Question

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

The correct option is A $2co{s}^{-1}\frac{\mu }{2}$

Angle of incidence = 2(angle of refraction)
i = 2r
apply snell’s law
$\Rightarrow {\mu }_{1}sini={\mu }_{2}sinr\Rightarrow 1\times sin2r={\mu }_{2}sinr{\mu }_1=1\left(assumerair\right)\Rightarrow 1\times 2sinrcosr=\mu sinr\Rightarrow \mu =2cosr\Rightarrow r=co{s}^{-1}\left(\frac{\mu }{2}\right)\Rightarrow r=\frac{i}{2}i=2co{s}^{-1}\frac{\mu }{2}$