In Young's double-slit experiment, the fringe width is denoted by β and is given as \(\beta=\frac{\lambda D}d\) where λ is the wavelength of light used, D is the distance between the slits and screen and d is the width of the slit. If the separation between the slits is doubled and the distance between the slits and the screen is halved, then the fringe width is given as
\(\beta'=\frac{\lambda D/2}{2d}=\frac{\lambda D}{4d}=\frac14\beta\)
Thus, the fringe width is altered by 1/4 times if the separation between the slits is doubled and the distance between the slits and the screen is halved.