Question

In a medium the speed of light wave decreases to $0.2$ times to its speed in free space The ratio of relative permittivity to the refractive index of the medium is $x:1$. The value of $x$ is ___
(Given speed of light in free space $=3\times 10^{8}m{s}^{-1}$ and for the given medium ${\mu }_r=1)$

Answer 1

Answer: 5

$V=\frac{C}{\mu }\Rightarrow \mu =\frac{C}{V}=\frac{C}{0.2C}$
$\mu =5$
$\mu =\sqrt{{ϵ}_r{\mu }_r}$
$\Rightarrow {ϵ}_r=\frac{{\mu }^2}{{\mu }_r}$
$\therefore \frac{{ϵ}_r}{\mu }=\frac{\mu }{{\mu }_r}=5$