Question

In Fig., $ABC$ is the cross section of a right-angled prism and $ACDE$ is the cross section of a glass slab. The value of $\theta$ so that light incident normally on the face $AB$ does not cross the face $AC$ is (given ${\sin }^{-1}\left(3/5\right)={37}^{\circ })$.

• A. $\theta \le {37}^{\circ }$
• B. $\theta <{37}^{\circ }$
• C. $\theta \le {53}^{\circ }$
• D. $\theta <{53}^{\circ }$

Answer 1

Answer: (B)

$\theta <{37}^{\circ }$

For the light to not cross the surface AC, there must be a total internal reflection at the interface.

Thus $\sin i>\frac{{\mu }_2}{{\mu }_1}=\frac{4}{5}$

Hence, $i>{53}^{\circ }$

Hence, $\theta <{37}^{\circ }$