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A large glass slab $\left(\mu=\frac{5}{3}\right)$ of thickness 8 $\mathrm{cm}$ is placed over a point source of light on a plane surface. It is seen that light emerges out of the top surface of the slab from a circular area of radius $R \mathrm{~cm}$. What is the value of $R$ ?
Solution:
2575 Upvotes
Verified Answer
The correct answer is:
6
$$
\frac{R}{t}=\tan \theta_C
$$
or $\quad R=t\left(\tan \theta_C\right)$
$$
\begin{aligned}
& \text { But, } \quad \sin \theta_C=\frac{1}{\mu}=\frac{3}{5} \\
& \therefore \quad \tan \theta_C=\frac{3}{4} \\
& \therefore \quad R=\frac{3}{4} t=\frac{3}{4}(8 \mathrm{~cm})=6 \mathrm{~cm} \\
&
\end{aligned}
$$
Hence the answer is 6 .
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