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.

- Case of two slits: If we substitute
*N*=2 into Eq. 17 and use the double-angle sine formula, we have for the numerator , so that the term in the denominator cancels, leaving , precisely the two-slit result, Eq. 13. - Principle maxima: we find extremely large maxima whenever the
denominator in Eq. 13 goes to zero. This occurs
whenever , equivalently, ,
where
*M*is some integer. This meansso 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 haveThe 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*. - Minima: Minima occur in the pattern whenever the numerator is
zero (and the denominator is not). Zeros in the numerator occur
whenever , equivalently, , where
*M*is any integer, so thatNote 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. - Lesser maxima: Of course, there are other maxima which must
appear approximately halfway between neighboring minima, the
of these happens
where

Thu Sep 13 15:26:14 EDT 2001