Question

A ray of light passes from vacuum into a medium of refractive index μ, the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is

• A. $\cos ^ { - 1 } ( \mu / 2 )$
• B. $2 \cos ^ { - 1 } ( \mu / 2 )$
• C. $2 \sin ^ { - 1 } ( \mu )$
• D. $2 \sin ^ { - 1 } ( \mu / 2 )$

Answer 1

Answer: (B)

$2 \cos ^ { - 1 } ( \mu / 2 )$

Answer 2

By using $\mu = \frac { \sin i } { \sin r }$ $\mu = \frac { \sin 2 r } { \sin r } = \frac { 2 \sin r \cos r } { \sin r }$

($\sin 2 \theta = 2 \sin \theta \cos \theta$)

$r = \cos ^ { - 1 } \left( \frac { \mu } { 2 } \right)$.

So, $i = 2 r = 2 \cos ^ { - 1 } \left( \frac { \mu } { 2 } \right)$.