The Diffraction Grating

A diffraction grating is a slide with a very large number of equally spaced, parallel slits (lines), often several hundred per millimetre. When monochromatic light passes through it, light from all the slits interferes to produce a few very sharp, bright maxima at particular angles, with darkness in between.The maxima occur where light from adjacent slits has a path difference of a whole number of wavelengths:nλ = d sin θwhere d is the slit spacing (distance between adjacent slits), θ is the angle from the straight-through direction, and n is the order of the maximum (n = 0 for the central, straight-through beam, then 1, 2, 3 ... on each side).If the grating has N lines per metre, then d = 1/N. For 500 lines per mm, N = 5.0 × 10⁵ m^-1, so d = 2.0 × 10^-6 m (2.0 µm). More lines per mm means a smaller d and so larger angles.sin θ cannot be more than 1, so the highest order you can see is the largest whole number below d/λ.Worked example: light of wavelength 600 nm falls on a grating with d = 2.0 µm.
First order: sin θ = 1 × 600 × 10^-9 / 2.0 × 10^-6 = 0.30, so θ = 17.5°.
Maximum order: d/λ = 3.33, so the highest order is n = 3.Because the maxima are so sharp and widely spread, gratings are used to measure wavelengths accurately and to split light into spectra.