Question

A glass prism is immersed in water as shown in the figure. A beam of light incidents normally on the face ab, it is internally reflected at the face ad so as to incident on face $bd.$ Given that refractive index of glass is $3/2$ and that of water is $4/3.$ What is the value of $\theta =\angle$ bad ?

• A. $\sin \theta <\left(2/3\right)$
• B. $\sin \theta >\left(8/9\right)$
• C. $\frac{2}{3}<\frac{8}{9}\sin \theta$
• D. None of these

Answer 1

Answer: (B)

$\sin \theta >\left(8/9\right)$

For total internal reflection to occur on the face ad,
$\theta >{\theta }_c$
Thereore,
$sin\theta >sin{\theta }_c$
$sin{\theta }_c=\frac{\frac{4}{3}}{\frac{3}{2}}$
Thus, $sin{\theta }_c>\frac{8}{9}$