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Q.

A ray of light form a denser medium strikes a rarer medium at an angle of incidence $i (s e e f i g u r e) .$ The reflected and refracted rays make an angle of $90^{0}$ with each other. The angles of reflection and refraction are $r a n d r^{'} .$ The critical angle is :

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a

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

b

$\sin^{- 1} (\cot i)$

c

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

d

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

answer is A.

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Detailed Solution

$\begin{array}{l} r + r^{'} + 90^{0} = 180^{0} (B y g e o m e t r y), r^{'} = 90^{0} - r \\ μ_{D} \sin i = μ_{R} \sin r^{'} = μ_{R} \sin (90^{0} - r) = μ_{R} \cos r \\ \frac{μ_{R}}{μ_{D}} = \tan r, θ_{c} = \sin^{- 1} (\frac{μ_{R}}{μ_{D}}) = \sin^{- 1} (\tan r) \end{array}$

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