Question

If the angle of incidence is twice the angle of refraction in a medium of refractive index $\mu$, then the angle of incidence is :

• A. $2co{s}^{-1}\frac{\mu }{2}$
• B. $2si{n}^{-1}\frac{\mu }{2}$
• C. $2co{s}^{-1}\mu$
• D. $2si{n}^{-1}\mu$

Answer 1

Answer: (A)

$2co{s}^{-1}\frac{\mu }{2}$

According to Snell's law,

$\mu =\frac{sini}{sinr}$

Given : $i=2r$

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

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

$co{s}^{-1}\frac{\mu }{2}=r=\frac{i}{2}$

$⟹i=2co{s}^{-1}\frac{\mu }{2}$