Q. Refractive index of a medium is $\mu$. The incidence angle is twice that of refracting angle. The angle of incidence is
A) $\cos^{- 1}\left( \frac{\mu}{2} \right)$
B) $\sin^{- 1}\left( \frac{\mu}{2} \right)$
C) $2\cos^{- 1}\left( \frac{\mu}{2} \right)$
D) $\sin^{- 1}\mu$
Explanation
(c) Angle of incidence $= 2$(Angle of refraction), $i = 2r$ [Given]
As $\mu = \frac{\sin i}{\sin r} = \frac{\sin{2r}}{\sin r}$
$= \frac{2\sin r\cos r}{\sin r}\ \ \ \ \lbrack\because\sin{2\theta} = 2\sin\theta\cos\theta\rbrack$
$= 2\cos r$
or $\cos r = \frac{\mu}{2}$ or $r = \cos^{- 1}\left( \frac{\mu}{2} \right)$
$\therefore i = 2r = 2\cos^{- 1}\left( \frac{\mu}{2} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.