Q115 / 150 · MHT CET 2009 · Physics
If angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$, then angle of incidence is
- Correct answerA$2 \cos ^{-1} \frac{\mu}{2}$
- B$2 \sin ^{-1} \frac{\mu}{2}$
- C$2 \cos ^{-1} \mu$
- D$2 \sin ^{-1} \mu$
Solution
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 $\quad \cos ^{-1} \frac{\mu}{2}=r$
$$
i=2 \cos ^{-1} \frac{\mu}{2}
$$
Hence, the correct answer is option: 'A'.