Armed now with the solution from a single slit (Eq. 4) and
the relation between amplitude and intensity (Eq. 3), we
are ready to compute the intensity pattern from a single slit. For
simplicity we take the observation screen to be curved like the inside
of a large dome of constant radius *R* (as in
Figure 1). As long as the radius of curvature of the
dome *R* is much larger than the actual size of the screen, this will
have no meaningful effect on our results.

For the intensity, we have now

where we have substituted Eq. 5 for and used the mathematical facts that for any product of complex numbers and that .

The main lesson we learn from Eq. 6 is that for a single
slit, the pattern on an observation screen at distance *R* from the
slit is constant and uniform, independent of the angle of observation
, as Figure 2 illustrates.

**Figure 2:** Intensity as a function of observation angle for
a single-slit is constant

Thu Sep 13 15:26:14 EDT 2001