Consider a light ray travelling in air is incident into a medium of refractive index √(2n). The incident angle is twice that of refracting angle. Then, the angle of incidence will be: (a) sin ⁻¹(√(n)) (b) cos ⁻¹(√(n/2)) (c) sin ⁻¹(√(2n)) (d) 2cos ⁻¹(√(n/2))

Answer: (d). Snell's law with i = 2r: √(2n) = (sin 2r)/(sin r) = 2cos r. cos r = (√(2n))/(2) = √(n/2). i = 2r = 2cos ⁻¹(√(n/2)). So the answer is (d).

Consider a light ray travelling in air is incident into a medium of… | JEE Main 2022 (27 Jun, Shift 1)

Q45JEE Main 2022 · 27 JUN · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

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

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Answer: (d)

Snell's law with $i = 2r$ : $\sqrt{2n} = \dfrac{\sin 2r}{\sin r} = 2\cos r$ .
$\cos r = \dfrac{\sqrt{2n}}{2} = \sqrt{\dfrac{n}{2}}$ .
$i = 2r = 2\cos^{-1}\left(\sqrt{\dfrac{n}{2}}\right)$ .
So the answer is (d).

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