Single-Slit Diffraction Pattern
When m l = a sin q the slit can be divided into zones whose light interferes destructively with light from other zones (unless m = 0) .
Angular width of central maximum is
Notes:
When light from such a slit is focussed on a distant screen, an interference pattern like the one plotted at right appears. The angular width of the whole pattern increases as the slit width decreases.
The intensity on the screen at each angle is the result of the superposition of all the light from the slit. When the path length difference between light from the two sides of the slit is zero, then all light will be in phase, and this corresponds to the center of the interference pattern. When this path length difference from the two sides is a full wavelength, though, there will always be some part of the light from the top half of the slit that will interfere destructively with light from a corresponding place in the bottom half of the slit, and there will be a minimum in the intensity pattern at that angle.
So, whenever the path length difference between the light from opposite sides of the slit is an integer number of wavelengths, there will be a minimum in the interference pattern -- these are labeled by the corresponding integers in the screen at right. In between the minima are places where there is at least some part of the light from the slit that isn’t cancelled by destructive interference with the light from the other parts.