Double Slit Experiment and Wave Interference Simulator

Compute exact fringe positions and the full intensity profile for one slit, two slits, N slits, or a diffraction grating, with the single-slit envelope and the interference term drawn separately.

At a glance

Computes
Fringe positions, intensity profile, diffraction envelope, and approximation error
You supply
Wavelength, slit width, slit separation, and screen distance
Use when
You need lab-report positions, intensities, or the small-angle error
Assumes
Far-field scalar diffraction, coherent light, and identical parallel slits
Configuration

Fringe spacing

2.8272 mm

Exact profile shown below; positions in the table include the small-angle comparison.

Relative intensity against Screen position (mm)

−20−10010200.00.20.40.60.81.0Observed intensityDiffraction envelopeInterference term
Series Observed intensity is drawn from 2000 of 4097 computed points; every point is used in the numbers below.Series Diffraction envelope is drawn from 2000 of 4097 computed points; every point is used in the numbers below.Series Interference term is drawn from 2000 of 4097 computed points; every point is used in the numbers below.
Sampling rule
uniform
Profile points
4,097
Aperture Fresnel number
0.118987
Far-field check
satisfied

Detection build-up is off. The analytic curve and its numeric table remain available.

Bright-fringe positions in the current view
Ordersin(theta)Small-angle y (mm)Exact y (mm)Difference (micrometres)
0 0.000000000 0.000000 0.000000 0.0000
1 0.002356000 2.827200 2.827208 0.0078
2 0.004712000 5.654400 5.654463 0.0628
3 0.007068000 8.481600 8.481812 0.2119
4 0.009424000 11.308800 11.309302 0.5022
5 0.011780000 14.136000 14.136981 0.9809
6 0.014136000 16.963200 16.964895 1.6951
7 0.016492000 19.790400 19.793092 2.6919
8 0.018848000 22.617600 22.621618 4.0185
Export

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How the double slit experiment works

Two narrow slits illuminated by one monochromatic wave produce evenly spaced bright bands. The spacing follows from path difference; each slit's finite width controls how bright the outer bands remain.

Wave interference: adding two waves

Interference is addition. A whole-wavelength path difference adds crest to crest, while a half-wavelength difference cancels. The two-source mode shows that same rule without a slit envelope.

Single-slit diffraction and the envelope

Each slit spreads light on its own. That diffraction envelope is plotted beside the interference term, so their product is visible on the same axes.

Missing orders

An interference maximum disappears when it lands exactly on a diffraction minimum. The calculation keeps the entered decimal widths as exact rational values when identifying that condition.

Where the small-angle formula fails

The table prints both y = m lambda L / d and the exact flat-screen geometry. Their difference is reported in micrometres for every listed order.

Diffraction gratings and resolving power

A grating is the same interference calculation with many illuminated slits. When peaks become narrower than a meaningful sampled curve, the instrument uses analytically placed line-spectrum peaks and a distinct two-uniform deterministic stream.

Single photons and the build-up pattern

Each detection is one point. Repeating the seeded sampling builds the same distribution predicted by the analytic intensity curve.

I/I0 = [sin(alpha)/alpha]^2 [sin(N beta)/(N sin(beta))]^2 How?

How this is calculated

Here alpha = pi a sin(theta) / lambda and beta = pi d sin(theta) / lambda. Removable singularities are evaluated by their analytic limits. The aperture Fresnel number sizes the far-field assumption separately from the small-angle approximation.

The velocity-frequency conversion is deliberately not another tool mode. For that conversion, use the wavelength and frequency calculator. For exponent notation used in the readouts, see scientific notation. The plotted I/I0 is a geometric ratio set by interference and diffraction, not an absorption ratio; absorption quantities are computed by the Beer-Lambert law calculator.

Formula: I/I0 = [sin(alpha)/alpha]^2 [sin(N beta)/(N sin(beta))]^2

Assumptions and limits
  • Far-field scalar diffraction with identical parallel slits.
  • Monochromatic coherent illumination.
  • Relative intensity only, not absolute irradiance.
  • The obliquity factor is omitted and the aperture Fresnel number is printed.
  • Ray optics is out of scope: focal length, image distance and magnification belong to the lens and mirror equation calculator.

Sources

  1. OpenStax University Physics Volume 3, 3.1 Young's Double-Slit Interference. OpenStax. Retrieved .
  2. OpenStax University Physics Volume 3, 4.3 Double-Slit Diffraction. OpenStax. Retrieved .
  3. OpenStax University Physics Volume 3, 4.4 Diffraction Gratings. OpenStax. Retrieved .
  4. NIST Atomic Spectra Database. NIST. Retrieved .