We have
The first minimum in the diffraction term occurs at α = π or, sinθ = λ/a. The second minimum occurs at α = 2π or, sinθ = 2λ/a.
The interference maxima occur at sinθ
The interference maxima lying between the sinθ = λ/a and sinθ = 2λ/a are
So, four fringes lie between the first and the second minima of the envelope.