A ray of light from a denser medium strikes a rare medium as shown in figure. The reflected and refracted rays make an angle of 90° with each other. The angles of reflection and refraction are r and r'. The critical angle would be (a) sin ⁻¹(tan r) (b) sin ⁻¹(sin r) (c) cos ⁻¹(tan r) (d) tan ⁻¹(sin r)

Answer: (a). From the figure, r + r' = 90° and i = r. Snell: μsin r = sin r' = cos r ⇒ 1/μ = tan r. sin C = 1/μ = tan r So the answer is (a) sin ⁻¹(tan r).

A ray of light from a denser medium strikes a rare medium as shown in… | NEET 1996 (AIPMT)

Q83NEET 1996 · AIPMTMedium

Refraction, Glass Slab & Apparent Depth

A ray of light from a denser medium strikes a rare medium as shown in figure. The reflected and refracted rays make an angle of $90^\circ$ with each other. The angles of reflection and refraction are $r$ and $r'$ . The critical angle would be

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Answer: (a)

From the figure, $r + r' = 90^\circ$ and $i = r$ .
Snell: $\mu\sin r = \sin r' = \cos r \Rightarrow \frac{1}{\mu} = \tan r$ .
$\sin C = \frac{1}{\mu} = \tan r$
So the answer is (a) $\sin^{-1}(\tan r)$ .

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