Question

A ray of light passes from glass, having a refractive index of $1.6$ to air. The angle of incidence for which the angle of refraction is twice the angle of incidence is

• A. $si{n}^{-1}\left(\frac{4}{5}\right)$
• B. $si{n}^{-1}\left(\frac{3}{5}\right)$
• C. $si{n}^{-1}\left(\frac{5}{8}\right)$
• D. $si{n}^{-1}\left(\frac{2}{5}\right)$

Answer 1

The correct option is B $si{n}^{-1}\left(\frac{3}{5}\right)$

According to Snell's law, when a light ray incidents on a surface separating two transparent media, the product $\mu \sin \theta$ of a light ray is constant.

where, $\mu$ is the refractive index of the medium and \theta is the angle of incidence/refraction.

Given, angle of refraction is double the angle of incidence
$\to r=2i$

light ray passes from a glass of refractive index $\mu =1.6$ to air.
$⟹1.6\sin \left(i\right)=\sin \left(2i\right)=2\sin \left(i\right)\cos \left(i\right)$

$⟹\cos \left(i\right)=0.8$

$⟹i={\cos }^{-1}\left(0.8\right)={\sin }^{-1}\left(0.6\right)$

Therefore, angle of incidence is ${\sin }^{-1}\left(\frac{3}{5}\right)$ .