Q. A ray of light passes from vacuum into a medium of refractive index$\mu$, the angle of incidence is found to be twice the angle of refraction. The angle of incidence is
A) $\cos^{- 1}\left( \frac{\mu}{2} \right)$
B) $2\cos^{- 1}\left( \frac{\mu}{2} \right)$
C) 2$\sin^{- 1}(\mu)$
D) $2\sin^{- 1}\left( \frac{\mu}{2} \right)$
Explanation
(b) Given, $i = 2r,\ \mu = \frac{\sin i}{\sin r} = \frac{\sin{2r}}{\sin r} = \frac{{2\ sin}{r\cos r}}{\sin r}$
$\cos{r = \frac{\mu}{2}\ or\ r = \cos^{- 1}\left( \frac{\mu}{2} \right)}$
$i = 2r = 2\ cos^{- 1}\left( \frac{\mu}{2} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.