JEE PYQ: Ray Optics Question 40
Question 40 - 2019 (10 Apr Shift 1)
A ray of light AO in vacuum is incident on a glass slab at angle 60$°$ and refracted at angle 30$°$ along OB as shown in the figure. The optical path length of light ray from A to B is:
(1) $\frac{2\sqrt{3}}{a} + 2b$
(2) $2a + \frac{2b}{\sqrt{3}}$
(3) $2a + \frac{2b}{\sqrt{3}}$
(4) $2a + 2b$
Show Answer
Answer: (4)
Solution
From the given figure As $\sin 60° = \mu \sin 30°$ $\Rightarrow \mu = \frac{\sin 60°}{\sin 30°} = \sqrt{3}$ $\frac{a}{AO} = \cos 60° \Rightarrow AO = 2a$ $\frac{b}{BO} = \cos 30° \Rightarrow BO = \frac{2b}{\sqrt{3}}$ Optical path length $= AO + \mu BO$ $= 2a + (\sqrt{3})\frac{2b}{\sqrt{3}} = 2a + 2b$
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