Why Do the "False Suns" Beside the Sun (Sundogs) Always Sit 22 Degrees Away?
― Hexagonal ice plates floating in the sky bend light by exactly 22 degrees
On a winter morning or evening, small rainbow-tinted patches of light sometimes appear on either side of the Sun. They are called sundogs. The light comes from hexagonal ice plates floating high in the sky. Each plate acts as a tiny prism and bends light by about 22 degrees. The plates also float flat, like falling leaves, all lined up horizontally. Put these two facts together and light gathers at just two spots, directly left and right of the Sun.
It is a clear winter evening. A thin, veil-like white cloud hangs in the western sky.
You glance up and see one more bright light on each side of the setting Sun. They are smudged patches, red on the side nearest the Sun and whiter further out.
Some people photograph them and say, "There are three suns!" But the side lights always sit about the same distance from the Sun. Stretch out your arm and spread your hand: the distance is about the width from thumb tip to little-finger tip. Why is it a fixed distance?
Only two reasons
Ice crystals in clouds are hexagonal, just like snowflakes. When light enters through one face and leaves through every-other face, it is the same as passing through a prism with a 60-degree corner. The bending angle can never be smaller than about 22 degrees. Light piles up most at that minimum angle.
Flat, plate-shaped ice falls with its broad face downward because of air resistance. When all the plates are horizontal, light is bent only sideways. So only two points, left and right of the Sun at the same height, turn bright.
The first reason decides "how many degrees away," and the second decides "where it appears." Let's take them in order.
Why does light gather at "22 degrees"?
Light passing through a prism is bent. How much it bends depends on the direction the light hits the prism. But whatever the direction, the bending angle has a lower limit. For ice, that limit is about 22 degrees.
With many ice crystals pointing every which way, the bending angles vary. But near the lower limit, a small change in direction barely changes the bending angle. So lots of light overlaps near 22 degrees. Inside 22 degrees, no light arrives at all. That is why the inner edge of a sundog is sharp.
The colours separate because each colour bends a little differently. Red light bends less, and blue light bends more. So red lands slightly inside (nearer the Sun) and blue slightly outside. The left side of Figure 1 shows the light's path through the ice.
Why two spots on the sides, and not a ring?
If the ice crystals pointed in random directions, light would be bent 22 degrees in every direction. That makes a ring of 22-degree radius centred on the Sun. This is the halo, shown at the bottom right of Figure 1.
Flat hexagonal plates, however, are pushed by the air as they fall and turn their broad face downward. It is like dropping a sheet of paper: it flutters, yet tends to fall face-down. When all the plates are horizontal, light passing through their sides can only be bent horizontally. So of the whole ring, only the two spots at the Sun's own height, left and right, turn bright. These are the sundogs.
As the Sun climbs, sundogs slip outward
In fact, "always 22 degrees" holds exactly only when the Sun is near the horizon. When the Sun is higher, light enters the plate from obliquely above. The path through the plate changes, and the prism bends the light more strongly than before.
As a result, the higher the Sun, the further the sundogs move outside the 22-degree halo. Above a Sun height of about 61 degrees, light can no longer leave the plate and the sundogs vanish. Part of why sundogs are so noticeable on winter mornings and evenings is that the Sun stays low for long stretches. Use the slider in Figure 2 to change the Sun's height.
Sundogs are often thought of as rare. But on mornings and evenings with thin cloud (cirrostratus or cirrus), they turn out to be fairly common. Most people miss them because they don't try to look right next to the dazzling Sun. Block the Sun with your hand or a building, and look to its left and right.
Even when hunting for sundogs, staring at the Sun itself can damage your eyes. Always block the Sun with your hand or a building first, then look at the sky around it. Looking at the Sun through binoculars or a camera viewfinder is also dangerous.
Summary
A sundog is light made by hexagonal ice plates floating high in the sky. Each plate acts as a 60-degree prism and bends light by at least about 22 degrees. Light piles up near that 22 degrees. Because the plates also line up flat, the light gathers at only two points, left and right of the Sun at the same height. When the Sun rises, the sundogs move outward beyond 22 degrees.
The 22 degrees of the "false sun"
is the lower limit of light's bending angle, set by hexagonal ice.
How small rainbow-coloured rings form around the Moon is explained in Why do we see rainbow-coloured rings around the Moon?, and why snow crystals are hexagonal is explained in the article on snow crystals.
- Hold your arm straight out and spread your hand wide. From thumb tip to little-finger tip is said to be roughly 20 degrees.
- On a morning or evening with thin white cloud, hide the Sun behind your thumb tip (never look at the Sun directly).
- Look near your little-finger tip. If you see a smudged patch of light that is red on the Sun side, it is a sundog. Do the same on the other side and check whether there is one on each side.
