$(a)\;\theta= \cos^{-1} \frac{2}{3} \\ (b)\;\theta < \cos ^{-1} \frac{2}{3} \\ (c)\;\theta > \cos ^{-1} \frac{2}{3} \\ (d)\; None $

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Light ray will pass the surface.

AC with out bending Since it is incident normally.

Suppose it strikes the surface AB at an angle of incidence i.

$i=90-\theta$

For required condition :

$90^{\circ}- \theta >C$

or $\sin(90^{\circ}-\theta ) > \sin C$

or $\cos \theta > \sin C =\large\frac{1}{3/2}$

$\qquad=\large\frac{3}{2}$

$\theta < \cos^{-1} \large\frac{2}{3}$

Hence b is the correct answer.

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