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  4. 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(1+(10/θ))(1/2) the value of θ is (Given for dielectric media, μ r =1 )

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Q. 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, $\mu_{ r }=1$ )

JEE MainJEE Main 2023Wave Optics

Solution:

$ \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 $