How did we know light is a "wave"?
― A spot of light appeared where there should have been none, right in the middle of a round shadow
Is light a stream of tiny particles, or is it a wave, like ripples on water? The debate was settled, surprisingly, by the calculations of someone who was against the wave idea. "If light really were a wave, the middle of a round object's shadow would have to be bright. That's absurd," he argued. But when people actually checked, a small point of light appeared right in the middle of the shadow.
On a sunny day, hold a coin up above the ground. It casts a round, black shadow on the ground. The middle of that shadow is, of course, pitch dark.
Light travels in straight lines, and the coin blocks it, so no light reaches behind it. That's what most people would assume.
But under the right conditions, a spot of light appears in exactly this place — the spot that should be the darkest of all. And its brightness is said to be almost the same as if the disc weren't there at all.
Why a bright spot in the middle of a shadow settled the debate
Waves bend slightly around the edges of objects, spilling a little onto the far side. Every point on the edge of a round disc is the same distance from the centre of its shadow. So the waves bending round from all sides arrive in step — crest meeting crest — making that spot bright.
If light were made of particles, any particle hitting the disc would simply stop — it couldn't get into the shadow at all. The middle of the shadow is the point furthest from the edge. Under the particle picture, there's no way for light to reach it.
In other words, whether the middle of the shadow lights up or not is a question where the two theories give exactly opposite answers. It was a single observation that could settle, once and for all, which one was right.
An opponent's own calculation ended up proving the wave theory
In the early 19th century, the particle theory of light was the mainstream view — it had been believed for over a hundred years as the view held by none other than Newton himself. Even after Thomas Young in England published experiments showing light's wave-like properties, he reportedly faced fierce criticism.
In 1818, the French Academy of Sciences ran a competition for papers explaining how light bends at the edge of a shadow. Among the entrants was Fresnel, an engineer who built roads and bridges. Treating light as a wave, he worked out, in detail, the pattern of stripes that forms at the edge of a shadow.
One of the judges, the mathematician Poisson, was a supporter of the particle theory. He applied Fresnel's theory to a round disc — and the maths said the middle of its shadow should be bright. Poisson is said to have presented this as proof that the theory was absurd. Figure 1 shows, from the side, why this happens.
The committee chair checked — and it really did light up
Arago, the chair of the judging committee, actually tried out this "absurd prediction." He is said to have used a small metal disc about 2 millimetres across, glued to a piece of glass. In a darkened room, lit by a point-like source of light, a sharp point of light appeared right in the middle of the shadow.
Fresnel went on to win the prize, and the wave nature of light became widely accepted. The opponent's own calculation had become the strongest piece of evidence for the theory he opposed. This spot of light is now known as "Arago's spot," or sometimes "Poisson's spot."
Try the slider in Figure 2 to change the distance from the disc to the screen. The further away, the bigger the spot of light gets. Even so, for a disc 2 millimetres across, at a distance of 1 metre, it's only about 0.4 millimetres.
So why don't we normally see this?
You've almost certainly never seen the middle of a coin's shadow light up. There are three main reasons.
First, the sun isn't a point. It's a disc about 0.5 degrees wide in the sky. Light arriving from different parts of the sun creates light spots in slightly different places, blurring them into nothing.
Second, roughness at the edge. The wavelength of light is only about one 2000th of a millimetre. Even a tiny chip in the edge is enough to throw off how the waves line up in the middle. Third, sunlight is a mix of colours, and the spot's size is different for each colour.
This spot of light is said to have already been observed around 1723 by the Italian-born astronomer Maraldi. But without a theory to explain it, it was simply forgotten. It took a theory before the same light could be recognised as "decisive evidence."
Summary
If light is a wave, waves bending round the edge of a round shadow meet in step at its centre and create brightness. If light is a particle, that spot should be pitch dark. Poisson, an opponent of the wave theory, predicted this with his own calculations, and Arago confirmed it by experiment. The spot is tiny, and gets blurred away by any spread-out source like the sun, which is why we never normally notice it.
The spot that should have been darkest of all lit up.
That single point settled what light really is.
Evidence that light is a wave is all around us. Why soap bubbles look rainbow-coloured and why streetlights look like a grid through umbrella fabric both come from the same overlapping of waves. The story of the first measurement of the speed of light can be read in how it was measured using Jupiter's moon.
- Face a bright window or white wall, and hold your index and middle fingers up about 5 cm in front of your eyes.
- Slowly bring the two fingers together until the gap is about as narrow as a sheet of paper.
- If you see several thin, dark lines running parallel to your fingers inside the gap, that's light bending round the edges and overlapping.
To see the light spot itself, you'd need a laser and a tiny steel ball, among other things. Never look into a laser beam or point one at anyone's eyes. Also avoid looking directly at the sun.
Want to know more? ― Terms, formulas, and how this connects to textbooksWe've labelled which level each part belongs to, from middle-school science to university-level courses
- Middle schoolcovered in middle-school science
- High schoolcovered in high-school physics
- High school+advanced high-school content, or a textbook sidebar topic
- Universitynot covered in high school — university-level optics/wave-optics content
- Researchnot even settled "fact" at university level — something researchers are actively investigating
Middle schoolTerminology: this phenomenon has names
- Diffraction: the bending of a wave around the edge of an object, spilling onto its far side. It's the same reason sound reaches you from behind a wall.
- Interference: when two or more waves overlap, reinforcing each other where crests meet, and cancelling where a crest meets a trough.
