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. $co{s}^{-1}\left(\frac{\mu }{2}\right)$
• B. $2co{s}^{-1}\left(\frac{\mu }{2}\right)$
• C. $2si{n}^{-1}\left(\mu \right)$
• D. $2si{n}^{-1}\left(\frac{\mu }{2}\right)$

Answer 1

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

By using $\mu =\frac{sini}{sinr}\Rightarrow \mu =\frac{sin2r}{sinr}=\frac{2sinrcosr}{sinr}$
$\Rightarrow r=co{s}^{-1}\left(\frac{\mu }{2}\right).So,i=2r=2co{s}^{-1}\left(\frac{\mu }{2}\right)$