Question

In a Young's double-slit experiment in air, the fringe width is found to be 0.44 mm. If the entire setup is immersed in water `(n = 4/3)` the fringe width will be ______.

Options

• 0.88 mm

• 0.59 mm

• 0.33 mm

• 0.44 mm

Answer 1

In a Young's double-slit experiment in air, the fringe width is found to be 0.44 mm. If the entire setup is immersed in water `(n = 4/3)` the fringe width will be 0.33 mm.

Explanation:

The formula for the fringe width is:

`beta = (lambdaD)/d`

∴ β ∝ λ

We also know that the wavelength is inversely proportional to the refractive index of the medium.

So, `lambda"'" = lambda/mu`

So, `lambda"'" = (3lambda)/4`

So, the ratio can be obtained as:

`(beta"'")/beta = (lambda"'")/lambda`

`beta"'" = 0.44/(4/3)`

⇒ β' = 0.33 mm