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Newton and Huygens: particles or waves?
Newton's corpuscular model and Huygens' wave model of light, how each explained reflection and refraction, the evidence each side relied on, and the experiments by Young, Fresnel, Arago and Foucault that settled the argument in favour of waves.
In 1818 the French Academy of Sciences ran a prize competition on diffraction. Augustin Fresnel entered a wave theory of light. One judge, Siméon Poisson, a firm believer in Newton's particles, worked through Fresnel's equations and found what he thought was a fatal flaw: they predicted a bright spot in the very centre of the shadow of a round disc. That was obviously absurd. Then another judge, François Arago, did the experiment. The spot was there.
Two models of light
By the late 1600s two rival explanations of light were on the table. Both could explain the basic facts that light travels in straight lines, reflects with equal angles, and bends (refracts) when it enters glass or water. They disagreed about what light is, and that disagreement led to one testable difference.
| Newton: corpuscular model | Huygens: wave model | |
|---|---|---|
| Published | Opticks, 1704 | Treatise on Light, 1690 |
| Light is | a stream of tiny, fast particles (corpuscles) | a wave disturbance travelling through a medium (the "aether") |
| Straight-line travel | particles move in straight lines unless a force acts | wavefronts advance perpendicular to themselves |
| Reflection | particles bounce elastically off a surface | wavelets from each point of the surface rebuild the reflected front |
| Refraction into water | water attracts the particles, so they speed up and bend towards the normal | waves slow down in water, so the wavefront pivots towards the normal |
| Colour | different-sized particles | (later) different wavelengths |
| Prediction: speed in water | faster than in air | slower than in air |
Huygens' principle
Huygens' key idea is a geometric rule for how any wave moves forward:
Every point on a wavefront acts as a source of secondary spherical wavelets. A short time later, the new wavefront is the surface tangent to (the envelope of) all these wavelets.
On a flat wavefront in open space the wavelets add up to a new flat wavefront further along, so the wave travels straight. When a wavefront hits a water surface at an angle, the part that enters the water first slows down, so its wavelets are smaller. The front pivots and travels at a smaller angle to the normal. Working through the geometry gives Snell's law,
$$n_1 \sin\theta_1 = n_2 \sin\theta_2, \qquad n = \frac{c}{v}$$
Newton explained the same bending by imagining that, very close to the surface, the water pulls each particle towards it. That adds to the particle's velocity component perpendicular to the surface, so it travels faster and closer to the normal. Both models give the same angle. They make opposite predictions for the speed.
Light in air strikes water ($n = 1.33$) at an angle of incidence of 40°. Find the angle of refraction, and the speed of light in water predicted by each model.
Why Newton's model won at first
For about a century most scientists followed Newton. Partly this was his enormous reputation, but he also had real arguments:
- Sharp shadows. Sound and water waves obviously bend around obstacles. Light seemed to cast sharp shadows. Newton argued that a wave would spread into the shadow.
- Light crosses empty space. Light reaches us from the Sun through what seemed to be a vacuum, while every known wave needed a medium.
- Polarisation. Light passing through a calcite crystal behaved as if it had "sides". Huygens' waves were longitudinal, like sound, and could not explain this.
The first argument fails because the amount of spreading depends on the ratio of wavelength to gap width. Light's wavelength is under a micrometre, so with everyday gaps and edges the spreading is tiny, though it is there if you look closely (Grimaldi described it in 1665). The third argument fails once light is understood as a transverse wave (7G). The second was not fully resolved until Maxwell showed that light is an electromagnetic wave, which needs no medium at all (7A).
Diffraction: the wave signature
Diffraction is the spreading of a wave as it passes through a gap or around an edge. Huygens' principle explains it naturally: points across a gap act as wavelet sources, and beyond the gap their wavelets spread in all directions. Particles travelling in straight lines would simply make a sharp-edged beam.
