Question

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. Then 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) $
• E. none of these

Answer 1

Answer: (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) $