When a plane wave front is incident on the slit, each point on the wave front acts as the source of spherical secondary wave fronts. Lets divide the wave front incident on the slit in a large number of elements, each of width ds, (infinitesimaly small).

The part of each secondary wave, originating from these small elements and travelling normal to the plane of slit will be focussed at P₀ while those travelling at an angle will reach P (Fig.2b). Considering first the wavelet emitted by the element ds situated at the center of slit (let us call it origin). Its amplitude will be directly proportional to length ds and inversely proportional to the distance x (it will produce spherical wave front). At P, it will produce an infinitesimal amplitude (electric field) which is expressed as

                                  

where 'a' is the amplitude of incident wave, and are its frequency and wave vector respectively.

The wave fronts reaching P from other elements ds will vary in phase due to extra path travelled by them. The displacements produced by another element ds at a distance s from the center(origin) will be given by