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 $\left.\mu_{ r }=1\right)$

Answer 1

$V =\frac{ C }{\mu} \Rightarrow \mu=\frac{ C }{ V }=\frac{ C }{0.2 C } $
$ \mu=5 $
$ \mu=\sqrt{\epsilon_{ r } \mu_{ r }}$
$ \Rightarrow \epsilon_{ r }=\frac{\mu^2}{\mu_{ r }} $
$ \therefore \frac{\epsilon_{ r }}{\mu}=\frac{\mu}{\mu_{ r }}=5$