**Figure 5:** Intensity as a function of observation angle for
a double-slit experiment

Eqs. 13 & 14 give the intensity as a function of angle of observation. Figure 5 shows the resulting pattern. Three aspects of the result are noteworthy.

- The peak intensity, , is greater than the intensity we
expect from simply summing the intensity of two slits. However, there
are also places where the intensity drops to zero. In fact,
*on average*, the intensity is exactly what we would expect from two slits, . - The maxima in the pattern occur when , which means , where
*M*is some integer. This condition becomes thenwhich means simply that the path difference is an even number of wavelengths so that the two waves arriving at are in phase, adding together

*constructively*. Under these conditions, the amplitude will then be exactly double, and because the intensity goes like the square of the amplitude, we expect 4 times the intensity, as Eq. 13 predicts. - The minima (where there is zero intensity, actually) occur when
, which means is an odd half multiple
of , , where
*M*is any integer. This conditions then becomeswhich simply means that the path difference is off by exactly one-half of a wavelength, so that the two waves arrive

*exactly*out of phase, and thus cancel completely, leaving zero amplitude and zero intensity.

Thu Sep 13 15:26:14 EDT 2001