In Young's double-slit experiment, the fringe width ($\beta$) is given by the formula: $\beta = \frac{\lambda D}{d}$ where: $\lambda$ = wavelength of the light used $D$ = distance of the screen from the coherent sources $d$ = separation between the coherent sources

According to the given conditions, the new separation is $d' = \frac{d}{2}$ and the new distance of the screen is $D' = 2D$. The new fringe width $\beta'$ will be: $\beta' = \frac{\lambda D'}{d'} = \frac{\lambda (2D)}{\frac{d}{2}} = 4 \left(\frac{\lambda D}{d}\right) = 4\beta$ Therefore, the fringe width becomes four times its original value.