Wave-Particle Duality of Light

Spec mapping: OCR H556 Module 4.5 — Quantum physics (wave-particle duality of electromagnetic radiation; the wave aspects of light revealed by interference, diffraction, polarisation and refraction; the particle aspects revealed by the photoelectric effect, atomic line spectra and single-photon detection; the principle of complementarity and the dependence of which aspect is observed on the experimental context). Refer to the official OCR H556 specification document for exact wording.

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:

$$\begin{aligned} w = (600 \times 10^{-9})(2.0)/(0.40 \times 10^{-3}) \\ = 3.0 \times 10^{-3} m = 3.0 mm \end{aligned}$$w=(600×10−9)(2.0)/(0.40×10−3)=3.0×10−3m=3.0mm​

A purely particle picture would predict no fringes: a stream of tiny bullets would simply produce two bright lines on the screen directly behind the slits, with no dark fringes in between. The fringe pattern is intrinsically a wave phenomenon. But this same pattern builds up even if the photons arrive one at a time — so "it's a wave" is not quite the whole story either. Each photon detects as a particle, but the probability of detection at each point is determined by the wave.

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Worked Example 2: When Is a Single Photon Detected?

A laser pointer emits 1.0 mW of red light at 650 nm. It is pointed at a photodiode that detects individual photons. At what rate do individual photons arrive at the detector? Does the detector see them as discrete pulses or as a continuous signal?

Solution.

Photon energy: E = hc/λ = 1240/650 ≈ 1.91 eV = 3.06 × 10⁻¹⁹ J.

Photon rate: N/t = P/E = (1.0 × 10⁻³)/(3.06 × 10⁻¹⁹) ≈ 3.3 × 10¹⁵ s⁻¹.

That is over three thousand million million photons per second. A photodiode cannot possibly resolve individual photon arrivals at this rate — it sees a continuous current. Only by drastically attenuating the beam (with neutral-density filters, say, by a factor of 10¹² or more) can the arrival rate be brought down to a level where individual photons are resolvable.

This is why in everyday life light appears continuous: the particle nature is buried beneath the avalanche of photons.

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Worked Example 3: Photons or Waves in a Microwave Oven?

A microwave oven operates at 2.45 GHz and delivers 800 W of power into the oven cavity. Calculate the photon energy and the photon flux. Comment on whether the microwave heating effect is best described as a particle or a wave phenomenon.

Solution.

Photon energy:

$$E = hf = (6.63 \times 10^{-34})(2.45 \times 10^{9}) \approx 1.62 \times 10^{-24} J$$E=hf=(6.63×10−34)(2.45×109)≈1.62×10−24J

In eV: E ≈ 1.0 × 10⁻⁵ eV — a tiny amount.

Photon flux:

$$N/t = P/E = 800 / (1.62 \times 10^{-24}) \approx 5 \times 10^{26} s^{-1}$$N/t=P/E=800/(1.62×10−24)≈5×1026s−1

Five hundred thousand million million million photons per second. The individual photons are so weak and so numerous that there is absolutely no way to treat them separately — the wave description in terms of macroscopic electric and magnetic fields is the only practical language. Microwave heating is a wave phenomenon, and the oven's metal cavity sets up a stationary-wave pattern of electric field inside. (The turntable exists to smooth out the nodes and antinodes.)

At the same time, in principle, the heating comes from absorbed photons. The two descriptions are consistent, but only the wave picture is useful in practice.

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Worked Example 4: Photons or Waves in X-Ray Imaging?

A medical X-ray source emits photons of wavelength 0.01 nm at a total power of 0.1 W. Calculate the photon energy and photon flux, and comment on whether X-ray imaging is particle- or wave-dominated.

Solution.

Photon energy:

$$E = hc/\lambda = 1240/(0.01) \approx 124\,000\,\text{eV} = 124\,\text{keV} = 2.0 \times 10^{-14}\,\text{J}$$E=hc/λ=1240/(0.01)≈124000eV=124keV=2.0×10−14J

Photon flux:

$$N/t = P/E = 0.1/(2.0 \times 10^{-14}) = 5 \times 10^{12} s^{-1}$$N/t=P/E=0.1/(2.0×10−14)=5×1012s−1

This is still a large number per second, but each individual photon now carries a huge energy. When an X-ray photon strikes a film grain or a CCD pixel, it produces a sharp, localised event whose energy is easily measurable. X-ray imaging is routinely treated as a particle (photon) phenomenon — the image is built up by counting individual photons.

