Physics Question from JEE Main 2023 · 29 January, Shift 1

In a Young's double slit experiment, two slits $A_1$ and $A_2$, separated by $a$, are illuminated with light of wavelength $800 \, \text{nm}$. The point $P$ on the screen is placed so that the line joining $A_1P$ is perpendicular to $A_1A_2$. The distance of the screen from the slits is $D = 5 \, \text{cm}$. If the first minimum is detected at $P$, the value of the slit separation $a$ will be: