Two ideal slits S1 and S2 are at a distance d apart, and illuminated by light of wavelength λ passing through an ideal source slit S placed on the line through S2 as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is
(3) Path difference between the waves reaching at P,
where Δ1 = Initial path difference
Δ2 = Path difference between the waves after emerging from slits.
(From Binomial expansion)
For obtaining dark at O, Δ must be equals to i.e.
For minimum distance n = 1 so