$\varepsilon_0$ and $\mu_0$ are the electric permittivity and magnetic permeability of free space respectively

Question

$\varepsilon_0$ and $\mu_0$ are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are $2\varepsilon_0$ and $1.5\mu_0$ respectively, the refractive index of the medium will nearly be:

Accepted Answer

1. **Speed of Light Relations:** The speed of light in vacuum is $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ and in a medium is $v = \frac{1}{\sqrt{\mu \varepsilon}}$.
2. **Refractive Index:** The refractive index $n$ is defined as the ratio $c/v$.
   $$ n = \frac{c}{v} = \sqrt{\frac{\mu \varepsilon}{\mu_0 \varepsilon_0}} $$
3. **Relative Permittivity and Permeability:** This can be expressed in terms of relative quantities $\mu_r = \mu/\mu_0$ and $\varepsilon_r = \varepsilon/\varepsilon_0$ as $n = \sqrt{\mu_r \varepsilon_r}$.
4. **Calculation:** Given $\varepsilon = 2\varepsilon_0$ (so $\varepsilon_r = 2$) and $\mu = 1.5\mu_0$ (so $\mu_r = 1.5$).
   $$ n = \sqrt{1.5 	imes 2} = \sqrt{3} $$

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