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
