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A ray of light from a denser medium strikes a rarer medium at an angle of incidence I (see figure). The reflected and refracted rays make an angle of $90^{0}$ with each other. The angles of reflection and refraction are r and r’. The critical angle is

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a

$\tan^{- 1} (\sin r)$

b

$\sin^{- 1} (\tan r')$

c

$\sin^{- 1} (\tan r)$

d

$\tan^{- 1} (\sin r')$

answer is A.

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Detailed Solution

${}_{2}^{1}μ = \frac{\sin 90^{0}}{\sin C} = \frac{1}{\sin C} [f o r c r i t i c a l a n g l e] ∴ C = s i n^{- 1} = (\frac{1}{{}_{2}^{1}μ}) . . . . . . . . . . . . (I) A p p l y i n g s n e l l ’ s l a w a t P, w e g e t {}_{2}^{1}μ = \frac{\sin r'}{\sin i} = \frac{\sin (90 - r)}{\sin r} [∵ i = r; r' + r = 90^{0}] ∴ {}_{2}^{1}μ = \frac{\cos r}{\sin r} (i i) From (i) and (ii), C = s i n^{- 1} (\tan r)$

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A ray of light from a denser medium strikes a rarer medium at an angle of incidence I (see figure). The reflected and refracted rays make an angle of 900 with each other. The angles of reflection and refraction are r and r’. The critical angle is