Question

A glass prism $\mu =1.5$ is dipped in water $(\mu =\frac{4}{3})$ as shown in figure. A light ray is incident normally on the surface $\text{AB}.$ It reaches the surface $\text{BC}$ after totally reflected if-

• A. $\sin \theta \ge \frac{8}{9}$
• B. $\frac{2}{3}<\sin \theta <\frac{8}{9}$
• C. $\sin \theta \le \frac{2}{3}$
  
• D. ​​​​​​ It is not possible
  

Answer 1

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

Given, ${\mu }_g=1.5;{\mu }_w=\frac{4}{3}$



For, TIR at the surface $\text{AC}$, $\theta >{\theta }_c$

Where, $\theta =\text{Angle of incidence}{\theta }_c=\text{Critical angle}$

And

$\sin {\theta }_c=\left(\frac{1}{{\mu }_{rel}}\right)$

$\Rightarrow \sin \theta \ge \sin {\theta }_c$

$\Rightarrow \sin \theta \ge \frac{1}{{}_w{\mu }_g}$

$\Rightarrow \sin \theta \ge \frac{{\mu }_w}{{\mu }_g}$

$\Rightarrow \sin \theta \ge \frac{8}{9}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(A\right)$ is the correct answer.