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 $$\mu_r = 1$$)

Solution :

Refractive index of medium is :

$$n = \frac{c}{v}$$

Given,

$$v = 0.2c$$

Therefore,

$$n = \frac{c}{0.2c}$$

$$= 5$$

Also,

$$n = \sqrt{\mu_r\epsilon_r}$$

Given,

$$\mu_r = 1$$

Hence,

$$n = \sqrt{\epsilon_r}$$

$$5 = \sqrt{\epsilon_r}$$

$$\epsilon_r = 25$$

Required ratio :

$$\epsilon_r : n$$

$$= 25 : 5$$

$$= 5 : 1$$

Therefore,

$$x = 5$$

Final Answer :

$$5$$