- Arago's spot (Poisson's spot): the spot of light that appears in the middle of the shadow of a round obstacle.
Middle schoolHigh schoolCheck it with a formula: the size of the light spot
Let's estimate the diameter of the light spot. Take a disc 2 mm across (radius 1 mm), green light, and a screen 1 metre away. All lengths are in millimetres.
| In symbols | d ≒ 0.77 × λ × L ÷ a |
| In words | Spot diameter = 0.77 × wavelength of light × distance to screen ÷ disc radius |
| Where it comes from | Adding up the waves arriving from every point on the edge, near the middle of the shadow, they're all in step at the exact centre, and fall out of step — cancelling — a little further out. The coefficient 0.77 comes from the position of the first point of total darkness (it's the first zero of a Bessel function, 2.405, divided by π). |
| Symbol | Meaning and unit |
| d | Spot diameter (millimetres) |
| λ | Wavelength of light (millimetres) |
| L | Distance from disc to screen (millimetres) |
| a | Disc radius (millimetres) |
| Wavelength of green light λ | 0.0005 mm (0.5 micrometres) |
| Distance to screen L | 1000 mm (1 metre) |
| Disc radius a | 1 mm |
| Apparent size of the sun | approx. 0.0093 radians (about 0.5 degrees) |
| Wavelength × distance | 0.0005 × 1000 ＝ 0.5 |
| Divide by disc radius | 0.5 ÷ 1 ＝ 0.5 |
| Multiply by the coefficient → spot diameter (mm) | 0.5 × 0.77 ≒ 0.39 |
| Compare: blur width with sunlight (mm) | 0.0093 × 1000 ＝ 9.3 |
| Blur width ÷ spot size | 9.3 ÷ 0.39 ≒ 24 |
The spot is about 0.4 mm across. With sunlight, light arriving from different parts of the sun shifts the spot's position by about 9 mm, blurring it over a region about 24 times the spot's size. That's why Arago used a point-like source and a darkened room.
High schoolHigh school+How overlapping waves determine brightness
High schoolIn high-school physics, Young's experiment (the double slit) teaches that two paths differing by a whole number of wavelengths produce brightness. Arago's spot extends that same idea to the entire edge of a disc. At the centre of the shadow, the path-length difference from every point on the edge is zero, so it must always be bright.
High school+Fresnel combined Huygens' principle — that every point on a wavefront acts as a source of new waves — with the idea of waves overlapping. If you divide the area around the disc into concentric rings (Fresnel zones) and add them up, the brightness at the centre of the shadow turns out to be almost the same as if the disc weren't there.
UniversityFresnel diffraction and Bessel functions
In university-level optics, this is treated as "Fresnel diffraction." Applying the Huygens-Fresnel principle (the Fresnel-Kirchhoff diffraction integral) to a disc, the brightness just off the axis turns out to be proportional to the square of the first-kind Bessel function J0. The relationship between the disc's size, the distance, and the wavelength is organised using a dimensionless quantity called the Fresnel number. It was this on-axis brightness that Poisson originally calculated.
📖 For the derivation and further reading: Arago spot (Wikipedia, Japanese) ／ Fresnel diffraction (Wikipedia, Japanese)
ResearchWhat's still not fully understood
- How far does this extend to things heavier than light? The same kind of light spot has been observed with beams of electrons and molecules too. How large and heavy a particle can still show wave behaviour is an ongoing question that probes the boundary of quantum mechanics.
- Precisely estimating the effect of edge roughness. How much a rough edge weakens the spot depends on the exact shape of the roughness, and comparing experiment with calculation is still an active area.
- Blocking out stars to find planets. In plans to block a star's light with a disc floating in space, in order to see a nearby planet, this light spot gets in the way. Petal-shaped discs that eliminate the spot are being investigated.
In other words, even this article describes things "as currently understood." It's certain that light is a wave — but later on, light was also found to behave like a particle, which made the story even richer.
How this connects to textbooks (by level)
| Level | Subject/Unit | Where in this article |
|---|---|---|
| Middle school | Science, "Properties of light" / "Properties of sound" | Light travelling in straight lines and shadows; sound bending round corners |
| High school | Physics, "Interference and diffraction of waves" / "Interference of light" | Path difference and brightness, Young's experiment |
| High school+ | Physics (advanced), Huygens' principle | Fresnel zones, brightness at the centre of a shadow |
| University | Optics / wave optics | Fresnel diffraction, Bessel functions, Fresnel number |
| Research | Matter-wave interference, space-telescope starshades | Light spots with heavy particles, petal-shaped starshades |
| ― | Everyday connections | Dark lines in the gap between fingers, blurring at a shadow's edge |
- Wikipedia, "Arago spot" (アラゴ・スポット, Japanese)
- A. Fresnel, "Mémoire sur la diffraction de la lumière", Mémoires de l'Académie des sciences (prize-winning paper, 1819)
- J. Worrall, "Fresnel, Poisson and the white spot: the role of successful predictions in the acceptance of scientific theories", The Uses of Experiment (Cambridge University Press, 1989)
- E. Hecht, Optics, Pearson
- M. Born, E. Wolf, Principles of Optics, Cambridge University Press
※This article is a general-audience science explainer. The figures given are approximations meant to aid understanding of the underlying mechanism. Details of the historical events (such as the exact size of the disc and the judging process) vary between accounts. If you try any experiment using a laser, take great care to avoid shining it into anyone's eyes.