When light propagates through a material medium of relative...

We know, $c = \dfrac{1}{\sqrt{{\mu}_{0}{ε}_{0}}}$

for any medium

$v = \dfrac{1}{\sqrt{\muε}}$ but $\mu = {\mu}_{r}{\mu}_{0}$ and $ε = {ε}_{r}{ε}_{0}$

$∴ v = \dfrac{1}{\sqrt{{\mu}_{r}{\mu}_{0}{ε}_{r}{ε}_{0}}}$

$= \dfrac{1}{\sqrt{{\mu}_{r}{ε}_{r}}} \times \dfrac{1}{\sqrt{{\mu}_{0}{ε}_{0}}} = \dfrac{c}{\sqrt{{\mu}_{r}{ε}_{r}}}$