Question

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

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

Answer 1

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

From figure it is clear that
Total internal reflection takes place at AC, only if $\theta >C$
$\Rightarrow sin\theta >sinC\Rightarrow sin\theta >\frac{1}{{}_{\omega }{\mu }_g}\Rightarrow sin\theta >\frac{1}{\frac{9}{8}}\Rightarrow sin\theta >\frac{8}{9}$