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. $2{\sin }^{-1}\left(\frac{\mu }{2}\right)$

Answer 1

The correct option is B $2{\cos }^{-1}\left(\frac{\mu }{2}\right)$

Using Snell's law for refraction,
$\sin i=\mu \sin \frac{i}{2}$
$\Rightarrow \mu =\frac{\sin i}{\sin \frac{i}{2}}=\frac{2\sin \frac{i}{2}\cos \frac{i}{2}}{\sin \frac{i}{2}}$
$\Rightarrow \frac{i}{2}={\cos }^{-1}\left(\frac{\mu }{2}\right)$
$\Rightarrow i=2{\cos }^{-1}\left(\frac{\mu }{2}\right)$