A diffraction grating – thousands of fine lines – splits light into its colours at precise angles. Spectrometers, CDs and the iridescence of some beetles all use this effect. The grating equation predicts where each wavelength appears.
How to use the Diffraction Grating Calculator
- Wavelength λ
- Grating density (lines/mm)
- Angle of incidence θᵢ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the wavelength, the number of lines per millimetre and the angle of incidence (0° for light hitting the grating straight on). Orders that cannot exist show a dash.
Tips
- Use the sign convention of the formula: real images and distances are positive in most lens equations.
- Wavelength units matter – nm for visible light, µm for infrared.
- Refractive index of air is about 1.000293; vacuum is exactly 1.
- Angles are measured from the normal to the surface.
Common mistakes to avoid
- Measuring angles from the surface instead of the normal.
- Mixing focal length in mm and object distance in m.
- Forgetting that a diverging lens has a negative focal length.
Inputs explained
| Field | What to enter |
|---|---|
| Wavelength λ | Units: nm, µm, mm, m, pm, Å |
| Grating density (lines/mm) | A number |
| Angle of incidence θᵢ | Units: °, rad, arcmin, arcsec, mrad |
Example values
How the main result changes when Wavelength λ changes and everything else stays at the example values above:
| Wavelength λ (nm) | Order 1 angle (°) |
|---|---|
| 266 | 9.1837 |
| 399 | 13.8511 |
| 532 | 18.6146 |
| 665 | 23.5157 |
| 798 | 28.6071 |
| 1,064 | 39.6726 |
Formula
d·(sin θ_m + sin θ_i) = m·λ, d = 1/NWorked example
Inputs — Wavelength λ: 532 nm; Grating density (lines/mm): 600; Angle of incidence θᵢ: 0 °.
Results — Grating spacing d = 1.66667 µm; Order 1 angle = 18.6146 °; Order 2 angle = 39.6726 °; Order 3 angle = 73.2557 °.
Key terms
- Grating equation
- d(sin θ_m + sin θ_i) = mλ.
Frequently asked questions
Why do higher orders disappear?
When mλ/d exceeds 1, no real angle exists.
How does line density affect the spread?
More lines per mm spread the colours over larger angles.
Why do CDs show rainbows?
Their tracks act as a reflection grating with about 625 lines/mm.
What is the zeroth order?
The undeviated beam, containing all wavelengths.
What formula does the Diffraction Grating Calculator use?
d·(sin θ_m + sin θ_i) = m·λ, d = 1/N.