Physics Question from JEE Main 2024 · 29 January, Shift 1

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

The figure shows: the slits $S_1$ and $S_2$ lie one above the other in a vertical barrier, a distance $d$ apart, with $S_1$ above $S_2$. A point source lies on a horizontal axis a distance $D$ to the left of the barrier, and the point $P$ lies on the same horizontal axis a distance $D$ to the right of the barrier. That axis passes through the lower slit $S_2$, so light reaches $P$ either straight along Source $\to S_2 \to P$ or along the slanted path Source $\to S_1 \to P$.