When light propagates through a material medium of relative permittivity $\epsilon_r$ and relative permeabilit

Question

When light propagates through a material medium of relative permittivity $\epsilon_r$ and relative permeability $\mu_r$, the velocity of light, $v$ is given by (c-velocity of light in vacuum)

Accepted Answer

The velocity of light in a medium is $v = \frac{1}{\sqrt{\mu \epsilon}}$, where $\mu = \mu_0 \mu_r$ and $\epsilon = \epsilon_0 \epsilon_r$. Thus $v = \frac{1}{\sqrt{\mu_0 \mu_r \epsilon_0 \epsilon_r}} = \frac{1}{\sqrt{\mu_0 \epsilon_0}} \cdot \frac{1}{\sqrt{\mu_r \epsilon_r}}$. Since $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$, we get $v = \frac{c}{\sqrt{\mu_r \epsilon_r}}$.

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