Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2 n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

(D) $2 \cos ^{-1}\left(\sqrt{\frac{n}{2}}\right)$

(B) $\cos ^{-1}\left(\sqrt{\frac{n}{2}}\right)$

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Geometrical Optics

Consider a light ray travelling in air is incident into a medium of refractive index

2 n

. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

(A) $sin^{- 1} (n)$
(B) $cos^{- 1} (\frac{n}{2})$
(C) $sin^{- 1} (2 n)$
(D) $2 cos^{- 1} (\frac{n}{2})$ ✓ Correct

Answer: (D)

Solution

Given

i = 2 r

and applying Snell's law:

sin i = 2 n sin r

. Substituting

i = 2 r

sin (2 r) = 2 n sin r

. Using

sin (2 r) = 2 sin r cos r

, we get

2 cos r = 2 n

, so

cos r = \frac{n}{2}

. Therefore

r = cos^{- 1} (\frac{n}{2})

and

i = 2 cos^{- 1} (\frac{n}{2})

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Single correct option

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