If µ₀ be the permeability and ε₀ be the permittivity of a medium, then its refractive index is given by:

$\sqrt{\mu_0 \varepsilon_0}$

Refractive index of medium is $=\frac{c}{v}$

Where $c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$ and $v=\frac{1}{\sqrt{\mu_0 \varepsilon_0 \mu_{r} \varepsilon_{r}}}$

∴  $\mu=\frac{1 / \sqrt{\mu_0 \varepsilon_0}}{1 / \sqrt{\mu_0 \varepsilon_0 \mu_{r} \varepsilon_{r}}}=\sqrt{\mu_{r} \varepsilon_{r}}$

Given, $\mu_{r}=\mu_0$ and $\varepsilon_{r}=\varepsilon_0$ then $\mu=\sqrt{\mu_0 \varepsilon_0}$