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A glass prism of refractive index $1.5$ is immersed in water (refractive index $\frac{4}{3}$ ) as shown in figure. A light beam incident normally on the face $A B$ is
$$
\text { totally reflected to reach the face } B C \text {, if }
$$
Options:
$$
\text { totally reflected to reach the face } B C \text {, if }
$$
Solution:
1849 Upvotes
Verified Answer
The correct answer is:
$\sin \theta>\frac{8}{9}$
$\sin \theta>\frac{8}{9}$
For total internal reflection on face $A C$ $\theta>$ critical angle $(C)$ and $\sin \theta \geq \sin C$
$$
\begin{aligned}
& \sin \theta \geq \frac{1}{w_{\mu_g}} \\
& \sin \theta \geq \frac{\mu_w}{\mu_g} \Rightarrow \sin \theta \geq \frac{\frac{4}{3}}{\frac{3}{2}} \\
& \therefore \quad \sin \theta \geq \frac{8}{9} .
\end{aligned}
$$
$$
\begin{aligned}
& \sin \theta \geq \frac{1}{w_{\mu_g}} \\
& \sin \theta \geq \frac{\mu_w}{\mu_g} \Rightarrow \sin \theta \geq \frac{\frac{4}{3}}{\frac{3}{2}} \\
& \therefore \quad \sin \theta \geq \frac{8}{9} .
\end{aligned}
$$
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