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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 $

1 Answer

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.
For required condition :
$90^{\circ}- \theta >C$
or $\sin(90^{\circ}-\theta ) > \sin C$
or $\cos \theta > \sin C =\large\frac{1}{3/2}$
$\theta < \cos^{-1} \large\frac{2}{3}$
Hence b is the correct answer.
answered Feb 12, 2014 by meena.p
edited Feb 12, 2014 by meena.p

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