Question

A glass prism $(\mu=1.5)$ is dipped in water $(\mu=4 / 3)$ as shown in figure. A light ray is incident normally on the surface $A B$. It reaches the surface $B C$ after totally reflected, if

• A. $\sin \theta \geq 8 / 9$
• B. $2 / 3 < \sin \theta < 8 / 9$
• C. $\sin \theta \leq 2 / 3$
• D. It is not possible

Answer 1

Answer: (A)

For TIR at $A C$

$\theta > C$
$\Rightarrow \sin \theta \geq \sin C \quad $
$\Rightarrow \sin \theta \geq \frac{1}{{ }_{w} \mu_{g}}$
$\Rightarrow \sin \theta \geq \frac{\mu_{w}}{\mu_{g}} $
$\Rightarrow \sin \theta \geq \frac{8}{9}$