question_answer

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: [JEE Main 10-4-2019 Morning]

A) \[2a+2b\]

B) \[2a+\frac{2b}{3}\]

C) \[\frac{2\sqrt{3}}{a}+2b\]                

D) \[2a+\frac{2b}{\sqrt{3}}\]

Correct Answer: A

Solution :

            From Snell's law \[1.sin60{}^\circ =\mu sin30{}^\circ \]             \[\Rightarrow \mu =\sqrt{3}\] Optical path\[=AO+\mu (OB)\] \[=\frac{a}{\cos {{60}^{o}}}+\sqrt{3}\frac{b}{\cos {{30}^{o}}}\]\[=2a+2b\]