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If angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$, then angle of incidence is
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Verified Answer
The correct answer is:
$2 \cos ^{-1} \frac{\mu}{2}$
According to Snell's law Refractive index, $\mu=\frac{\sin i}{\sin r}$
Given $i=2 r$
$\therefore$
$$
\mu=\frac{\sin 2 r}{\sin r}
$$
or $\mu=\frac{2 \sin r \cos r}{\sin r}$
or $\quad \cos ^{-1} \frac{\mu}{2}=r$
$$
i=2 \cos ^{-1} \frac{\mu}{2}
$$
Given $i=2 r$
$\therefore$
$$
\mu=\frac{\sin 2 r}{\sin r}
$$
or $\mu=\frac{2 \sin r \cos r}{\sin r}$
or $\quad \cos ^{-1} \frac{\mu}{2}=r$
$$
i=2 \cos ^{-1} \frac{\mu}{2}
$$
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