Why do small rainbow rings appear around the moon?
― The smaller the cloud droplets, the bigger the ring
On an autumn evening, when you're out moon-gazing, a faint rainbow-coloured ring sometimes appears around the moon through thin cloud. This is called a "corona." It forms when light bends around the edges of tiny water droplets in the cloud. Strangely, the smaller the droplets, the bigger the ring becomes.
It's a night for moon-viewing, and as you look up, thin cloud drifts across the moon.
Just as you think the moon might disappear, a round glow blurs into view around it — bluish-white on the inside, reddish-brown on the outside. As the cloud moves, the ring grows and shrinks.
You might recall the old saying, "a ring around the moon means rain." But this small ring is a different thing from that "halo."
There are just two reasons
When moonlight hits a water droplet in a cloud, it bends slightly around the droplet's edge and spreads out. This bending is called "diffraction." The directions where the spreading waves reinforce each other and where they cancel each other out line up as rings centred on the moon.
The smaller the droplet, the larger the bending angle. Also, red light, with its longer wavelength, bends more than other colours. That's why the outer edge of the ring looks red, and clouds with uniformly sized droplets show the clearest colours.
Let's look at this step by step. At the end, we'll also cover how to tell it apart from a "halo."
Water droplets make light "bend around" them
A cloud is a mass of water droplets about a hundredth of a millimetre across. Moonlight doesn't just pass straight through the gaps between them. Because light is a wave, it changes direction slightly at the edge of each droplet and spreads out.
It's the same as ripples on a pond bending around the far side of a post. Where the bent waves overlap crest-to-crest, they brighten; where crest meets trough, they dim. These bright and dark directions form concentric circles around the moon.
Try adjusting the dial in Figure 1 to change the size of the cloud droplets. Make the droplets smaller, and you'll see the ring grow noticeably larger.
Some clouds show clear colours, others don't
The angle light bends through also depends on its colour. Red light, with its longer wavelength, bends more than blue light, with its shorter wavelength. That's why the bluish-white circle of light is bordered in reddish-brown on the outside, followed further out by green and red rings.
But vivid rainbow colours only appear when the cloud droplets are all a similar size. If the sizes vary, each droplet produces a ring of a different size, and they all overlap. The colours blend together, leaving just a hazy white glow around the moon.
Droplets are most likely to be uniform in freshly formed, thin cloud. High clouds arranged like fish scales, or the fast-moving edges of clouds, make good things to watch for. The same mechanism is behind "iridescent clouds," where the cloud itself glows in rainbow colours.
The "halo" of folklore is a ring formed when light bends (refracts) through ice crystals high in the sky. Its radius is always about 22°—roughly the span of an outstretched hand at arm's length. A corona sits right around the moon, with a radius of only a few degrees. The red colouring is also reversed: a halo is red on the inside, while a corona is red on the outside.
On days when cedar or cypress pollen fills the air, a corona sometimes appears around the sun, known as a "pollen corona." Because pollen grains tend to be quite uniform in size, the colours are said to come out especially clearly. Never look at the sun directly, as it can damage your eyes — view it with the sun hidden behind a building or utility pole.
Summary
The small rainbow ring around the moon is a "corona," formed when light bends around the edges of water droplets in cloud. The smaller the droplets, the more the light bends, and the bigger the ring. By measuring the ring's size, you can even estimate the size of cloud droplets you could never reach.
The size of the ring around the moon
is a ruler for the size of cloud droplets.
For more on light spreading as a wave, see the white rainbow in fog, how streetlight looks through umbrella fabric lines up into a pattern, and how a bright spot appears at the centre of a round shadow.
- When thin cloud passes over the moon, look for a bluish-white glow with a reddish-brown edge around it.
- Hold your arm out and raise your thumb; count how many thumb-widths (about 2°) the ring's radius spans.
- As the cloud drifts, watch whether the ring's size and the sharpness of its colours change.
The bigger the ring, the smaller the droplets in that cloud. If the ring is as big as your outstretched hand, it's not a corona — it's a "halo" from ice crystals.
Want to know more? ― Terms, formulas, and how this connects to textbooksWe've labelled each section by level, from junior-high science to university-level courses
- JHSCovered in junior high school science
- HSCovered in high school physics
- HS+Advanced high school content, or a textbook sidebar topic
- UnivNot covered in high school — university-level optics/atmospheric optics
- ResearchNot yet settled even at university level — an active research topic
JHSTerms: this phenomenon has a name
- Corona: a small coloured ring that forms right around the moon or sun, caused by water droplets in cloud.
- Diffraction: the bending of waves around the edge of an obstacle or through a gap. This also happens with sound waves and water waves.
- Halo: a ring with a radius of about 22° formed when light bends (refracts) passing through ice crystals. A different phenomenon from a corona.
JHSHSCheck it with a formula: how big is the ring's radius?
