Question

When a ray of light traveling from vacuum to a medium of refractive index $\mu$, the angle of incidence is twice the angle of refraction. The incident angle 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

Answer: (B)

$2co{s}^{-1}\left(\frac{\mu }{2}\right)$

By Snell's Law, $\frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$

$\frac{sin2r}{sinr}=\frac{\mu }{1}$

$\frac{2sinrcosr}{sinr}=\mu$

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

So the incident angle $=2co{s}^{-1}\left(\frac{\mu }{2}\right)$