In Young's double-slit experiment, the separation between the slits is halved and the distance between the slits and the screen in doubled. The fringe width is

Answer

4

Explanation

If d is separation between the slits and D is separation between plane of the slits and screen, then fringe width of the pattern can be written as follows:
`((sqrt(I_1) + sqrt(I_2)))/((sqrt(I_1) - sqrt(I_2))) = 3`
`omega_1 = (lambda D)/d`
In second case, fringe width can be written as follows:
`omega_2 = (lambda (2D))/((d//2)) = 4 (lambda D)/(d) = 4 omega_1`
`implies (omega_2)/(omega_1) = 4`