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If refractive index of water is $\frac{4}{3}$ and that of a given glass slab immersed in it is $\frac{5}{3}$. The value of critical angle for a ray of light tending to go from glass to water is
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Verified Answer
The correct answer is:
$\sin ^{-1}\left(\frac{4}{5}\right)$
Given, refractive index of water, ${ }_w \mu_a=4 / 3$
Refractive index of glass slab, ${ }_g \mu_a=5 / 3$ Refractive index of combined media
$$
\begin{aligned}
& =\frac{g \mu_a}{{ }_w \mu_a}=\frac{5}{3} \times \frac{3}{4} \\
\Rightarrow \quad \mu & =\frac{5}{4}
\end{aligned}
$$
Critical angle, $C=\sin ^{-1}\left(\frac{1}{\text { refractive index }}\right)$
$$
\Rightarrow \quad C=\sin ^{-1}\left(\frac{4}{5}\right)
$$
Refractive index of glass slab, ${ }_g \mu_a=5 / 3$ Refractive index of combined media
$$
\begin{aligned}
& =\frac{g \mu_a}{{ }_w \mu_a}=\frac{5}{3} \times \frac{3}{4} \\
\Rightarrow \quad \mu & =\frac{5}{4}
\end{aligned}
$$
Critical angle, $C=\sin ^{-1}\left(\frac{1}{\text { refractive index }}\right)$
$$
\Rightarrow \quad C=\sin ^{-1}\left(\frac{4}{5}\right)
$$
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