Experiment · interference
Two waves can reinforce each other or… cancel out completely. Play with a virtual ripple tank, build slits and barriers, and then see how the same laws draw fringes of laser light — and how single photons, one after another, build up a pattern that none of them “knows” on its own.
You have reduced motion turned on, so the animation starts paused. Press “Play” whenever you like.
In ripple tank mode: drag sources with the mouse or a finger, click the water to add a source. When the canvas has focus, the arrow keys move the selected source, Enter selects the next one, Delete removes it. In light mode, drag across the screen to measure a distance; the arrow keys move the measurement marker, Enter starts a new measurement.
In the “Two sources” setup, move the sources or change the phase of source B so that the water at target ⊕ stops moving (intensity below 10% of the surroundings for more than a second).
to doTurn on “Mystery laser”, measure the fringe spacing Δy on the screen (drag across the screen) and calculate λ = Δy·d/L. Your result must be accurate to within 2.5%.
to doTurn on single photons and collect at least 500 hits with both slits open. Can you see the fringes yet?
to doChoose d and a so that one of the bright fringes (order 2–6) disappears completely, even though both slits are open.
to doWater waves, sound and light behave alike: when they meet, they don't bounce off each other like balls — they pass through each other and add up. Every pattern in this experiment comes from this one simple rule.
At every point, the displacements of both waves add together (the superposition principle). Crest + crest gives a higher crest — that is constructive interference. Crest + trough gives calm water — that is destructive interference.
Δs = |r₁ − r₂| is the difference in distance from the two sources, and m = 0, 1, 2, … Points with a constant path difference lie on hyperbolas — that is why the calm lines in the “Two sources” setup are hyperbolas. Shifting a source's phase by 180° swaps the calm and reinforcement lines.
Every point of a slit becomes a new source of waves (Huygens' principle). When the slit is comparable to the wavelength, the wave spreads out behind it almost in a semicircle. A grating is many slits spaced d apart — the waves reinforce each other only in directions that satisfy the formula above.
In the early 19th century, Thomas Young showed that light from two slits forms bright and dark fringes on a screen — so light is a wave. For small angles, the fringe spacing grows with λ and L, and shrinks when the slits are farther apart.
The first factor is two-slit interference (closely spaced fringes), the second is diffraction at each slit of width a (a broad envelope). When d is a multiple of a, one of the bright fringes lands on a dark minimum of the envelope and disappears.
The wave's frequency does not change, but in shallow water (small h) the wave travels more slowly, so it is shorter. When it arrives at a slant, its front turns — this is refraction, exactly like light entering glass.
Light comes in packets — photons. Each photon lands in one random spot, but the probability of landing is proportional to the intensity I(y). After hundreds of hits, fringes emerge. Cover one slit and they vanish: they need both paths at once.
The water is a grid of 300 × 200 points spaced 1 mm apart. In each step (about 2 ms), the displacement of a point changes depending on its neighbors. The calculation is stable when v·Δt/Δx ≤ 1/√2 (the CFL condition) — here it is 0.5.
Simplifications. Tank: an ideal wave equation without dispersion — real water waves a few centimeters long travel at a speed that depends on wavelength and slowly die down, which we ignore here. The tank edges absorb waves like a gentle beach. In the shallows we assume v ≈ 0.55·v₀ (depth about 30% of the deep part). Light: the Fraunhofer formula for a screen far from the slits (L ≫ d), long slits and perfectly coherent light; the diagram at the top is not to scale, and photons are drawn only within the visible part of the screen.