Q 12-09-195JEE MainJEE Main 2019 (10 Apr, Shift 1)Medium
A ray of light $AO$ in vacuum is incident on a glass slab at angle $60^\circ$ and refracted at angle $30^\circ$ along $OB$ (both angles measured from the normal at $O$). The point $A$ is at a height $a$ above the surface of the slab and $B$ is at a depth $b$ below it. The optical path length of the light ray from $A$ to $B$ is:
Answer: (B) $2a + 2b$
Refractive index $\mu = \dfrac{\sin60^\circ}{\sin30^\circ} = \sqrt3$.
$AO = \dfrac{a}{\cos60^\circ} = 2a$ and $OB = \dfrac{b}{\cos30^\circ} = \dfrac{2b}{\sqrt3}$.
$$\text{Optical path} = AO + \mu\,OB = 2a + \sqrt3\cdot\frac{2b}{\sqrt3} = 2a + 2b$$
Solution by Sreeraj P, M.Sc Physics