Question

A light wave travelling linearly in a medium of dielectric constant $4$, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be:
(Given : relative permeability of medium ${\mu }_r=1$)

• A. ${20}^{\circ }$
• B. ${10}^{\circ }$
• C. ${30}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is D ${60}^{\circ }$

For $TIR$, $i>{\theta }_c$

$\Rightarrow \sin i>\sin {\theta }_c$
$\Rightarrow \sin i>\frac{{\mu }_R}{{\mu }_D}$ ...............$\left(1\right)$

Also we know,
$\mu =\sqrt{{\mu }_r{ϵ}_r}$

$\frac{{\mu }_R}{{\mu }_D}=\frac{\sqrt{1\times 1}}{\sqrt{4\times 1}}=\frac{1}{2}$

Thus from, $\left(1\right)$, we get:
$\sin i>\frac{1}{2}$

$\Rightarrow i>{30}^o$
only option is ${60}^o$

Hence, the correct option is $\text{(}d)$.