Question

If the angle of incidence is twice the angle of refraction in a medium of refractive index $ \mu , $ then the 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 Snells law
$ \mu =\frac{\sin i}{\sin r} $
$ i=2r $
$ \mu =\frac{\sin 2r}{\sin r}\Rightarrow \mu =\frac{2\sin r\cos r}{\sin r} $
$ {{\cos }^{-1}}\frac{\mu }{2}=r $