The Fraunhofer diffraction pattern is the Fourier transform of the aperture function. It is obtained by evaluating the Fraunhofer diffraction integral.
Consider a screen in the

plane. The rectangular aperture is in a plane parallel to it (the

plane). The perpendicular distance between the screen and aperture is given by
. The dimensions of the aperture are
.
Consider a monochromatic plane wave normally incident on the aperture. The field distribution at a point
on the screen is given by the Fraunhofer diffraction integral:
,
,
,
and
is the amplitude of the incident plane wave in the plane of the aperture. The value of the integral turns out to be
,
.
The intensity of a light wave is proportional to the square of the amplitude, hence the intensity distribution on the screen is given by
,
where
is a constant. In this Demonstration, the intensity distribution has been plotted schematically (for simplicity,
has been taken to be unity).
Snapshot 1: pattern obtained from a square aperture (0.1cm x 0.1cm) and violet light at a distance of 1000cm
Snapshot 2: pattern obtained from a square aperture (0.1cm x 0.1cm) and green light at a distance of 1000cm
Snapshot 3: pattern obtained from a square aperture (0.1cm x 0.1cm) and orange light at a distance of 1000cm
As the wavelength of the light increases, the width (the spacing between bright or dark spots) of the pattern also increases. This is seen clearly in the first three Snapshots.
Snapshots 4 and 5: the single slit limit is obtained when one of the dimensions is much larger in comparison to the other
Snapshot 6: if the dimension of the aperture decreases (0.05cm x 0.05cm in this case), then the width of the pattern increases, and vice versa; compare with Snapshot 1
[1] A. Ghatak,
Optics, 5th ed., India: Tata McGrawHill Education Pvt. Ltd, 2012.