A long slit of infinitesimal width which is illuminated by light diffracts the light into a series of circular waves and a wave front emerges from the slit in a cylindrical wave of uniform intensity. A slit which is wider than a wavelength produces interference effects in the space downstream of the slit. The slit is assumed to behave as though it has a large number of point sources spaced evenly across the width of the slit. The analysis also simplifies if we consider light of a single wavelength.
Light incident at a given point in the space downstream of the slit is made up of contributions from each of these point sources. If the relative phases of these contributions vary by 2π or more we may expect to find minima and maxima in the diffracted light. These phase differences are caused by differences in the path lengths over which contributing rays reach the point from the slit.
We can calculate the angle at which the first minimum is obtained in the diffracted light. The light from a source is located at the top edge of the slit. This interferes destructively with a source located at the middle of the slit when the path difference between them is equal to λ/2. Furthermore, the source just below the top of the slit will interfere destructively with the source located just below the middle of the slit at the same angle. Therefore we can reason that along the entire height of the slit the condition for destructive interference for the entire slit is the same as the condition for destructive interference between two narrow slits a distance apparent that is half the width of the slit.