How to calculate intensity of dark fringes in interference pattern?

Question

What formula is to be used for calculating the intensity of dark fringes in interference pattern of double slit experiment?

Answer 1

I(θ) = I(max) cos ² β ((sin α )/ α ) ²

β = (πd/λ)sinθ

α = (πa/λ)sinθ

d = slit separation

a = slit size

Yeah, it's ugly.  The β term tells you the interference part, the α term tells you the dispersion part.  If you're ignoring dispersion, you can set α=1.