Question

A galss prism of refractive index $1.5$ is immersed in water (refractive index $\frac{4}{3}$). A light beam incident normally on the face AB is totally reflected to reach the face BC, if

• A. $\text{sin}\theta \ge \frac{8}{9}$
• B. $\frac{2}{3}<\text{sin}\theta \le \frac{8}{9}$
• C. $\text{sin}\theta \le \frac{2}{3}$
• D. $\text{sin}\theta \le \frac{8}{9}$

Answer 1

The correct option is A $\text{sin}\theta \ge \frac{8}{9}$

Since, ray MN is incident normally on face AB, hence$\angle MNQ=\theta ,\theta \ge C$
For total internal reflection to occur, the angle of incidence should be more than the critical angle
$\text{sin}\theta \ge \text{sin C}$
Now, using Snell's law
$\frac{1.5}{\frac{4}{3}}=\frac{1}{\text{sin C}}$
$\text{or sin C}=\frac{8}{9}\Rightarrow \text{sin}\theta \ge \frac{8}{9}$