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A ray of light strikes a material of refractive index $\mu= \sqrt 3$. If the reflected and refracted light are perpendicular to each other, what is the angle of incidence.

$(a)\;30^{\circ} \\ (b)\;45^{\circ} \\ (c)\;60^{\circ} \\ (d)\;90^{\circ} $

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$\large\frac{\sin \theta }{\sin r} $$=\mu$
Now we have $ \angle r +90^{\circ} + \angle NOB =180^{\circ}$
$\angle NOB =\angle \theta$
$\therefore \angle =90^{\circ}-\theta$
$\large\frac{\sin \theta}{\sin (90 -\theta)} $$= \sqrt 3$
$\large\frac{\sin \theta}{\cos \theta} $$=\sqrt 3$
$\tan \theta= \sqrt 3$
$\theta =60^{\circ}$
Hence c is the correct answer.
answered Jan 20, 2014 by meena.p

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