Diffraction
Light can interfere with itself even when it shines through a single narrow slit (called an aperture. The light from one side of the apertur will have farther to travel than the light from the other side, resulting in interference.
The pattern that results is a little different from the two-slit interference pattern: the central bright fringe, called the central maximum, is twice as wide as the other bright fringes. The formula we use to locate these fringes looks very similar to that for interference:
but with one major difference: this formula gives us the position of the dark fringes, not the bright fringes. To avoid confusion we number the dark fringes with the letter $p$, so there are dark fringes at $\lambda L/a$, $2\lambda L/a$, $3\lambda L/a$, and so forth. (Not at $p=0$, though.) We also use the width of the slit $a$ instead of $d$.
In real-life two-slit interference experiments, we often see both interference and diffraction effects, because the individual slits have width themselves. Because the slits are necessarily narrower than the distance between them, the diffraction pattern is more spread out, as is shown here. This can result in one of the two-slit bright fringes disappearing, as in this example where $n$ jumps from 3 to 5.
Circular Aperture
If the aperture is circular, rather than a single thin slit, then the resulting diffraction pattern is a series of concentric circles. The formula for the distance from the center to the $p$th dark fringe is
where $a$ is the diameter of the circular aperture. (The 1.22 comes from advanced math--specifically, Bessel functions, in case you were curious.)