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Question

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


A
23a+2b
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B

2a+2b3

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C
2a + 2b
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D
2a+2b3
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Solution

The correct option is C 2a + 2b

From the figure,


cos60=aAO

AO=acos60=2a...(i)

andcos30=bBO

orBO=bcos30=2b3....(ii)
Optical path length of light ray
= AO + μ (BO) ... (iii)

Here, μ can be determined using Snell's law, i.e.

μ=sin60sin30=3/21/2=3....(iv)
Substituting the values from Eqs. (i), (ii) and (iv)

Optical path=2a+(3×23b)
= 2a + 2b


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