In a medium,the speed of a light wave decreas | vedclass

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(A) The speed of light in a medium $V$ is related to the speed of light in free space $C$ by the refractive index $\mu$ as $V = \frac{C}{\mu}$.Given $

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$5$

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(A) The speed of light in a medium $V$ is related to the speed of light in free space $C$ by the refractive index $\mu$ as $V = \frac{C}{\mu}$.Given $V = 0.2C$,we have $\mu = \frac{C}{V} = \frac{C}{0.2C} = 5$.The refractive index is also given by $\mu = \sqrt{\epsilon_r \mu_r}$.Given $\mu_r = 1$,we have $\mu = \sqrt{\epsilon_r}$,which implies $\epsilon_r = \mu^2$.Substituting $\mu = 5$,we get $\epsilon_r = 5^2 = 25$.The ratio of relative permittivity $\epsilon_r$ to the refractive index $\mu$ is $\frac{\epsilon_r}{\mu} = \frac{25}{5} = 5$.Thus,the ratio is $5:1$,so $x = 5$.

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