When light propagates through a material medium of relative permittivity, $\varepsilon_r$ and relative permeab

Question

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

Accepted Answer

1. **Speed in Vacuum:** The speed of light in a vacuum ($c$) is related to the permeability ($\mu_0$) and permittivity ($\varepsilon_0$) of free space by the equation: $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$.
2. **Speed in Medium:** In a material medium, the speed of light ($v$) is determined by the absolute permeability ($\mu$) and permittivity ($\varepsilon$) of that medium: $v = \frac{1}{\sqrt{\mu \varepsilon}}$.
3. **Relative Properties:** The absolute values are related to the relative values by $\mu = \mu_0 \mu_r$ and $\varepsilon = \varepsilon_0 \varepsilon_r$ .
4. **Substitution:** Substituting these into the velocity equation:
   $$ v = \frac{1}{\sqrt{(\mu_0 \mu_r) (\varepsilon_0 \varepsilon_r)}} = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} \cdot \frac{1}{\sqrt{\mu_r \varepsilon_r}} $$
   Since $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$, we get:
   $$ v = \frac{c}{\sqrt{\mu_r \varepsilon_r}} $$

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