Question

A ray of light AO in a vacuum is incident on a glass slab at an angle of 60° and refracted at an angle of 30° along OB as shown in the figure. The optical path length of the light ray from A to B is ______.

Options

• 2a + 2b

• `(2sqrt3)/a + 2b`

• `2a + (2b)/3`

• `2a+(2b)/sqrt3`

Answer 1

The optical path length of the light ray from A to B is 2a + 2b.

Explanation:

We have, AO = `a/(cos 60°)`, BO = `b/(cos 30°)`, n = `(sin 60°)/(sin 30°)`

Path = AO + nBO

= `a/(cos 60°) + (sin 60°)/(sin 30°) xx b/(cos 30°)`

= `a/(1/2) + (sqrt3/2)/(1/2) xx b/(sqrt3/2)`

= `2a + sqrt3 xx (2b)/sqrt3`

= 2a + 2b