If we consider the Fraunhofer conditions,we see that the wave arrives at the single slit as a plane wave. Divided into segments, each of which can be regarded as a point source, the amplitudes of the segments will have a constant phase displacement from each other, and will form segments of a circular arc when added as vectors. The resulting relative intensity will depend upon the total phase displacement  according to the relationship.

I = I₀ sin²[δ/2] /[δ/2]²

The total phase angle can be related to the deviation angle θ.

δ = 2πa sinθ / λ

The intensity as a function of angle θ -

I = I₀ sin²[πa sinθ/λ ] /[πa sinθ/λ]²