Question

A ray of light falls into a medium of $R.l.\mu$ from vacuum. The angle of incidence is found to be twice the angle of refraction. Then, the angle of incidence is

• A. $2{\sin }^{-1}\left(\mu \right)$
• B. $2{\cos }^{-1}\left(\mu \right)$
• C. $2{\sin }^{-1}\left(\mu /2\right)$
• D. $2{\cos }^{-1}\left(\mu /2\right)$

Answer 1

Answer: (D)

$2{\cos }^{-1}\left(\mu /2\right)$

We know,

${\mu }_1\sin i=\mu \sin r$ $({\mu }_1=1)$

Given,

$r=\frac{i}{2}$

$\sin i=\mu \sin \frac{i}{2}$

$2\sin \frac{i}{2}\cos \frac{i}{2}=\mu \sin \frac{i}{2}$

$i=2{\cos }^{-1}\frac{\mu }{2}$

Hence option $\text{D}$ is the correct answer.