Diffraction Grating

If instead of two slits you have three, four, or even more evenly-spaced slits, then you get the same basic interference pattern, but the bright fringes are narrower and brighter, and the dark spaces are larger. Otherwise the formula is the same:

where $d$ is now the distance between each slit and its neighboring slit. This is the basic idea behind a diffraction grating, which has a large number of slits cut into an otherwise opaque film. Instead of giving the distance $d$ between slits, diffraction gratings are often printed with their "number of lines per meter" (or millimeter). Since we can think of the distance $d$ between slits as "the number of meters per line", $d$ is the reciprocal of this value. For example, $$1000\u{lines\over mm} \implies d=\frac1{1000}\u{mm\over line} = 10^{-3}\u{mm}=1\u{\mu m}$$

If light of many different wavelengths (such as light from the sun) shines through a diffraction grating, each wavelength will form its own pattern, with the larger wavelengths creating fringes farther away from the center (since $y\sim \lambda$). Because the diffraction grating makes the bright fringes very narrow, we are able to see all the different colors at once as a spectrum. Diffraction gratings are therefore used to analyze light and identify the wavelengths present, which can tell us much about the source of the light and any materials the light passed through, a process called spectroscopy. (Prisms also break light into its component colors, but prisms are harder to manufacture without defects in the glass.)

Reflection gratings are like diffraction gratings which are mounted on a mirror: light hits the surface of the grating, and then splits as it reflects. A CD or a DVD are a good demonstration of this effect, since the grooves on its surface are small and close together.