**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.

Thu Sep 13 15:26:14 EDT 2001