SKEDSOFT
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
Where 
is the path difference. The net amplitude at P will be sum of effect due to all the elements ds and can be obtained by integrating dEs from s=-d/2 to d/2 where d is the width of the slit. In doing so, we can first sum the amplitude produced by the symmetrically placed elements ds and then integrate it from s=0 to d/2. The contribution due to a pair of symmetrically placed element ds is
Using the trigonomerical identity 
We have
Net effect at P is now
We can treat 
constant,
where 
The resultant wave reaching at P , is therefore, a simple harmonic one. The amplitude of this varies as position P is varied (
varies). The resultant amplitude is given by
Where 
The intensity of light at any point on screen is, thus given by
An intensity pattern as shown in fig. 2(c). is observed on screen
