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. [2023]

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Solution

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 $\tan^{- 1} {(1 + \frac{10}{θ})}^{\frac{1}{2}}$ ; the value of $θ$ is ______. (Given for dielectric media, $μ_{r} = 1$ ) [2023]

Ans.
(7)

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

$μ_{2} = \sqrt{6.8 \times 1} = \sqrt{6.8}$

$μ_{1} \sin i = μ_{2} \cos i$

$\tan i = \frac{μ_{2}}{μ_{1}} = \sqrt{\frac{6.8}{2.8}}$

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

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

$θ = 7$

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