Question

A glass prism of refractive index $1.5$ is immersed in water (refractive index $4/3)$. A light beam normally on the face $AB$ is totally reflected to reach on the face $BC$ if

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

Answer 1

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

The phenomenon of total internal reflection takes place during reflection at $P$.
$\sin \theta =\frac{1}{{}_g^w\mu }....\left(i\right)$
where $\theta$ is the angle of incidence at $P$.
Now, ${}_g^w\mu =\frac{{}_g^{a}h}{{}_g^a\mu }=\frac{1.5}{4/3}=1.125$
Putting in (i),
$\sin \theta =\frac{1}{1.125}=\frac{8}{9}$
Therefore, $\sin \theta$ should be greater than $\frac{8}{9}$.