The narrower the gap compared with the wavelength, the more the wave spreads. For a single gap of width $a$, the first dark direction on either side of the central beam is at
$$\sin\theta = \frac{\lambda}{a}$$
When $a$ is about the same as $\lambda$ the wave spreads almost into a semicircle. When $a$ is thousands of wavelengths, as with a doorway and light, the spreading is far too small to notice.
Compare how much sound (wavelength 0.50 m) and green light (wavelength 500 nm) spread out after passing through a doorway 0.90 m wide.
The evidence that settled it
- Young, 1801–1803. Thomas Young passed light through two narrow slits and saw bright and dark bands: interference. Two beams of particles should simply add up. Two waves can cancel (7F).
- Fresnel, 1818. Augustin Fresnel put Huygens' principle into precise mathematics and predicted diffraction patterns in detail, assuming light is a transverse wave (which also explained polarisation).
- Arago, 1819. The bright spot in the centre of a disc's shadow, predicted from Fresnel's theory by Poisson as an objection, was observed.
- Foucault and Fizeau, 1850. Using rotating mirrors, Léon Foucault showed that light travels slower in water than in air, as Huygens predicted. This directly contradicted Newton's model of refraction.
By 1850 the wave model was accepted. Notice how science worked here: each model made predictions, and experiments decided between them. Newton's authority delayed the change, but evidence won in the end. And the story is not over: in 7I you will see that some experiments need light to behave as particles after all.
- At the default angle of 40°, read the refracted angle. Check it with Snell's law and $n = 1.33$. Do the two models disagree about the angle?
- Compare the speeds the two models predict in water. Then press Show Foucault's 1850 result. Which model survives?
- Set the angle to 0°. Does either model bend the light now? What still changes?
- Switch to Through a gap. With a gap of 2 wavelengths, the spread to the first minimum is ±30°. Check it with $\sin\theta = \lambda/a$.
- Widen the gap to 4 and then 8 wavelengths. How does the spread change? Narrow it to 1 wavelength. Why did Newton think light did not diffract?
Test yourself
Newton's and Huygens' models of light made different predictions about
Both gave Snell's law. Newton predicted faster in water; Huygens predicted slower.
According to Huygens' principle, the new position of a wavefront is found from
Each point is a wavelet source; the new front is the surface tangent to all the wavelets.
Light of wavelength 600 nm passes through a gap. Which gap width gives the most diffraction?
Spreading is greatest when the gap is closest to the wavelength. 0.0010 mm = 1000 nm.
The observation of a bright spot at the centre of the shadow of a disc was strong evidence because
Poisson derived it from Fresnel's wave theory, expecting it to be false. Arago observed it.
Label the two models of refraction
Sort the observations by which model they support (as understood around 1850).
Put these events in time order.
Huygens proposed that each point on a wavefront is a source of secondary . The spreading of a wave through a gap is called , and it is greatest when the gap is similar to the . Newton's model predicted light would travel faster in water, but Foucault found it was . Polarisation shows light is a wave.
Analyse how experimental evidence was used to choose between Newton's and Huygens' models of light.
Newton (1704) modelled light as particles which, near the surface of water, are attracted and speed up, bending towards the normal. Huygens (1690) modelled light as waves in which every point on a wavefront is a source of wavelets; on entering water the waves slow down, so the wavefront pivots towards the normal. Both models gave Snell's law, so refraction angles alone could not decide between them, but they predicted opposite speeds in water.
Newton's model was accepted at first, partly because of his reputation and because shadows seemed sharp, suggesting light did not diffract. Later evidence favoured waves. Young (1801) produced interference fringes with two slits; particles would add, but waves can cancel. Fresnel's wave theory predicted a bright spot in the centre of a disc's shadow, which Arago observed in 1819. Diffraction was shown to be small only because light's wavelength is tiny. Finally, Foucault (1850) measured light travelling slower in water than in air, contradicting Newton's prediction directly and confirming Huygens'. The wave model was therefore accepted.