Wave-Particle Duality of Light

The story so far:

• In the nineteenth century, light was believed to be a wave. Young's double-slit experiment (1801) and Maxwell's electromagnetic theory (1865) made this seem unshakeable.
• In 1905, Einstein showed that the photoelectric effect required light to be quantised into discrete photons — a return to something like Newton's old corpuscular theory.
• In 1924, de Broglie proposed that matter, too, was wavelike, and by 1927 this had been confirmed for electrons.

So by the late 1920s, both light and matter were known to be both wave and particle. This was not resolved by picking one or the other. It was resolved by accepting that both descriptions are partial views of a single underlying reality — a view known as wave-particle duality, or in a more sophisticated formulation, complementarity.

This lesson focuses on the wave-particle duality of light specifically: when does light behave as a wave, when does it behave as a particle, and how do we make sense of a single entity that does both? It draws on the OCR A-Level Physics A specification (H556), Module 4.5.

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The Evidence on Both Sides

Let us tabulate the experimental evidence.

Evidence that light is a wave:

1. Interference. Young's double-slit experiment produces bright and dark fringes that can only be explained by superposition of two waves.
2. Diffraction. Light bends around edges and spreads through slits in a way that is characteristic of waves.
3. Polarisation. Light can be restricted to a single plane of oscillation — a purely transverse-wave phenomenon.
4. Refraction. Light slows down in denser media according to n = c/v, and bends at interfaces according to Snell's law — the behaviour of a wave changing speed at a boundary.
5. Electromagnetic theory. Maxwell's equations predict a self-propagating wave of oscillating E and B fields at speed 1/√(μ₀ε₀) = c.

Evidence that light is a particle (stream of photons):

1. Photoelectric effect. The existence of a threshold frequency, instantaneous emission, and the linear dependence of KE_max on f are all explained only by single-photon absorption.
2. Compton scattering. X-rays scattered off electrons change wavelength by an amount that is exactly predicted if photons carry momentum h/λ and collide with electrons like billiard balls.
3. Blackbody radiation. The spectrum of thermal radiation is only correctly predicted by quantising the electromagnetic field into discrete hf units.
4. Single-photon detection. Photomultiplier tubes and avalanche photodiodes register individual photons as discrete clicks, consistent with particle-like events.
5. Atomic line spectra. Discrete emission and absorption lines, at frequencies set by hf = E_1 - E_2, require quantised photon exchange (the subject of Lesson 10).

Both sets of evidence are overwhelming. Neither can be dismissed as experimental artifact. The only reasonable conclusion is that light has both wave and particle aspects, and that different experiments reveal different aspects.

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When Does Each Picture Apply?

A useful rule of thumb is:

Light propagates as a wave. Light is emitted and absorbed as a particle (photon).

When light travels through space, or through a medium, or around obstacles, it spreads out and interferes as a wave. When it is produced by an atomic transition, or destroyed by absorption in a photodetector, the exchange happens in single-photon units.

This division works for most A-Level problems. For example:

• Young's double-slit experiment. The light propagates through the two slits as a wave, producing the interference pattern on the screen. But when it is detected (by a photographic plate, a CCD, or the retina), individual photons register as discrete events. The fringes build up statistically from many single-photon detections.
• Diffraction grating. Wave propagation produces the characteristic maxima at d sin θ = nλ. Detection at each maximum is again a photon-by-photon process.
• Photoelectric effect. The light travels through space as a wave (we can speak of its intensity and frequency in the usual wave terms), but each individual act of liberating an electron is a single-photon absorption event.
• Atomic line spectrum. When an excited atom emits light, it does so as a photon — a single, discrete transition. The photon then propagates away as a wave until it is absorbed elsewhere.

flowchart LR
    E[Atomic transition] --> PE[Photon emitted]
    PE --> WP[Wave propagation]
    WP --> P[Photon detected]
    WP --> D[Diffracts and interferes]

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Complementarity

Niels Bohr, the great Danish physicist who led much of the early development of quantum theory, articulated the principle of complementarity: wave and particle pictures are complementary — each captures one aspect of light, neither is complete on its own, and which picture applies depends on what question you ask.

More operationally: a given experiment will probe either the wave aspect or the particle aspect of light, but never both simultaneously. In the double-slit experiment, if you set up a detector at the slits to determine which slit the photon passed through (a particle-like measurement), the interference pattern on the far screen disappears. You have revealed the particle aspect by the measurement, and in doing so have destroyed the wave aspect.

Conversely, if you let the photon pass through both slits without trying to determine which (a wave-like measurement), you see the interference pattern — but you cannot then say which slit the photon "really" went through. The question is not merely unanswerable; it is physically meaningless.

This is one of the most striking and puzzling features of quantum mechanics. It demands a rethinking of what we mean by the "reality" of a physical system. For A-Level you do not need to grapple with the philosophy, but you should understand the operational content: which aspect of light you observe depends on what you measure.

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Key Quantitative Criterion: Wavelength versus Apparatus Size

There is also a useful quantitative criterion for when wave-like behaviour is observable. Diffraction and interference become significant when the wavelength of the light is comparable to or larger than the size of the apparatus or obstacles involved.

Scenario	Relation between λ and a	Behaviour
Narrow slit, visible light	λ ~ a	Strong diffraction; wave picture dominates
Ordinary reflection from a large mirror	λ << a	Geometric optics; particle picture (ray optics) dominates
Photoelectric absorption	Size of electron << λ	Absorption is point-like; particle picture dominates
Radio broadcast antenna	λ >> a	Wave dominates everything

Notice that the particle picture dominates at both ends: at very short wavelengths (where diffraction becomes negligible and photons behave as tiny projectiles) and at the moment of absorption (where the entire photon energy is delivered at a single point). The wave picture dominates in the middle: during free propagation through apparatus of comparable size.

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Worked Example 1: Why Double-Slit Patterns Require Wave Language

In a Young's double-slit experiment, light of wavelength 600 nm passes through two slits 0.40 mm apart and forms fringes on a screen 2.0 m away. Compute the fringe spacing, and note why this result cannot be derived from a photon-as-tiny-bullet picture.

Solution. Using the fringe-spacing formula w = λD/a:

w = (600 × 10⁻⁹)(2.0)/(0.40 × 10⁻³)
  = 3.0 × 10⁻³ m = 3.0 mm