Let's estimate the radius of the ring that green light makes with cloud droplets 10/1000 mm (10 micrometres) across. We'll convert the angle into something tangible by comparing it to the moon's apparent diameter.
| As a symbolic formula | θ ≒ 1.22 × λ ÷ d (θ in radians) |
| In words | Ring radius angle = 1.22 × light's wavelength ÷ cloud droplet diameter |
| Where it comes from | It's the formula for the direction in which light waves bent around a droplet's edge exactly cancel out (the first dark ring). A round droplet produces the same diffraction pattern as a round hole of the same size. |
| θ | Ring radius angle (radians; 1 radian is about 57.3°) |
| λ | Wavelength of light (in micrometres; about 0.55 for green light) |
| d | Cloud droplet diameter (in micrometres) |
| 1.22 | A coefficient that arises for round shapes (determined by diffraction from a circle) |
| Wavelength of green light | about 0.55 micrometres |
| Cloud droplet diameter (example) | about 10 micrometres |
| 1 radian in degrees | about 57.3° |
| Apparent diameter of the moon | about 0.5° |
| Coefficient × wavelength | 1.22 × 0.55 ≒ 0.671 |
| Divide by droplet diameter (radians) | 0.671 ÷ 10 ≒ 0.0671 |
| Convert to degrees | 0.0671 × 57.3 ≒ 3.84 |
| As a multiple of the moon's diameter | 3.84 ÷ 0.5 ≒ 7.7 |
| If the droplet is half the size (5 micrometres) | 3.84 × 2 ≒ 7.7 |
| How many times bigger is a halo (22°)? | 22 ÷ 3.84 ≒ 5.7 |
For a 10-micrometre droplet, the ring's radius is about 3.8°, close to 8 moons laid side by side. If the droplet is half that size, the ring doubles to about 7.7°. A halo is roughly 6 times bigger still, making the two easy to tell apart at a glance.
HSHS+Diffraction of waves, and why the colours separate
HSIn high school physics, you learn about "diffraction," where waves bend around gaps or edges, and "interference," where overlapping waves reinforce or cancel each other. A corona is an example of both happening at once. The formula also shows that longer-wavelength red light produces a bigger ring.
HS+A droplet is an obstruction rather than a hole, but it produces the same diffraction pattern as a hole of the same size. This is called "Babinet's principle." That's why the well-known formula for diffraction through a round hole can be applied directly to cloud droplets.
UnivFraunhofer diffraction and the Airy disk
When parallel light arriving from far away bends around a small circle, it produces a "Fraunhofer diffraction" pattern. The bright central disc is called the "Airy disk," and the angle to its edge is 1.22 × λ ÷ d. The bluish-white circle of a corona is essentially this pattern projected onto the sky. When droplets get close to the wavelength of light in size, this approximation breaks down, and "Mie scattering" theory is needed for an accurate calculation.
📖 For the derivation and further reading: Airy disk (Japanese Wikipedia) ／ Fraunhofer diffraction (Japanese Wikipedia)
ResearchWhat's still not fully understood
- Can ice crystals also produce a corona? There are reports of coronas caused by small ice crystals high in the sky, and researchers are investigating under what conditions this happens.
- The shape of pollen coronas. Pollen coronas are said to sometimes form distorted rather than perfectly circular shapes. How this relates to pollen grain shape and alignment is still being studied.
- Measuring cloud droplet size from a corona. There are attempts to estimate droplet size from a ring's size and colour. But how much of the spread in droplet sizes can be read out this way remains an open research question.
So this article, too, describes things "as currently understood." The ring-size formula is also just a guideline for the case of uniform, round water droplets.
Connections to textbooks (by level)
| Level | Subject/Unit | Where in this article |
|---|---|---|
| JHS | Science, "Properties of Light" / "How Clouds Form" | Clouds as tiny water droplets, differences in light's colours |
| HS | Physics, "Diffraction and Interference of Waves" | Light bending around droplet edges, red light making bigger rings |
| HS+ | Advanced physics, "Babinet's Principle" | Droplets and holes producing the same pattern |
| Univ | Optics / Atmospheric optics | Fraunhofer diffraction, Airy disk, Mie scattering |
| Research | Atmospheric optics / Cloud physics | Ice-crystal coronas, pollen corona shape, estimating droplet size |
| ― | Everyday connection | Telling a corona apart from a halo on a moon-viewing night |
- Corona (Japanese Wikipedia)
- Shibata Kiyotaka, Kō no Kishōgaku (The Meteorology of Light) (光の気象学), Asakura Shoten
- M. Minnaert, "Light and Color in the Outdoors", Springer
- D. K. Lynch, W. Livingston, "Color and Light in Nature", Cambridge University Press
※This article is a general-audience science explainer. The figures given are approximations meant to aid understanding of the underlying mechanism. When viewing a corona around the sun, never look directly at the sun.