Physics · Wave optics
Diffraction grating calculator.
Enter the grating lines per millimetre and the wavelength. Get the angle of each bright order and the highest order that can appear.
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Diffraction grating equation
Bright lines from a grating appear where d sinθ = mλ, for m = 0, ±1, ±2 and so on. The spacing d is the reciprocal of the line density, so 600 lines per millimetre gives d = 1/600 mm = 1.667 µm. Because sinθ cannot exceed 1, the highest order is the whole number part of d/λ.
Worked example. 633 nm light on a 600 lines/mm grating: d = 1667 nm. First order sinθ = 633/1667 = 0.3798, so θ = 22.32°. Second order sinθ = 0.7596, θ = 49.43°. A third order would need sinθ = 1.139, which is impossible, so the highest order is 2.
The simple equation assumes light arrives perpendicular to the grating (normal incidence).
Frequently asked questions
What is the diffraction grating equation?
d sin(theta) = m lambda, where d is the spacing between lines, theta is the angle from straight ahead, m is the order (0, 1, 2, ...) and lambda is the wavelength.
How do I get d from lines per millimetre?
Divide 1 mm by the number of lines. 600 lines/mm gives d = 1/600 mm = 1.667 micrometres.
How many orders can I see?
The largest whole number m with m x lambda less than d. For 633 nm on a 600 lines/mm grating that is 2.
Why does a finer grating spread light more?
A smaller d gives a larger sin(theta) for the same wavelength and order, so each order lands at a wider angle.
Does this work at an angle of incidence?
No. This tool assumes normal incidence, where the beam hits the grating at 90 degrees to its surface.
Sources
Checked
OpenStax gives the grating equation and the worked step d = 1 cm / 10,000 lines. The highest-order rule (sin theta at most 1) is the direct consequence of the same equation. Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Classroom wave-optics model at normal incidence. Not for spectrometer calibration.