Diffraction Gratings

A CD works like a grating by accident. Its surface has thousands of tiny closely spaced ridges, and when white light hits it, each wavelength bends at a slightly different angle, fanning the light into a rainbow. A true diffraction grating does this on purpose: it is a plate etched with thousands of parallel slits, each spaced a distance d apart, with d = 1/n where n is the number of lines per unit length. Light passing through all those slits spreads out and overlaps, and at certain angles the waves from every single slit arrive in phase and add up. That condition is d sin(theta) = m lambda, where m is the order number (0, 1, 2...).

The sharpening is the part that surprises people. With only two slits, the bright fringes are wide and fuzzy, because nearby angles still get mostly constructive interference. With thousands of slits, that forgiveness disappears. Stray even slightly from the exact angle that satisfies d sin(theta) = m lambda, and now thousands of waves are out of step by thousands of slightly different amounts, so they cancel almost completely. The peak positions do not move, but they become razor-thin lines instead of smears. More slits means more waves available to destroy the in-between angles, not more brightness smeared everywhere.

This is what lets a grating separate colors cleanly enough to do real science. Since the grating equation depends on lambda, different wavelengths produce maxima at different angles, so a mix of light spreads into a spectrum of sharp lines rather than a single blended smear. Pointing a grating at starlight spreads it into these narrow lines, and the exact angles reveal which elements absorbed or emitted that light, letting astronomers read a star's composition from across the galaxy.