Diffraction gratings

A double slit produces bright fringes wherever light from the two slits arrives in phase, at angles satisfying d sin θ = mλ, but those fringes are broad and only moderately bright, because there are only two waves to add up. A diffraction grating uses the exact same physics — the same governing equation, with d now the spacing between adjacent slits — but with thousands of slits instead of two. The bright fringes still occur at the same angles the two-slit formula predicts, since the condition for constructive interference between any pair of adjacent slits is unchanged. What changes dramatically is the sharpness: with thousands of slits all interfering constructively at once, the bright fringes become intensely bright and extremely narrow, while the destructive interference between all those slits crushes everything in between to near-total darkness. More slits does not just add brightness; it is what sharpens a broad double-slit fringe into a sharp, precisely located line.

That sharpness is precisely why gratings, not double slits, are the practical tool for measuring wavelength. Because the bright-fringe angle depends on wavelength, a grating illuminated with light of several different wavelengths sends each one to a slightly different, sharply defined angle rather than producing overlapping smears — separating white light into a clean, well resolved spectrum, and letting the wavelengths present in an unknown light source be read off precisely from where its bright lines land. This is the working principle behind spectroscopy: a grating spectrometer measures exactly the angles at which a source's light forms bright fringes and converts those angles back into wavelengths using the grating equation, turning a light source's colour composition into a directly measurable quantity.