Wave Optics

JEE Main level, single correct, medium

161 of 191

Question 161 of 191

An unpolarised light is incident at an interface of two dielectric media having refractive indices of 2 (incident medium) and 232 \sqrt{3} (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ____\_\_\_\_.

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Answer: (B) 60∘60^{\circ}

For reflected and refracted rays to be perpendicular, if ii is the angle of incidence and rr is the angle of refraction, then i+r=90°i + r = 90°, giving r=90°−ir = 90° - i.
Applying Snell's law: n1sin⁡i=n2sin⁡rn_1 \sin i = n_2 \sin r
2sin⁡i=23sin⁡(90°−i)2 \sin i = 2\sqrt{3} \sin(90° - i)
2sin⁡i=23cos⁡i2 \sin i = 2\sqrt{3} \cos i
tan⁡i=3\tan i = \sqrt{3}
i=60°i = 60°

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