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If the speed of an electromagnetic wave in a particular medium is such that $v = c$, the speed of light, does this mean that the permeability $\mu = \mu_0$, i.e. that of a vacuum and the index of refraction is also $n = \frac{c}{v} = 1$? Also $\epsilon = \epsilon_0$?

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when the light moves in vaccum, the value of epsilon is ofcourse equal to epsilon nought. –  newera Jun 6 '13 at 10:41
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As for $\mu$ or $\varepsilon$, not necessarily, this only means that $\sqrt{\frac{\varepsilon\mu}{\varepsilon_0\mu_0}}=1$ at the specific frequency. This is possible, e.g., if $0<\mu<1$. The above is about phase velocity, although, as far as I understand, your statement is not necessarily true for group velocity either. As for the velocity of the front of the wave, it is always equal to the velocity of light in vacuum, as far as I remember. As for $n$, yes, your statement seems correct (at least if we do not consider losses in the medium).

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As for the velocity of the front of the wave, it is always equal to the velocity of light in vacuum I don't think this is right. It sounds like you're talking about the signal velocity: en.wikipedia.org/wiki/Signal_velocity The signal velocity is usually equal to the group velocity, which is usually less than c. –  Ben Crowell Jun 6 '13 at 13:18
    
@Ben Crowell: en.wikipedia.org/wiki/Front_velocity –  akhmeteli Jun 6 '13 at 14:15
    
I see, +1. I hadn't been aware of precursor signals. –  Ben Crowell Jun 6 '13 at 16:41
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