Question

A glass prism of refractive index $1.5$ is immersed in water $[\mu =\frac{4}{3}]$ as shown in figure. 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. $\sin \theta <\frac{2}{3}$
• D. $\cos \theta \ge \frac{8}{9}$

Answer 1

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

From

Total internal reflection takes place at $AC$, only if
$\theta >C$
$\sin \theta >\sin C$
$\sin \theta >\frac{1}{{}_w{\mu }^g}$

$\sin \theta >\frac{1}{\frac{9}{8}}\Rightarrow \sin \theta >\frac{8}{9}$