Why Are All the Dapples of Light
Under a Tree Perfectly Round?
Scattered across the ground under a row of trees, dappled sunlight forms little round patches. Think about it, and it's strange. The gaps between the leaves are jagged — some triangular, some long and thin — yet every patch of light on the ground is a neat circle. As it turns out, that circle isn't the shape of the gap at all. It's the shape of the sun. What's scattered at your feet is a swarm of tiny "images of the sun."
A summer afternoon, under a row of ginkgo trees. The ground is covered with round grains of light, large and small, swaying and dancing as the wind stirs the leaves.
Look up, and the gaps in the leaves that the sunlight is streaming through are nothing like round. Jagged notches, overlapping crescents, long thin slits. So why does the light that reaches the ground look as if it all agreed, in advance, to be round?
This isn't a new question. 2,300 years ago, Aristotle wrote down the very same puzzle: why does light passing through a square hole come out round?
The answer comes in two steps
When a hole is small enough, the light passing through it stops showing the "shape of the hole" and starts showing the "shape of the light source." This is the pinhole effect — the same principle behind the earliest cameras.
The round dapples under a tree are "images of the sun," projected onto the ground by countless tiny gaps between the leaves. Whatever shape the gap is, every grain of light ends up the same round shape.
"The shape of the hole disappears, and the shape of the light source appears" — let's look at the heart of this puzzle, step by step.
How a tiny hole turns into a "projector"
Light travels in straight lines. Consider light leaving the right edge of the sun, and light leaving the left edge of the sun. Both pass through the same small hole, but because they travel straight, the light from the right edge lands on the left side of the ground, and the light from the left edge lands on the right side.
In other words, a small hole sorts the light coming from each part of the sun into a different spot on the ground. The result of that sorting is that the sun's shape gets faithfully reproduced on the ground (flipped top-to-bottom and left-to-right). This is the pinhole effect, and as long as the hole is only a few millimetres across, the projected image is barely affected by the shape of the hole. The jaggedness of the hole's edge is reduced to a minor role — it only slightly blurs the rim of the image.
The most beautiful proof that "the shape is the sun's shape" comes during a partial solar eclipse. When the moon covers part of the sun and it becomes crescent-shaped, every single dapple of light under the trees turns into a crescent, all at once — even though not a single leaf gap has changed. Next time there's an eclipse, don't just look up (you'll need proper eclipse glasses) — look down at the dapples under a tree too. It's also a safe way to observe an eclipse without any special equipment.
What happens with a big hole?
Of course, sunlight passing through a large opening, like a window, lights up the floor in the shape of the window just fine. A hole only becomes a projector when it's much smaller than the image it would cast. So where's the cutoff?
The rule of thumb is to compare the size of the hole with the size of the sun's image at that distance. The image of the sun works out to roughly 1/100th of the distance from the hole to the ground (the calculation is in the collapsible section). For a gap in a branch 5 m up, the image is about 5 cm across. If the gap is only a few millimetres, it's much smaller than the image, so you get a crisp "photograph of the sun." But if the gap is 10 cm wide, the image loses out to the shape of the gap, and you just get "hole-shaped light." The reason the dapples vary in size from place to place is that the height of the branch (the projection distance) varies. Gaps in higher branches cast bigger, blurrier-edged grains of light.
Summary
Dappled light is round for two reasons. ① A gap just a few millimetres wide sorts light in straight lines and turns into a "projector" that shows the shape of the light source (the pinhole effect). ② The light source being projected — the sun — is round, so every grain of light comes out round. The proof comes on an eclipse day: when the sun is partly hidden, every dapple is partly hidden too.
Dappled light isn't just "ordinary light" passing through gaps in leaves.
It's hundreds of photographs of the sun, scattered at your feet.
For the story of lenses that focus sunlight to a single point and start a fire, see this article. A lens bends light to form an image; a pinhole sorts light in straight lines to form an image. Different tools, but both are, at heart, making "an image of the sun."
- Use a toothpick to poke a small hole (2–3 mm) in aluminium foil or thick paper. Instead of a round hole, try cutting a triangle or star shape on purpose
- On a sunny day, let the sunlight through the hole fall onto a shaded patch of ground or a sheet of white paper, 1–2 m away
- Check that the projected light is round no matter what shape the hole is. Also try moving the paper closer to the hole and watch the hole's own shape appear
※Never look directly at the sun. Only look at the image projected onto the paper. Changing the distance lets you watch the switch from "shape of the hole" to "circle" happen live, so you can find the "cutoff" described above for yourself.
Want to know more? — Terms, equations, and textbook connectionsClearly labelled by level, from lower-secondary science through university-level subjects
- Lower sec.Covered in lower-secondary school science
- Upper sec.Covered in upper-secondary "Physics Basics" / "Physics"
- Upper sec.+Advanced upper-secondary "Physics," or textbook sidebar material
- UniversityNot covered in secondary school — university-level content (optics, ecology)
- ResearchNot yet settled even at university level — an active research question
Lower sec.Terminology: this phenomenon has a name and a history
- Pinhole effect: the phenomenon where a small hole projects an image of the light source. It's the principle behind the pinhole camera.
- Camera obscura: a device in which a small hole in the wall of a dark room projects an upside-down view of the outside scene. It's the origin of the word "camera," and was also used by painters as a sketching aid.
