A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to each other. If ' r ' and ' r₁ ' are the angle of reflection and refraction respectively and ' C ' is the critical angle, then the angle of incidence is (a) cot ⁻¹(sin C) (b) sin ⁻¹(tan C) (c) tan ⁻¹(sin C) (d) cos ⁻¹(tan C)

Answer: (c). Perpendicular reflected and refracted rays: r + r₁ = 90° (Brewster condition). Denser to rarer: μsin i = sin r₁ = cos i ⇒ tan i = 1/μ. 1/μ = sin C ⇒ tan i = sin C So the answer is (c) tan ⁻¹(sin C).

A ray of light travels from a denser medium to a rarer medium. The… | MHT CET 2021 (20 Sep, Shift 1)

Q60MHT CET 2021 · 20 SEP · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

A ray of light travels from a denser medium to a rarer medium. The reflected and the refracted rays are perpendicular to each other. If ' $r$ ' and ' $r_1$ ' are the angle of reflection and refraction respectively and ' $C$ ' is the critical angle, then the angle of incidence is

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Answer: (c)

Perpendicular reflected and refracted rays: $r + r_1 = 90^\circ$ (Brewster condition).
Denser to rarer: $\mu\sin i = \sin r_1 = \cos i \Rightarrow \tan i = \frac{1}{\mu}$ .
$\frac{1}{\mu} = \sin C \Rightarrow \tan i = \sin C$
So the answer is (c) $\tan^{-1}(\sin C)$ .

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Refraction, Glass Slab & Apparent Depth question from MHT CET 2021 (20 Sep, Shift 1)

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