In two separate set-ups of the Young's double slit experiment, fringes of equal width are observed when lights of wavelength in the ratio of `1:2` are used. If the ratio of the slit separation in the two cases is `2:1`, the ratio of the distance between the plane of the slits and the screen in the two set-ups are

Options

A. `4:1`
B. `1:1`
C. `1:4`
D. `2:1`

Answer

A

Explanation

As `beta=(D lambda)/(d)`
`rArr (beta_(1))/(beta_(2))=((D_(1))/(D_(2)))(lambda_(1))/(lambda_(2))) ((d_(2))/(d_(1)))`
`rArr 1=((D_(1))/(D_(2))) ((1)/(2)) ((1)/(2)) rArr (D_(1))/(D_(2))=(4)/(1)`