Grades 9–12 · Materials & Matter
How can thousands of tiny gaps separate the colors in light?
A diffraction grating contains many regularly spaced lines or gaps. Light spreading from neighboring gaps overlaps. In most directions, waves partly cancel; in certain directions, they reinforce to form narrow bright peaks.
In the diagramRepeated gaps reinforce particular directionsNormal incidence • spacing d = 1,000 nmIncoming lightNormalBright directionm = 1 • λ = 500 nm • d sin θ = mλsin θ = 0.5 → θ = 30°Ideal transmission grating; brightness is not solved.
For light arriving perpendicular to an ideal transmission grating, the extra path between adjacent gaps is d sin θ. Here d is gap spacing and θ is the outgoing angle measured from the straight-ahead normal. Reinforcement occurs when that difference equals a whole number m of wavelengths: d sin θ = mλ.
With spacing 1,000 nanometers, first-order green light of wavelength 500 nanometers has sin θ = 0.5, so θ = 30°. First-order red light at 700 nanometers appears farther from the center, near 44.4°. Different wavelengths separate into different directions instead of becoming new colors.
The central order, m = 0, stays straight ahead for every wavelength. Some higher orders cannot exist: second-order 700-nanometer light would require sin θ = 1.4. Opposite orders appear symmetrically on the other side. The illustration calculates peak directions, while leaving brightness and peak width to a fuller wave model.
About this explanation
Starting knowledge: Understand wavelength, wave superposition and the sine function.
Sources
- OpenStax, Rice University — University Physics Volume 3: Diffraction Gratings