The refractive index and the permeability of a medium are respectively $\frac{4}{3}$ and $4\times {10}^{-7}H{m}^{-1}$ . The relative permittivity of the medium is _______

Refractive index ,  $n=\frac{C}{V}$
Where ‘C’ is velocity of light in vacuum and ‘V’ is velocity of light in medium
$V=\frac{C}{n}=\frac{3\times {10}^8}{4/3}=\frac{9}{4}\times {10}^8 = 2.25\times {10}^{8}m/s$
Here,$$\begin{gathered} \mu =4\times {10}^{-7}\frac{H}{m} \\ We know, V=\frac{1}{\sqrt{\mu \in }}=\frac{1}{\sqrt{\mu {\in }_0{\in }_r}} \\ \Rightarrow {\in }_r=\frac{1}{V^2\mu {\in }_0}=\frac{1}{{(2.25\times {10}^8)}^2\times 4\times {10}^{-7}\times 8.85\times {10}^{-12}}=5.58 \end{gathered}$$