Again, several features of our result, Eq. 17, are noteworthy. Figure 7 shows this result for a case with N=6 slits.
Figure 7: Intensity as a function of observation angle for an N-slit experiment for the case N=6. In this case, principle maxima appear in the location of every sixth minima, so that there are five minima between principle maxima, and thus four lesser maxima between principle maxima.
so that the path difference between all of the slits is always an exact number of wavelengths, leading to complete constructive interference. To see how large the maxima can be, we take the limit . From the small-angle formula, we then have
The physical reason for the factor of is just that the amplitudes of all N waves add, so the amplitude is N times as large, but the intensity, of course, goes like the amplitude squared.
Note that the spacing between minima is thus exactly 1/N times the spacing between principle maxima. Often, you can use this to determine the number of slits from the appearance of the diffraction pattern.