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Q.

A ray of light entering from air to glass (µ = 1.5) is partly reflected and partly refracted. If the reflected and refracted rays are at right angles to each other, the angle of refraction is

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a

$\sin^{- 1} (\frac{3}{\sqrt{13}})$

b

$\sin^{- 1} (\sqrt{\frac{2}{13}})$

c

$\sin^{- 1} (\frac{2}{\sqrt{13}})$

d

$\sin^{- 1} (\frac{\sqrt{2}}{13})$

answer is C.

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Detailed Solution

If refracted and reflected rays perpendicular then:
$\begin{array}{l} μ = \tan i (air to glass) \\ \frac{3}{2} = \tan i, \sin i = \frac{3}{\sqrt{13}}; μ = \frac{\sin i}{\sin r} \\ \frac{3}{2} = \frac{\sqrt{13}}{\sin r}; r = \sin^{- 1} \frac{2}{\sqrt{13}} \end{array}$

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