The position of the nth minimum in a single slit diffraction pattern on a screen at distance D is given by yn=anDλ.
For the 1st minimum, n=1, so y1=aDλ.
For the 3rd minimum, n=3, so y3=a3Dλ.
The linear separation between the 1st and 3rd minima on the same side of the central maximum is Δy=y3−y1.
Δy=a3Dλ−aDλ=2aDλ.
Answer: 2aDλ