Diffraction Grating Calculator
Angles of the diffraction maxima for a grating — from lines per mm and wavelength, every visible order, the maximum order, angular dispersion and the spot spacing on a screen.
How it works
d(sin θₘ + sin θᵢ) = m·λ; d = 1 ÷ lines per metre; dispersion dθ/dλ = m ÷ (d·cos θ); resolving power R = m·N
A grating’s many slits reinforce light only in directions where adjacent paths differ by whole wavelengths, so each wavelength leaves at its own angle — the principle of every spectrometer. Finer gratings spread the spectrum more; higher orders spread it further still but overlap. The maximum order is set by sinθ ≤ 1, and resolving power (how close two lines can be and still be separated) is simply the order times the number of lines illuminated.
Worked example
600 lines/mm (d = 1.667 µm) with a 532 nm laser: first order at 18.6°, second at 39.7°, third at 73.3°, and no fourth order; on a screen 1 m away the first-order spots sit 33.7 cm either side.
Frequently asked questions
Why do orders overlap in white light?
Second-order 400 nm lands at the same angle as first-order 800 nm; spectrometers use filters or gratings blazed for one order.
Reflection or transmission grating?
The same equation applies; reflective gratings are blazed to throw most light into one order.
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This calculator is for educational purposes. Double-check important results before acting on them.