# What should be the value of angle $\theta$ so that light entering normally through the surface AC of a prism of refractive index $(n= \large\frac{3}{2})$ does not cross the second refracting surface AB.

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

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.
edited Feb 12, 2014 by meena.p