"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."<quoted text>
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.
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.
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).
Why thank you.
Yon distant galaxy's light we see, 13.2 billion light years away, started out as a whole bunch of different light sources bouncing around within the galaxy. Much like ours does? So you have a lot of light sources modifying that pinpoint we see. That pinpoint started out galaxy sized, but we get a very tiny perspective of it. It becomes a very narrow beam towards us comprised of a lot of action. This beam has been getting modified for 13.2 billion years by your calculations by beams from other galaxies, plasma clouds, and various other cosmic bric a brac. EM fields like you referred to, but spread out. There is no empty pure vacuum between here and there. A thin sea of particles and fields, coupled with the mixing at the source. Each field that warps the path, or particles that absorb and emit slows down that light. That beam is the same as a flashlight beam at a distance. So, your spectrography and distance estimates can be considerably off.
I posted this yesterday. One would think, judging by the definition of these photos that simple old triangulation should be able to be employed and compared to the assumptions based on light speed and spectrography. Are you aware of such being done?