In the arrangement shown in the figure, slits ${\mathrm{S}}_3$ and ${\mathrm{S}}_4$ are having a variable separation $Z$. Point $\mathrm{O}$ on the screen is at the common perpendicular bisector of ${\mathrm{S}}_1{\mathrm{S}}_2$ and ${\mathrm{S}}_3{\mathrm{S}}_4$. (Assume $D>>d$)



The minimum value of $Z$ for which the intensity at $\mathrm{O}$ is zero is