Figure 10: N finite-slit interference experiment
Finally, we consider the pattern created by N identical slits at spacing d, but each with finite width a (Figure 10). As you might expect, this case becomes a simple combination of the result for the finite slit with the result for N slits.
The reasoning for this is as follows. If you view any one of the N finite slits, say slit n, by itself from different angles, it will appear to change its intensity according to the single-slit formula , where . If we now open all N slits at once and view the result at angle , what we see is the result of the interference of N slits, each with this same intensity. Thus, if we set from Eq. 17 equal to , we will find the result for N finite slits. This result is just the product of our two previous results:
where , , and is the central maximum intensity from any one of the slits alone.