Two-Source Interference

The set-up — two coherent sources separated by a small distance produce overlapping waves. Where they meet, superposition produces a fixed pattern of maxima and minima in space.

Conditions for an observable pattern — the sources must be coherent (same frequency, constant phase difference), the waves must have similar amplitudes so that cancellation is close to complete, and for transverse waves they must be polarised in the same plane.

Where the maxima and minima are

Path difference = nλ → constructive → maximum

Path difference = (n + ½)λ → destructive → minimum

with n = 0, 1, 2, …

Reading the pattern — the central maximum lies where the path difference is zero, equidistant from both sources. Moving outwards, each successive maximum corresponds to an extra whole wavelength of path difference.

Example: with two loudspeakers playing the same note from one amplifier, walking parallel to the line joining them passes through alternating loud and quiet regions. The quiet regions are not places where the sound fails to arrive — sound arrives from both speakers and cancels.

Producing coherent sources — the reliable method is to start from a single source and split it, so the two paths share the same original oscillation. Young used a single slit illuminated by monochromatic light, followed by two slits. A modern equivalent uses a laser, which is coherent enough to illuminate both slits directly.

Why two separate lasers still will not do — even two lasers of identical frequency have no fixed phase relationship between them, so the pattern would shift constantly and average out.

Water and microwaves — the same effect is easily shown in a ripple tank with two dippers driven by one motor, and with two microwave transmitters fed from one source. Seeing it in three different kinds of wave is what makes the point that interference is a property of waves in general, not of light in particular.