Question 169: EM waves

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 $$=3 	imes 10^{8} \mathrm{~m} \mathrm{~s}^{-1}$$ and for the given medium $$\mu_{\mathrm{r}}=1$$)

Accepted Answer

We know that $v=\frac{c}{n}=\frac{c}{\sqrt{\varepsilon_{r}}}$
Putting the values:
$0.2 c=\frac{c}{\sqrt{\varepsilon_{r}}}$
$\Rightarrow \sqrt{\varepsilon_{r}}=5$
$\Rightarrow$ Required ratio $=\frac{\varepsilon_{r}}{n}=\frac{\varepsilon_{r}}{\sqrt{\varepsilon_{r}}}=\sqrt{\varepsilon_{r}}=5$
$\Rightarrow x=5$

EM waves

Integer / Numeric Answer Type