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A ray of light travelling in a transparent medium of refractive index $\mu$ falls, on a surface separating the medium from air at an angle of incidence of $45^{\circ}$. For which of the following value of $\mu$ the ray can undergo total internal reflection?
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Verified Answer
The correct answer is:
$\mu=1.50$
For total internal reflection
$$
\begin{aligned}
& \mathrm{i}>\mathrm{c} \\
\Rightarrow & \sin \mathrm{i}>\sin \mathrm{c} \\
\Rightarrow & \sin 45^{\circ}>\frac{1}{\mu} \\
\Rightarrow & \mu>\sqrt{2} \\
\Rightarrow & \mu>1.4
\end{aligned}
$$
$$
\begin{aligned}
& \mathrm{i}>\mathrm{c} \\
\Rightarrow & \sin \mathrm{i}>\sin \mathrm{c} \\
\Rightarrow & \sin 45^{\circ}>\frac{1}{\mu} \\
\Rightarrow & \mu>\sqrt{2} \\
\Rightarrow & \mu>1.4
\end{aligned}
$$
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