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# A light enters a transparent glass slab of refractive index $\mu=\large\frac{3}{2}$. The reflected ray and refracted ray are mutually perpendicular, The angle of incidence is

$(a)\;\sin ^{-1} \bigg(\frac{3}{2}\bigg) \\ (b)\;\sin ^{-1} \bigg(\frac{2}{3}\bigg) \\ (c)\;\tan ^{-1} \bigg(\frac{3}{2}\bigg) \\ (d)\;\tan ^{-1} \bigg(\frac{2}{3}\bigg)$

$i+r+90=180^{\circ}$
We have $\mu =\large\frac{\sin i}{\sin r}$
$\large\frac{3}{2} =\frac{\sin i}{\sin (90-i)}$
$\qquad =\large\frac{ \sin i}{ \cos i }$
$\qquad= \tan i$
$i= \tan ^{-1} \bigg(\large\frac{3}{2}\bigg)$
Hence c is the correct answer.

edited Jul 14, 2014