Diffraction Grating Calculator
Calculate the diffraction angle for different orders of light through a diffraction grating.
Find wavelength separation and angular dispersion.
Diffraction Angle
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