For small angles, double-slit interference gives:
- Fringe spacing: β = λD / d
- Bright fringes: y = mλD / d
- Dark fringes: y = (m + 1/2)λD / d
In exact angle mode, replace the small-angle step with: d·sinθ = mλ (or (m+1/2)λ), where θ = arctan(y/D).
- Choose the method matching your measurement type.
- Enter slit separation d and screen distance D.
- Provide β for spacing, or y and m for positions.
- Enable exact angle when y is not small.
- Select an output unit, then press calculate.
- Use the CSV or PDF buttons to save results.
| Method | d | D | Measurement | Computed λ |
|---|---|---|---|---|
| Spacing | 0.25 mm | 1.0 m | β = 2.0 mm | 500 nm |
| Bright | 0.30 mm | 1.5 m | y = 7.5 mm, m = 1 | 1500 nm |
| Dark | 0.20 mm | 1.2 m | y = 1.8 mm, m = 0 | 600 nm |
Example values are illustrative. Use your setup numbers.
1) What this calculator solves
Double-slit interference links a measured fringe pattern to the light wavelength. With slit separation d and screen distance D, you can compute λ from either the spacing between adjacent bright fringes (β) or the position y of a chosen bright or dark feature.
2) Inputs that matter most
Smaller d produces wider fringes, while larger D also increases spacing. Typical classroom setups use d around 0.10–0.50 mm and D from 0.5–2.0 m. Keep units consistent; the calculator converts them internally.
3) Using fringe spacing (β) for precision
The spacing method uses β = λD/d, rearranged as λ = βd/D. Accuracy improves when you measure several fringes, compute an average β, and avoid parallax. Measure across N bright gaps, then divide the total distance by N to get β. This reduces ruler-reading error. With photos, convert pixel spacing to length. For example, d = 0.25 mm, D = 1.0 m, β = 2.0 mm gives λ ≈ 500 nm, which sits in the green region.
4) Bright and dark positions
Bright fringes follow y = mλD/d (m = 1, 2, 3…). Dark fringes follow y = (m + 1/2)λD/d (m = 0, 1, 2…). Choose a clear, well-defined feature and measure y from the central maximum.
5) Small-angle vs exact angle mode
When y is small compared with D, the small-angle approximation works well. If y/D is not tiny, exact angle mode uses θ = arctan(y/D) and d·sinθ relations. This can noticeably change results for wider patterns or short screen distances.
6) Expected wavelength ranges
Visible light is roughly 380–750 nm. Values outside this range can still be valid for infrared or ultraviolet sources, but they are a helpful sanity check. If your result seems off by a factor of 10 or 100, re-check units (mm vs m is the most common slip).
7) Reporting and uncertainty tips
Record your measured d and D with their instrument resolution. Repeat y or β measurements and use an average. A simple uncertainty estimate can be built from percentage errors: the relative uncertainty in λ approximately adds the relative uncertainties in your measured quantities. For instance, 1% error in d, 0.5% in D, and 2% in β gives about 3.5% in λ, useful for lab reports.
1) Should I use fringe spacing or fringe position?
Use fringe spacing when you can measure multiple fringes and average β. It reduces random error compared with a single y measurement and is often the most stable method.
2) What value of m should I enter?
For bright fringes, m starts at 1 for the first bright fringe next to the center. For dark fringes, m starts at 0 for the first minimum next to the center.
3) When does exact angle mode matter?
If y is not small compared with D, the small-angle approximation can drift. Turn on exact angle mode when y/D is noticeable, such as large offsets or short screen distances.
4) My wavelength looks too large or too small—why?
Most issues come from unit mix-ups. Check whether d, D, y, or β were entered in mm while intended in m. Also confirm you measured y from the central maximum.
5) Can this be used for lasers outside visible light?
Yes. The formulas apply to infrared and ultraviolet sources too. The “visible range” note is only a sanity check; the calculator will output any physically valid wavelength.
6) What does “predicted fringe spacing” mean?
After computing λ, the calculator recomputes β = λD/d as a cross-check. If predicted β disagrees with your measured spacing, re-check your inputs and measurement method.