Question

The central fringe of the interference pattern produced by the light of wavelength 6000 Å is found to shift to the position of the fourth bright fringe after a glass plate of refractive index 1.5 is introduced in the path of one of the beams. The thickness of the glass plate would be ______.

Options

• 4.8 μm

• 8.23 μm

• 14.98 μm

• 3.78 μm

Answer 1

The central fringe of the interference pattern produced by the light of wavelength 6000 Å is found to shift to the position of the fourth bright fringe after a glass plate of refractive index 1.5 is introduced in the path of one of the beams. The thickness of the glass plate would be 4.8 μm.

Explanation:

Shift in fringe pattern = `(4lambdaD)/d`

Also, shift due to glass plate = `((mu - 1)tD)/d`

`(4lambdaD)/d = ((mu - 1)tD)/d`

`t = (4lambda)/(mu - 1) = (4 xx 6000 xx 10^-10)/(1.5 - 1)`m

= `8 xx 6 xx 10^-7` m

= 4.8 μm