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A glass slab has refractive index ' $\mu$ ' with respect to air and the critical angle for a ray of light in going from glass to air is ' $\theta$ ' If a ray of light is incident from air on the glass with angle of incidence ' $\theta$ ', then the corresponding angle of refraction is
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Verified Answer
The correct answer is:
$\sin ^{-1}\left(\frac{1}{\mu^2}\right)$
In the first case $\theta$ is the critical angel
Hence, $\sin \theta=\frac{1}{\mu}$
In the second case, $\frac{\sin \theta}{\sin r}=\mu$
$$
\begin{aligned}
& \therefore \sin r=\frac{\sin \theta}{\mu} \\
& \therefore \sin r=\frac{1}{\mu^2} \\
& \therefore \sin r=\left(\frac{1}{\mu^2}\right)
\end{aligned}
$$
Hence, $\sin \theta=\frac{1}{\mu}$
In the second case, $\frac{\sin \theta}{\sin r}=\mu$
$$
\begin{aligned}
& \therefore \sin r=\frac{\sin \theta}{\mu} \\
& \therefore \sin r=\frac{1}{\mu^2} \\
& \therefore \sin r=\left(\frac{1}{\mu^2}\right)
\end{aligned}
$$
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