What is the Maxima Condition in Holography?

[Debam1224]

Homework Statement

I came across one problem from Holography which is a subtopic in my DSE Paper(Laser and Fibre Optics) in Bsc. The problem is as follows:

Suppose the reference wave in hologram is given by. Eᵣ = E₀ e^{-i(ωt- k𝓏 - kₙ sin θ)}and the spherical wave emanating from point source is given as
Eₛₚₕ= E₁ e^{-i(ωt- k𝓏 - (kₓ²/2z₀))}
Then find out the resultant intensity in the plate. Show that the condition for maxima in the hologram is given by ∆x = 4λ (Choose θ = 15°)

I've attached what I've done. The intensity part is correct. But I'm confused about the maxima part because the question has specifically asked for
4λ whereas I got nλ. So, should I just put n=4 or is it wrong? I would really appreciate your views and answers. P.S.: Entirely typed in latex, not copied from any book.

Relevant Equations

Resultant Electric Field,
Eᵣ= E₁ + E₂
Intensity, I = |Eᵣ|²