JEE Main & Advanced Physics Ray Optics Sample Paper Topic Test - Refraction of Light Through Plane Surfaces

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

B) \[2{{\cos }^{-1}}(\mu /2)\]

C) \[2{{\sin }^{-1}}(\mu )\]

D) \[2{{\sin }^{-1}}\,(\mu /2)\]

Correct Answer: B

Solution :

[b] By using \[\mu =\frac{\sin i}{\sin r}\]\[\Rightarrow \]\[\mu =\frac{\sin 2r}{\sin r}=\frac{2\sin r\cos r}{\sin r}\]

\[(\sin 2\theta =2\,\sin \theta \cos \theta )\]\[\Rightarrow \] \[r={{\cos }^{-1}}\left( \frac{\mu }{2} \right)\]

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