for adding velocities).
answered Oct 7, 2021 at 14:53
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To determine the speed of light in a moving medium you use relativistic velocity addition. The first velocity is the speed of light in the medium (when the medium is at rest) and the second velocity is the speed of the medium.
