In a double slit experiment, the two slits are `1mm` apart and the screen is placed `1m` away. A monochromatic light of wavelength `500nm` is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single-slit pattern?

Options

A. `0.1 mm`
B. `0.5 mm`
C. `0.02 mm`
D. `0.2 mm`

Answer

D

Explanation

Here, `d = 1 mm, D = 1m, lambda = 500 nm`
In double slit experiment, angular width `= (beta)/(D)`
as `beta = (lambdaD)/(d) :. (beta)/(D) = (lambda D)/((d)/(D)) = (lambda)/(D)`
In single slit experiment, angular width `= (2 lambda)/(d')`
According to Question,
`(10 lambda)/(d) = (2 lambda)/(d') or d' = 0.2 d` `[ because d = 1 mm]`
`d' = 0.2 mm`