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

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 $\tan^{- 1} {(1 + \frac{10}{θ})}^{\frac{1}{2}}$ , the value of $θ$ is ______.

(Given for dielectric media, $μ_{r} = 1$ )

TestHub · Accepted Answer

As given in the question, we can write μ 1 = ε r μ r = 2 . 8 × 1 = 2 . 8 and μ 2 = ε r μ r = 6 . 8 × 1 = 6 . 8 Now applying Snell's law and considering r = 90 ° - i , we get μ 1 sin i = μ 2 cos i ⇒ tan i = μ 2 μ 1 = 6 . 8 2 . 8 ⇒ tan i = 2 . 8 + 4 2 . 8 1 2 ⇒ i = tan - 1 1 + 10 7 1 2 Therefore, θ = 7 .

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