Library / Foundations: Physics / FPH-32
Foundations: Physics
Diffraction grating
Angle of a bright maximum from a diffraction grating.
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- FPH-32
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- v1
- Field
- Foundations: Physics
- Result
- θ [°]
For normal incidence, d is the line spacing and m the integer order. Convert lines per mm to lines per metre before taking the reciprocal to obtain d in m.
A grating with many fine lines sends each colour of light off at its own angle, which lets you measure wavelength accurately.
Calculator
- Line spacing d2 µm
- sin θ0.3
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The maximum order seen is limited because sin θ cannot exceed 1.
- Finer gratings give larger angles and better resolution of close wavelengths.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (°) | Local step | Change in result |
|---|---|---|---|---|---|---|
| m Order | 1 to 3 | 17.46 | 64.16 | 46.7 | +10% | +1.81 ° |
| N Lines per mm | 100 to 1,200 | 3.44 | 46.05 | 42.61 | +10% | +1.81 ° |
| λ Wavelength | 400 to 700 nm | 11.54 | 20.49 | 8.95 | +10% | +1.81 ° |
Sweep of Wavelength
| Wavelength (nm) | Angle of maximum (°) |
|---|---|
| 400 | 11.54 |
| 437.5 | 12.64 |
| 475 | 13.74 |
| 512.5 | 14.85 |
| 550 | 15.96 |
| 587.5 | 17.08 |
| 625 | 18.21 |
| 662.5 | 19.34 |
| 700 | 20.49 |
Sweep one variable
Variables and how each one contributes
Angle of maximum
What the equation gives you. Everything else feeds it.
Lines per mm
Number of lines per millimetre. More lines spread the colours further apart.
Wavelength
Wavelength of the light. Longer wavelengths are bent further.
Order
Order of the maximum. Higher orders appear at larger angles.
Worked example with the values above
- Line spacing: d = 1/(500 × 10³) = 2×10−6 m.
- sin θ = mλ/d = 1 × 6×10−7 / 2×10−6 = 0.3.
- θ = 17.46 °.
Assumptions and limits
- Normal incidence.
- Monochromatic light.
Common mistakes
- Using lines per mm as d directly.
- Asking for a higher order that does not exist.
Statistics and uncertainty
Angular readings of ±0.1° on a spectrometer give a wavelength accurate to about 0.6% at 17°.
Where it is used
- Spectrometers and wavelength measurement.
- Optical filters and laser systems.
Maths you need
- Interference: maxima when path difference = mλ
- Arcsine: inverse sine