At the same time, X-rays obey Bragg diffraction from crystals (a wave phenomenon). Both descriptions apply; which one is useful depends on the experiment.

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Summary Table

Wavelength regime	Dominant description	Examples
Radio (m – km)	Wave	Radio transmission, microwave ovens
Visible (~500 nm)	Both required; wave for propagation, photon for detection	Young's slits, photoelectric effect
X-ray (~0.01 nm)	Photon (for imaging); wave (for Bragg diffraction)	Medical radiography, crystallography
Gamma (< 0.001 nm)	Photon	Nuclear decay, particle physics

Notice that at every frequency, light has both aspects. What changes is which aspect is more useful in practice, and what sort of experiment is needed to bring each aspect to the fore.

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The Deeper Truth

At a deep level, wave-particle duality for light is just a special case of quantum mechanics, in which every "particle" is described by a wave function whose squared amplitude gives the probability of detection. For light, the wave function is intimately related to the electromagnetic field, and the particle interpretation is built up from photon-number states of that field.

The full theory of quantum electrodynamics (QED), developed by Feynman, Schwinger, Tomonaga and Dyson in the 1940s, reconciles these pictures with complete mathematical consistency. For A-Level, you can regard wave-particle duality as an empirical fact about light and matter, and use whichever description (wave or photon) best suits the problem at hand.

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Wave / Particle Decision Tree — Visual Reference

The following mermaid flow shows the operational rule of thumb: identify whether the experiment probes propagation (wave) or exchange (particle) of light, then choose the appropriate description.

flowchart TB
    Q["What does the experiment probe?"]
    Q --> P["Propagation:<br/>interference, diffraction,<br/>polarisation, refraction"]
    Q --> E["Exchange (emission/absorption):<br/>photoelectric, Compton, line spectra,<br/>single-photon detection"]
    P --> W["Use WAVE picture<br/>E, B fields; w = λD/a; d sin θ = nλ"]
    E --> Ph["Use PHOTON picture<br/>E = hf; p = h/λ; hf = φ + KEmax"]
    W --> S["Both describe the same physical reality<br/>QED unifies them at undergraduate level"]
    Ph --> S

The same photon goes through both stages in a typical experiment: it propagates as a wave from source to detector, then is exchanged as a particle when it is absorbed. The dual description is not a contradiction; it is the operational structure of quantum reality.

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Synoptic Links

• Photoelectric effect (Module 4.5, lessons 3-5) — particle face of light revealed: threshold frequency, instantaneous emission, $KE_{\max} = hf - \phi$KEmax​=hf−ϕ. Wave theory cannot explain a frequency threshold; photon theory does.
• Interference and diffraction (Module 4.4) — wave face of light revealed: Young's double slits, diffraction grating $d\sin\theta = n\lambda$dsinθ=nλ, single-slit pattern. Particle (photon-as-bullet) theory cannot explain dark fringes between bright ones.
• Atomic line spectra (Module 4.5, lesson 10) — particle face of light revealed: $hf = E_{\text{upper}} - E_{\text{lower}}$hf=Eupper​−Elower​ for single-photon emission/absorption. Continuous wave theory would give a continuous spectrum; the observed discrete lines require single-photon quantisation.
• de Broglie matter waves (Module 4.5, lessons 6-7) — same physics, applied to massive particles instead of photons. Wave-particle duality is universal: not just for light, not just for matter, but for all quantum entities.

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Specimen question modelled on the OCR H556 paper format

Question (9 marks): Wave-particle duality is a fundamental feature of light and matter.

(a) Give one example of an experiment that reveals the wave nature of light, and one example of an experiment that reveals the particle nature of light. For each, state briefly the observation that is explained only by that description. [4]

(b) A laser pointer emits $1.5$1.5 mW of red light at wavelength $\lambda = 650$λ=650 nm.

(i) Calculate the energy carried by a single photon of this light, in joules. [2]

(ii) Calculate the rate at which photons leave the laser pointer. Comment on whether the photon (particle) nature is observable in everyday use. [3]

AO breakdown