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

The fringe width in Young's double-slit experiment is determined by the relation $\beta = \frac{\lambda D}{d}$, where $\lambda$ is the wavelength, $D$ is the slit-to-screen distance, and $d$ is the slit separation.

When the slit separation is halved ($d' = d/2$) and the screen distance doubled ($D' = 2D$), the new fringe width becomes:

$\beta' = \frac{\lambda D'}{d'} = \frac{\lambda (2D)}{d/2} = \frac{2\lambda D}{d/2} = 4\frac{\lambda D}{d} = 4\beta$

The fringe width thus increases by a factor of four.

Answer: D