In the Young's double slit experiment, the distance between the slits varies in time as $d(t) = d_{0} + a_{0}\sin\omega t$; where $d_{0}$, $\omega$ and $a_{0}$ are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as:\\
(1) $\frac{2\lambda D d_{0}}{d_{0}^{2} - a_{0}^{2}}$\\
(2) $\frac{2\lambda D a_{0}}{d_{0}^{2} - a_{0}^{2}}$\\
(3) $\frac{\lambda D}{d_{0}^{2}} a_{0}$\\
(4) $\frac{\lambda D}{d_{0} + a_{0}}$