I should also point out that there are materials where the index of refraction depends on *direction* through the material. Or where the index of refraction is different for different polarities of light. Calcite is an example of the latter. That is why it can be used to separate polarities.If the statement/question is rephrased, so that the material is of uniform density, temperature, and pressure (the three are related; a change in one requires a change in the others)... and consistent throughout... THEN would light's speed be constant through the material?
In other words, in addition to uniformity (properties are the same at all locations), you also need isotropy (conditions are the same in all directions). Water at constant density satisfies these properties, though.
Finally, E&M fields can affect the index of refraction, so you would also need a uniform E&M field in the material (before the light comes through). Although that could also be put into the uniformity and isotropy conditions.
No problem. It's nice to have someone who actually wants to learn.Thanks for putting up with me.
Did those animations at the wiki site help at all? I particularly liked the one where the phase and group velocities were in opposite directions.
Another way to look at the difference is that phase velocity is how fast the peaks move in a 'carrier' of constant frequency and amplitude. Group (more specifically, signal) velocity is how fast *changes* in frequency or amplitude can move. Since we need to change the carrier wave to form a signal, it is the latter that is relevant for communication (and also the one limited by c).