Fraunhofer diffraction describes the diffraction pattern of electro-magnetic radiation observed in the far field from a slit or series of slits (i.e. grating).
In the figure below, the path length difference, at point 'P', between the two rays passing through the slit is (d/2)*sin(θ). When this path difference is equal to half a wavelength then the two rays are 180o out of phase. This occurs for every pair of rays from the top and bottom halves of the slit.
Thus all rays passing through the slit to reach point 'P' destructively interfere to give a dark fringe. This example considers the slit in 2 parts, by considering it in 4, 6, 8, etc it can be shown that a dark fringe will occur whenever:
- where n=1, 2, 3,...