Question 110 of 295

A ray of light $AO$ in vacuum is incident on a glass slab at angle $60^{\circ}$ and refracted at angle $30^{\circ}$ along $OB$ as shown in the figure. The optical path length of light ray from $A$ to $B$ is:

A$\dfrac{2\sqrt{3}}{a}+2b$B$2a+2b$C$2a+\dfrac{2b}{\sqrt{3}}$D$2a+\dfrac{2b}{3}$

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Answer: (B) $2a+2b$

Optical path length $=OA+\mu OB$
$=\dfrac{a}{cos {60}^{o}}+\dfrac{\mu b}{cos {30}^{o}}$
$=2a+\mu \left(\dfrac{2b}{\sqrt{3}}\right)$
From Snell’s law,
$sin {60}^{o}=\mu sin {30}^{o}$
$\mu =\sqrt{3}$
Optical path length $=2a+\sqrt{3}\left(\dfrac{2b}{\sqrt{3}}\right)$
$=2\left(a+b\right)$