Library / Foundations: Physics / FPH-31
Foundations: Physics
Double-slit fringe spacing
Spacing of interference fringes on a screen.
- Ref
- FPH-31
- Rev
- v1
- Field
- Foundations: Physics
- Result
- w [mm]
Fringe spacing w on a distant screen depends on wavelength λ, screen distance D and slit separation s. Use for small angles and coherent light.
Light passing through two slits makes bright and dark bands; the bands are further apart for longer wavelengths and closer slits.
Calculator
- Fringe spacing in metres0.0024 m
- Fringes within 10 mm4.167
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.
- Measure the fringe spacing and you can find the wavelength of the light.
- Red light gives wider fringes than blue.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (mm) | Local step | Change in result |
|---|---|---|---|---|---|---|
| D Screen distance | 0.5 to 10 m | 0.6 | 12 | 11.4 | +10% | +10 % |
| s Slit separation | 0.1 to 2 mm | 0.6 | 12 | 11.4 | +10% | −9.09 % |
| λ Wavelength | 380 to 750 nm | 1.52 | 3 | 1.48 | +10% | +10 % |
Sweep of Screen distance
| Screen distance (m) | Fringe spacing (mm) |
|---|---|
| 0.5 | 0.6 |
| 0.7271 | 0.8725 |
| 1.057 | 1.269 |
| 1.538 | 1.845 |
| 2.236 | 2.683 |
| 3.252 | 3.902 |
| 4.729 | 5.674 |
| 6.877 | 8.252 |
| 10 | 12 |
Sweep one variable
Variables and how each one contributes
Fringe spacing
What the equation gives you. Everything else feeds it.
Wavelength
Wavelength of the light. Directly proportional.
Screen distance
Distance from slits to screen. Directly proportional.
Slit separation
Distance between the slits. Inversely proportional.
Worked example with the values above
- Convert units: λ = 6×10−7 m, s = 5×10−4 m.
- w = λD/s = 6×10−7 × 2 / 5×10−4 = 0.0024 m.
- w = 2.4 mm.
Assumptions and limits
- Small angles and D much larger than s.
- Coherent, monochromatic light.
Common mistakes
- Mixing nm, mm and m.
- Measuring to the wrong fringe.
Statistics and uncertainty
Measuring several fringes and dividing by their count reduces the reading error on w.
Where it is used
- Measuring wavelengths.
- Laser and optics calibration.
Maths you need
- Interference: path difference
- Unit conversion: nm, mm and m