Fraunhofer Diffraction at a Single Slit and the Width of the Central Maximum

When a plane monochromatic wavefront falls normally on a single narrow slit of width $a$, Huygens' principle again applies -- but now every point across the width of the same slit acts as a source of secondary wavelets, and it is the interference of wavelets from different parts of the SAME slit (rather than from two separate slits) that produces the pattern observed on a distant screen (or in the focal plane of a lens), called Fraunhofer diffraction. Dividing the slit into pairs of strips and working out the path difference $a\sin\theta$ between wavelets leaving the two edges of the slit, for a general direction $\theta$ from the slit's normal, gives minima (points of exactly zero intensity) wherever

(the value $n=0$ is excluded, since $\theta=0$ is the position of the strong central maximum, not a minimum). Between consecutive minima lie secondary maxima, but these fall off rapidly in intensity moving away from the centre and are very much fainter than the central maximum -- so the diffraction pattern from a single slit is dominated by one strong, broad central band flanked by a row of much fainter subsidiary bands, quite unlike the row of equally bright fringes produced by the double slit. …