Double-Slit LabBeta

About Double-Slit Lab

This simulation solves the two-dimensional scalar wave equation directly on a grid (a finite-difference time-domain scheme). A plane wave enters from the left, passes the wall with its slits, and when it reaches the screen column on the right the simulation time-averages the squared amplitude there and adds it to the graph. The dashed line is the Fraunhofer (far-field) theory curve. All lengths are in grid cells. The grid is 420 cells wide; the slit-to-screen distance L defaults to 249 cells and the Slit–screen distance L slider moves it anywhere from 40 to 249.

By default it is a wave model. Switch on the which-path detector and the tool computes two separate waves, each with only one slit open, and adds their intensities at the screen (|ψ₁|² + |ψ₂|²). Adding intensities instead of amplitudes drops the interference term, so the fringes vanish and only the single-slit envelope remains. This builds in the result that which-path information destroys coherence between the two paths; it does not model the measurement itself. The dots in the Real experiment setup panel are drawn at random with a probability proportional to the computed intensity, to show what one-photon-at-a-time detection looks like. They are not trajectories of individual particles.

The fringe spacing formula, checked against this screen

With slit separation d, the path difference between the two waves at angle θ is d·sinθ. Bright fringes sit where that equals a whole number of wavelengths: d·sinθ = nλ. For small angles sinθ ≈ tanθ = y/L, so neighbouring bright fringes are Δy ≈ λL/d apart. That is the number shown as Predicted fringe spacing in the side panel.

At the defaults (λ = 14, d = 50, L = 249) the panel shows 14 × 249 / 50 = 69.7 cells. Read the first bright peak off the graph and it sits a little further out. The exact condition sinθ = 14/50 = 0.28 gives θ ≈ 16.3°, and y = L·tanθ = 249 × 0.28 / 0.960 ≈ 72.6 cells. The panel's First bright fringe y₁ = L·tan(asin(λ/d)) row shows this exact value. The 4% gap is the small-angle approximation failing, not a bug. Double d to 100 and sinθ drops to 0.14; the formula gives 34.9 and the exact position is 35.2, practically the same.

Experiment 1: change the wavelength and the spacing

Doubling λ from 14 to 28 should double the spacing. But sinθ = 28/50 = 0.56 pushes the first bright fringe out to about y = 168 cells, which on a short browser window is off the edge of the screen. The graph then shows a single broad central peak. If λ is larger than d (try λ = 40, d = 30), sinθ would have to exceed 1, so a first-order fringe cannot exist at all.

The laser colour follows along. The grid wavelengths 6–40 are mapped onto visible light from 400 to 700 nm, so a longer λ slides from green toward red. The same is true on a real bench: red light spreads its fringes wider than blue light through the same slits.

Experiment 2: a fringe that goes missing

The pattern on the screen is the two-slit interference term (cos²) multiplied by the diffraction envelope of one slit (sinc²). A wider slit a makes the envelope narrower, and wherever a zero of the envelope lands on an interference maximum, that fringe disappears.

Set λ = 6, d = 60, a = 30, so d/a = 2. Bright fringes should appear near y = 25, 51, 78 and 109 cells, but the ones at 51 (second order) and 109 (fourth order) coincide with envelope zeros and nearly vanish. With the theory curve on, the dashed line drops to zero right there. One caveat: at λ = 6 a wavelength spans only six cells, so numerical dispersion on the grid is noticeable and peak heights can drift from the theory.

Experiment 3: close one slit

Switch to a single slit with a = 30 and λ = 8. The first dark point is at a·sinθ = λ, so sinθ = 0.267 and y ≈ 249 × 0.267 / 0.964 ≈ 69 cells. Halve a to 15 and that dark point moves roughly twice as far out. Narrower openings spread the wave more; that is diffraction in one sentence.

Now switch back to two slits. Fine fringes appear inside the broad peak you just saw. This is the point that makes the experiment famous: the two-slit pattern is not the sum of two one-slit patterns. Adding the results of each slit open on its own gives a smooth hump with no stripes.

Experiment 4: one detection at a time

Under Real experiment setup, turn the photon detection rate down to 1 or 2 and press Clear screen. The first dots look scattered at random. After a few hundred, stripes start to show; after a few thousand, the density of dots matches the intensity graph. This is what the 1989 Hitachi electron film showed with real electrons. Changing any slit setting resets the count.

Scaling up to a real lab bench

A helium-neon laser (λ = 633 nm) through slits 0.25 mm apart onto a wall 1 m away gives Δy = 633×10⁻⁹ × 1 / 0.25×10⁻³ ≈ 2.5 mm. That is hard to count by eye, which is why classroom setups often put the screen 2–3 m away. The formula needs L to be much larger than d; here L/d = 4,000. In the simulation L/d is only about 5, which is why the approximation error is visible on screen.

Worked examples

How to use it

1. Leave the default double slit running until the wavefront reaches the screen, then switch the view to Intensity.
2. Turn on the theory curve and move λ, d and a one at a time; each change clears the screen and it builds up again.
3. Compare the predicted fringe spacing in the side panel with the peak positions on the graph.

Frequently asked questions

Related guides

• The Double-Slit Experiment: From Thomas Young to Single Electrons, and What 'Observation' Really Means