- Real image: an image formed by light actually converging at a point, which can be cast onto a screen. The round dapples under a tree are real images of the sun.
- Aristotle's problem: "Why does sunlight passing through a square hole form a round image?" First raised in ancient Greece, it took nearly 2,000 years to be correctly explained.
Lower sec.Upper sec.Working it out: the size of dappled light tells you the height of the branch
The sun's apparent size (angular diameter) is about 0.5 degrees, or about 0.0093 radians. The size of the image is simply this angle multiplied by the projection distance.
| Sun's angular diameter (radians) | About 0.0093 (roughly "1/100th of the distance") |
| Distance from hole to ground | Take it as 5 m |
| Diameter of the image (dapple) | 5 × 0.0093 ≒ 0.047 (m) = about 5 cm |
| Dapple diameter measured on the ground | Say 9 cm = 0.09 m |
| Distance to the branch (gap) | 0.09 ÷ 0.0093 ≒ 9.7 (m) |
Just by holding a ruler up to a dapple of light, you can measure the height of a branch you could never reach by looking up alone. Ancient peoples used the same principle, measuring the sun's angular diameter from images cast by a camera obscura.
| Image size at 5 m height | About 47 mm (from ①) |
| Size of the leaf gap | Take it as 3 mm |
| Image is how many times the hole size | 47 ÷ 3 ≒ 16 (times) |
Since the image is far bigger than the hole (10x or more is the rule of thumb), the hole's shape leaves almost no trace on the image. Conversely, a 10 cm gap is bigger than the 47 mm image, so the light keeps the "shape of the hole." That's why sunlight through a window is window-shaped.
Upper sec.Upper sec.+Why did it take 2,000 years?
Upper sec.At the heart of the explanation is the combination of "light travels in straight lines" and "the sun is not a point but an extended source." Each point on the sun casts a "hole-shaped" patch of light onto the ground through the gap, and when countless "hole shapes" overlap, each shifted by about 0.5 degrees, the overall outline converges on the shape of the sun (a circle). The image is the result of that overlap.
Upper sec.+The geometrically correct formulation of this "overlap from an extended source" is credited to Ibn al-Haytham in the 11th century, and to Kepler in the 16th–17th centuries. In the course of this analysis, Kepler established modern optical terms like "focus" and "ray." In a sense, the puzzle of dappled light helped give birth to the science of optics.
UniversityShrink the hole too far, and it blurs again: diffraction
By geometry alone, "the smaller the hole, the sharper the image" — but in reality, shrink the hole too far and the wave nature of light (diffraction) starts blurring the image again. The hole diameter that gives the sharpest image is roughly the square root of the product of the wavelength and the distance (√(λL)); at a distance of 5 m in visible light, that works out to about 1.5 mm. The typical size of a gap between leaves happens to sit close to this optimum. Dappled light looks unexpectedly sharp partly because nature's own holes happen to be "just the right" size.
ResearchStill being studied: dappled light as the forest's "food delivery"
- How do forest-floor plants make use of moving dapples of light? Much of the light reaching a forest's understorey arrives as "sunflecks" — dapples that flicker for a few seconds to a few minutes as the wind moves the leaves. How well plants can exploit this "patchy, fickle light" for photosynthesis is an active area of research into the speed of photosynthetic responses. Evidence is building that species able to switch quickly to strong momentary light have an advantage on the forest floor.
- How to estimate a whole forest's photosynthesis. When satellites and climate models calculate a forest's productivity, the level of detail used to represent the patchiness of dappled light is known to change the results, and models are still being refined.
- The physics of flicker. The flickering of dappled light combines the motion of the leaves, atmospheric turbulence, and the brightness distribution across the sun's face (dimmer toward the edge). Quantitative analysis of this combination is studied as a topic in eclipse observation and atmospheric optics.
In other words, even this article describes "the explanation as currently understood." The question at Aristotle's feet now extends all the way to calculations of forest ecosystems.
Connections to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Lower sec. | Science / straight-line propagation of light, observing the sun | How the pinhole works, Figure 1, calculations ① ② |
| Upper sec. | Physics / how light travels, real images | Explanation via overlapping images from an extended source |
| Upper sec.+ | Physics / advanced optics, history of science | 2,000 years from Aristotle to Kepler |
| University | Optics (diffraction) / forest ecology | Optimal hole diameter √(λL), sunflecks |
| Research | Plant physiological ecology / atmospheric optics (ongoing) | Photosynthetic response to dynamic light, physics of flicker |
| ― | Everyday connections | Safe ways to observe an eclipse, the hole experiment, working out branch height |
- National Astronomical Observatory of Japan (国立天文台), explanatory material on how to observe solar eclipses (safe pinhole-projection observation, dappled-light crescents).
- Standard optics textbooks (pinhole imaging, optimal aperture diameter from diffraction).
- Lindberg, D. C., Theories of Vision from al-Kindi to Kepler, University of Chicago Press, 1976 (history of science on Aristotle's problem and the camera obscura).
- Way, D. A. & Pearcy, R. W., Sunflecks in trees and forests: from photosynthetic physiology to global change biology, Tree Physiology 32(9), 1066–1081, 2012 (review of sunfleck research).
※This article is a general-audience science explainer. The figures given are approximate, meant to help you understand the underlying mechanism. Never look directly at the sun. Always use proper eclipse-viewing equipment, or a projection method like the one described here, to observe a solar eclipse.