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Refractive index of a medium is $\mu$. If the angle of incidence is twice that of the angle of refraction, then the angle of incidence is
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Verified Answer
The correct answer is:
$\cos ^{-1}\left(\frac{\mu}{2}\right)$
Given, angle of incidence, $\mathrm{i}=2 \times$ angle of refraction, $\mathrm{r}$ from Snell's law
$$
\begin{aligned}
& \mu_1 \sin \mathrm{i}=\mu_2 \sin r \\
& 1 \times \sin 2 r=\mu \sin r \\
& 2 \sin r \cos r=\mu \sin r
\end{aligned}
$$
$\operatorname{Cos} r=\frac{\mu}{2}$
$$
\begin{aligned}
& \mu_1 \sin \mathrm{i}=\mu_2 \sin r \\
& 1 \times \sin 2 r=\mu \sin r \\
& 2 \sin r \cos r=\mu \sin r
\end{aligned}
$$
$\operatorname{Cos} r=\frac{\mu}{2}$
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