JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Wave Optics

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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

)

Answer: 7

Solution

For dielectrics with

μ_{r} = 1

the refractive indices are

ε_{r}

, so

μ_{1} = 2.8

and

μ_{2} = 6.8

. The reflected and refracted rays are perpendicular at the Brewster angle, where

tan i = \frac{μ _{2}}{μ _{1}} = \frac{6.8}{2.8}

. Writing this as

\frac{2.8 + 4}{2.8} = 1 + \frac{4}{2.8} = 1 + \frac{10}{7}

and comparing with

(1 + \frac{10}{θ})^{1/2}

, the value of

θ

7

JEE Main · 2023 · 29 Jan 2023 · Shift 2 · Integer answer

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