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

$\mu_1=\sqrt{2.8 \times 1}=\sqrt{2.8}$

$\mu_2=\sqrt{6.8 \times 1}=\sqrt{6.8}$

$\mu_1 \sin i=\mu_2 \cos i$

$tan i =\frac{\mu_2}{\mu_1}=\sqrt{\frac{6.8}{2.8}}$

$\tan i =\left(\frac{2.8+4}{2.8}\right)^{1 / 2}$

$i =\tan ^{-1}\left(1+\frac{10}{7}\right)^{1 / 2}$

$\theta=7$

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