We shine red laser light through a single slit, and we see a diffraction pattern on a screen some distance from the slit. If we increase the width of the slit, what happens to the central maximum in the diffraction pattern?
It gets narrower. This is true for single slits, double slits, and diffraction gratings. The smaller the object the wave interacts with, the more spread there is in the interference pattern. Increasing the size of the opening reduces the spread in the pattern.
Let's return to our two-source situation, two sources separated by a distance that we'll now call a. Now we remove the barrier between the sources, which changes the interference pattern. We still get a bright spot at the center of the screen due to constructive interference, but we find that at all the other places where we had constructive interference taking place for the two sources, we now have destructive interference.
Condition for destructive interference for a single slit: a sin(q) = ml, where m is any integer other than zero.
Our situation above is essentially what happens when light shines on a narrow opening, or when sound or any other wave encounters an opening comparable in size to the wavelength. Bringing in Huygen's Principle, every point in the opening can be treated as a source of wavelets, waves that spread out spherically. This is why we can treat the opening as containing a large number of sources. We call this a diffraction pattern, but it still comes from interference of waves.
Why do we have destructive interference occuring for the single slit at the same angles where we had constructive interference occuring for two sources? Let's go to a place on our screen that was one wavelength (l) further from one source than the other. If we now have N sources spread out across the space between the two sources, we have have half the sources giving path length differences between 0 and l/2, and the other half giving path length differences between l/2 and l. By destructive interference, the light from one half of the slit completely cancels the light from the other half.