In Young’s double slit experiment, if the separation between...

$\beta = \dfrac{\lambdaD}{d}$

${\beta}^{'} = \dfrac{\lambda{D}^{'}}{{d}^{'}}$

${D}^{'} = 2D, {d}^{'} = \dfrac{d}{2}$

${\beta}^{'} = \dfrac{\lambda \times 2D}{\dfrac{d}{2}} = \dfrac{4\lambdaD}{d}$

${\beta}^{'} = 4\beta$

Fringe width becomes $4$ times.