Question

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are $2.8$ (medium $-1$ ) and $6.8$ (medium 2), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be ${\tan }^{-1}{\left(1+\frac{10}{\theta }\right)}^{\frac{1}{2}}$ the value of $\theta$ is ___
(Given for dielectric media, ${\mu }_r=1$ )

Answer 1

Answer: 7

${\mu }_1=\sqrt{2.8\times 1}=\sqrt{2.8}$
${\mu }_2=\sqrt{6.8\times 1}=\sqrt{6.8}$
${\mu }_1\sin i={\mu }_2\cos i$
$\tan i=\frac{{\mu }_2}{{\mu }_1}=\sqrt{\frac{6.8}{2.8}}$
$\tan i={\left(\frac{2.8+4}{2.8}\right)}^{1/2}$
$i={\tan }^{-1}{\left(1+\frac{10}{7}\right)}^{1/2}$
$\theta =7$