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