Diffraction Grating Calculator
Calculate the diffraction angle for different orders of light through a diffraction grating.
Find wavelength separation and angular dispersion.
A diffraction grating splits light into its component wavelengths. The grating equation gives the angles at which constructive interference occurs:
mλ = d sin(θ) d = 1/N (where N = lines per mm)
Where:
- m = Diffraction order (0, ±1, ±2, …)
- λ = Wavelength (m)
- d = Grating spacing = slit-to-slit distance (m)
- θ = Diffraction angle
- N = Number of lines per mm
Angular dispersion: dθ/dλ = m / (d cos(θ)) — how much the angle changes per unit wavelength
Resolving power: R = mN_total — how well the grating separates closely spaced wavelengths
Diffraction gratings vs. prisms:
| Property | Prism | Grating |
|---|---|---|
| Dispersion mechanism | Refraction | Diffraction |
| Visible spectrum | Blue bends most | Red diffracts most (1st order) |
| Multiple orders | No | Yes |
| Common use | Decoration | Spectroscopy |
Applications:
- Spectroscopy: Gratings are the heart of spectrometers in chemistry, astronomy, and environmental monitoring
- Astronomy: Spectrographs on telescopes use gratings to measure stellar composition and redshift
- CDs and DVDs: The closely spaced tracks (d ≈ 1.6 μm) act as a reflection grating, producing rainbow colors
- Laser wavelength selection: Tunable lasers use gratings to select specific wavelengths
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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