Calculator Inputs
Example Data Table
| Case | Mode | A₁ | A₂ | Wavelength (m) | Path Data | Total Phase | Effective Amplitude | Normalized Intensity |
|---|---|---|---|---|---|---|---|---|
| Example 1 | Direct path | 4 | 4 | 2 | Δx = 0.5 m | 90° | 5.656854 | 0.5 |
| Example 2 | Direct path | 5 | 3 | 1.5 | Δx = 1.5 m | 360° | 8 | 1 |
| Example 3 | Double slit | 6 | 6 | 5.5e-7 | d = 2.5e-4 m, L = 2 m, y = 0.0044 m | 360° | 12 | 1 |
These examples show direct path inputs and screen-based interference geometry.
Formula Used
1) Path-induced phase difference
Path phase = 2π(Δx / λ). Total phase = initial phase + path phase.
2) Combined intensity with coherence
I = I₁ + I₂ + 2γ√(I₁I₂)cos(φ), where I₁ = A₁² and I₂ = A₂².
3) Effective resultant amplitude
Aeff = √I. This is an amplitude-equivalent result from the combined intensity.
4) Visibility
Visibility = (Imax − Imin) / (Imax + Imin).
5) Double-slit path difference
For small angles, Δx ≈ dy / L, where d is slit spacing, y is screen position, and L is screen distance.
6) Fringe spacing
Fringe spacing β = λL / d. Bright fringes occur near y = mβ.
How to Use This Calculator
- Choose Direct path difference if Δx is already known.
- Choose Double-slit geometry if you know d, L, and y.
- Enter amplitudes, frequency, and either wavelength or wave speed.
- Add any initial phase offset between the two sources.
- Set coherence between 0 and 1 for realistic fringe contrast.
- Press Calculate Interference to see the result above the form.
- Review resultant amplitude, intensity, visibility, phase, and fringe outputs.
- Use the CSV and PDF buttons to export the calculated report.
FAQs
1) What does this calculator compute?
It estimates total phase difference, effective resultant amplitude, combined intensity, visibility, fringe order, and, in double-slit mode, fringe spacing and nearby bright or dark locations.
2) Why are there two calculation modes?
Direct path mode uses a known path difference. Double-slit mode derives path difference from slit spacing, screen distance, and observation position for standard laboratory geometry.
3) What does the coherence factor change?
A coherence value of 1 gives maximum fringe contrast. Lower values weaken the interference term, making bright fringes dimmer and dark fringes less deep.
4) Can the two amplitudes be different?
Yes. Unequal amplitudes still interfere, but visibility decreases. Perfect cancellation becomes harder because one wave cannot fully balance the other at destructive conditions.
5) Why can wavelength be auto-calculated?
When wavelength is blank, the calculator uses wave speed divided by frequency. This is useful when your experiment provides medium speed and source frequency instead.
6) What is normalized intensity?
It is the current intensity divided by the maximum possible intensity for the entered pair of waves. Values near 1 are bright; values near 0 are dark.
7) Are the double-slit results exact?
They use the small-angle approximation, where path difference is roughly slit separation times screen position divided by screen distance. This is very accurate for modest screen angles.
8) Which units should I use?
Use consistent SI units: meters, hertz, meters per second, and degrees. Both amplitudes should share the same scale so the relative intensity remains meaningful.