Q. If angle of incidence is twice the angle of refraction in a medium of refractive index $\mu,$ then angle of incidence is
A) $2\cos^{- 1}\left\lbrack \frac{\mu}{2} \right\rbrack$
B) $2\sin^{- 1}\left\lbrack \frac{\mu}{2} \right\rbrack$
C) $2\cos^{- 1}\lbrack\mu\rbrack$
D) $2\sin^{- 1}\lbrack\mu\rbrack$
Explanation
(a) According to Snell’s law
Refractive index, $\mu = \frac{\sin i}{\sin r}$
Given $i = 2r$
$\therefore\ \mu = \frac{\sin{2r}}{\sin{\ r}}$
Or $\mu = \frac{2\sin{r\cos r}}{\sin r}$
Or $\cos^{- 1}\frac{\mu}{2} = r$
$\Rightarrow i = 2\cos^{- 1}\left\lbrack \frac{\mu}{2} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.