Question

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} \frac{\mu}{2} $
• B. $ 2 \,sin ^{-1} \frac{\mu}{2} $
• C. $ 2\, cos^{-1} \mu $
• D. $ 2\, sin ^{-1} \mu $

Answer 1

Answer: (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\, rcos\, r}{\sin\, r} $
or $ \cos^{-1} \frac{\mu}{2}= r $
$ \Rightarrow i = 2 \cos^{-1}\frac{\mu}{2} $