Question

A glass prism of refractive index $1.5$ is immersed in water $($refractive index $\frac{4}{3}$$)$. A light beam incident normally on the face $AB$ is totally reflected of face $AC$ 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. None of the above

Answer 1

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


Let, ${\theta }_c$ be the critical angle at face $AC$, then
$\sin {\theta }_c=\frac{{\mu }_w}{{\mu }_g}=\frac{\frac{4}{3}}{\frac{3}{2}}=\frac{8}{9}$
Angle of incidence on face $AC$ is $i=\theta$.

Total internal reflection will take place on this surface, if

$i>{\theta }_c$

$\Rightarrow$ $\theta >{\theta }_c$

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

$\therefore$ $\sin \theta >\frac{8}{9}$

$\begin{array}{c}\text{Why this question}:\\ \text{This question checks the application of TIR}\\ \text{and normal incidence in the case of a prism.}\end{array}$