In a double slit experiment shown in figure, when light of wavelength $400 \mathrm{~nm}$ is used, dark fringe is observed at $P$. If $\mathrm{D}=0.2 \mathrm{~m}$, the minimum distance between the slits $S_1$ and $S_2$ is $\underline{\hspace{2cm}}$$\mathrm{mm}$.