A ray of light passes from vaccum into a medium of refractive index $n$. If the angle of incidence is twice the angle of refraction, then the angle of incidence in terms of refractive index is

• A

  $\operatorname{Sin}^{-1}\left(\frac{n}{2}\right)$
• Correct answer
  B

  $2 \operatorname{Cos}^{-1}\left(\frac{n}{2}\right)$
• C

  $2 \operatorname{Sin}^{-1}\left(\frac{\mathrm{n}}{2}\right)$
• D

  $\operatorname{Cos}^{-1}\left(\frac{n}{2}\right)$

Solution

$\begin{aligned} & 1 \times \sin i=n \sin \frac{i}{2} \\ & 2 \sin \frac{i}{2} \cos \frac{i}{2}=n \sin \frac{i}{2} \\ & 2 \cos \frac{i}{2}=n \\ & \cos \frac{i}{2}=\frac{n}{2} \\ & \frac{i}{2}=\cos ^{-1}\left(\frac{n}{2}\right) \\ & i=2 \cos ^{-1}\left(\frac{n}{2}\right)\end{aligned}$

Hence, the correct answer is option: 'B'.