Diffraction and Interference

Young's fringes were dismissed for over a decade. What finally forced the wave theory to be taken seriously wasn't more fringes — it was a mathematically predicted, seemingly absurd bright spot at the dead centre of a shadow, confirmed by direct experiment.

What diffraction and interference actually are

This lesson is a conceptual one: it explains why diffraction and interference count as decisive evidence for the wave theory of light, rather than re-deriving the fringe-spacing or single-slit mathematics already covered in the AS Waves topic — revisit those lessons directly if the formulas themselves are needed.

Diffraction is the spreading of a wave as it passes through a gap or around an obstacle. It's most noticeable when the gap or obstacle is comparable in size to the wave's own wavelength — a sound wave (wavelength of the order of a metre) diffracts noticeably around an open doorway, while light (wavelength of the order of hundreds of nanometres) only diffracts noticeably through very narrow slits or around very small obstacles. Interference is what happens when two or more waves overlap in the same region of space: at each point, the waves superpose, adding constructively where they're in phase and destructively where they're out of phase, producing the pattern of reinforcement and cancellation seen in fringes.

The two effects are closely related in practice — a double slit needs diffraction at each slit to spread the light out far enough for the two beams to overlap and interfere at all — but they are conceptually distinct: diffraction is about a single wave's behaviour at a gap or edge, while interference is about the combination of two or more waves.

Why only waves can do this

Both diffraction and interference are, without exception, wave phenomena. A stream of classical particles travelling in straight lines has no mechanism to bend around a corner or spread out from a narrow gap the way a wave does — a particle either passes through a gap in a straight line or it doesn't; it can't "spread" into a range of directions purely from passing through a narrow enough gap. Likewise, as covered in the previous lesson, particles cannot cancel each other out to produce dark bands, since interference relies on the wave property of superposition — adding displacements (or field values) at a point, which can be positive, negative, or zero — and particles simply don't have a displacement to superpose in this way.

This is why diffraction and interference, wherever they're observed — with light, with sound, with water waves, or (much later in this module and elsewhere in the course) with matter itself — are treated as unambiguous signatures of wave behaviour. Observing either effect for some phenomenon is close to a direct proof that the phenomenon has a wave character, at least in part.

Fresnel and the spot of Arago

Young's qualitative fringe explanation, on its own, was not enough to overturn Newton's corpuscular theory — as the previous lesson explains, the wave theory languished for over a decade despite Young's result. The turning point came from a much more rigorous mathematical treatment of wave optics developed by the French physicist Augustin-Jean Fresnel in the 1810s.

Fresnel built a full mathematical theory of diffraction, treating every point on a wavefront as a source of secondary wavelets (extending Huygens' older, more qualitative idea) and showing how to add up their combined effect at any point beyond an obstacle or aperture. When Fresnel submitted this theory to a scientific committee for evaluation, one of the judges — a firm supporter of the corpuscular theory — worked through the mathematics and pointed out what seemed to be an absurd, obviously wrong consequence: Fresnel's equations predicted that if a small circular disc were placed in the path of a beam of light, a bright spot of light should appear at the exact centre of the disc's shadow, where common sense said there should be only darkness.

The prediction was tested directly, and the bright spot — now often called the spot of Arago, after the physicist who carried out the confirming experiment — was there exactly as Fresnel's mathematics said it would be. It was, in effect, a case of the wave theory correctly predicting a result so counter-intuitive that its own critics thought it was a proof the theory must be wrong — only for the experiment to vindicate the theory outright.

The wave theory of light was now on far firmer ground than it had been after Young's experiment alone — though, as the earlier lesson on Young's double-slit experiment notes, it would still be a matter of decades before Maxwell's electromagnetic theory turned "light behaves like a wave" into "light unavoidably must be a wave," as covered next.