If you find one closer to midday, check whether the sundog has drifted farther out than one hand-width. The higher the Sun, the farther out it should be.
For those who want more ― terms, formulas and links to textbooksEach part is labelled with its level, 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 material, or textbook sidebars
- UniversityUniversity-level courses (optics, atmospheric optics) not taught in high school
- ResearchTopics researchers are still investigating, not yet taught as settled
Middle schoolTerms: this phenomenon has names
- Sundog (parhelion): patches of light at the same height on either side of the Sun. They come from refraction by horizontally aligned, plate-shaped ice crystals.
- Halo (22-degree halo): a ring of light of about 22 degrees radius around the Sun or Moon. It comes from refraction by randomly oriented ice crystals.
- Refraction: the bending of light's path at a boundary when it passes from air into ice or water. It is a property of light taught in middle school.
- Minimum deviation: the smallest value of the angle (deviation) by which a prism bends light. The 22 degrees of sundogs and halos is this.
Middle schoolHigh schoolChecking with a formula: how much does an ice prism bend light?
For a prism with apex angle A, we find the angle at which light is bent least (the minimum deviation). Every-other face of a hexagonal ice crystal forms a prism with a 60-degree apex angle.
| In symbols | D ＝ 2 × arcsin( n × sin( A ÷ 2 ) ) − A |
| In words | Minimum deviation ＝ 2 × (the angle whose sine is refractive index × sine of half the apex angle) − apex angle |
| Where it comes from | Apply the law of refraction (Snell's law) twice, at entry and exit, then impose the condition that light passes symmetrically through the prism (when the bending is smallest) |
| D | Minimum deviation (degrees). The lower limit of the angle by which light is bent from its original direction |
| n | Refractive index of ice (no unit). How strongly light bends relative to air |
| A | Apex angle of the prism (degrees). 60 degrees for every-other face of a hexagon |
| arcsin | The operation that recovers an angle from the value of its sine |
| Apex angle A (every-other face of the hexagon) | 60 degrees |
| Refractive index n of ice (mid-range visible colour) | Taken to be 1.31 |
| Sine of 30 degrees | 0.5 |
| Angle whose sine is 0.655 | About 40.9 degrees |
| Half the apex angle | 60 ÷ 2 ＝ 30 |
| Refractive index × sine of 30 degrees | 1.31 × 0.5 ＝ 0.655 |
| Double that angle (about 40.9 degrees) | 40.9 × 2 ＝ 81.8 |
| Subtract the apex angle to get the minimum deviation | 81.8 − 60 ＝ 21.8 |
Light is bent by at least about 21.8 degrees. This is the origin of "22 degrees." For red light (index about 1.307) it is about 21.6 degrees, and for blue light (about 1.317) about 22.4 degrees. That is why red lies on the inside.
| Width of a spread hand at arm's length | About 20 degrees |
| Apparent diameter of the Sun | About 0.5 degrees |
| Distance to the sundog divided by the Sun's size | 21.8 ÷ 0.5 ≒ 44 |
A sundog appears about 44 Sun-widths to the side. Remember it as "a little beyond one hand-width" and it will be easier to find.
High schoolHigh school+Why is the "minimum" the bright place?
High schoolIn high-school physics you learn that changing the angle at which light enters a prism changes the deviation, and that it is smallest at one particular angle of incidence. At that minimum, a small change in the incidence angle hardly changes the deviation. Light from many incidence angles overlaps at the same deviation, so that direction looks bright. The rainbow's roughly 42 degrees is explained by the same kind of extremum in the bending angle inside a water drop.
High school+When the Sun is high, light enters the plate's side face obliquely. Looking only at the horizontal bending, this behaves like a prism with a larger refractive index than the real one. This apparent index is called the "Bravais index," and with the Sun's height h it is written √( n² − sin²h ) ÷ cos h. The motion in Figure 2 is computed from this formula. When the apparent index exceeds 2, light can no longer leave the plate, which corresponds to a Sun height of about 61 degrees.
UniversityAtmospheric optics: the halo family
Light phenomena caused by ice crystals in the atmosphere are collectively called halos. In university atmospheric optics, the patterns that appear are worked out by ray tracing for each combination of crystal shape (plate or column) and orientation (horizontal, random, or spinning). A combination of a plate's base and side faces (apex angle 90 degrees) gives the 46-degree halo, and light reflected from the top face of horizontal plates gives the sun pillar. When light is reflected two or more times inside horizontal plates, it forms the parhelic circle, which runs all the way around the sky at the Sun's height.
📖 Derivations and further reading: Sundog (Wikipedia) ／ Halo (Wikipedia) ／ Snell's law (Wikipedia)
ResearchWhat is still not clearly known
- How well aligned are the plates? From the spread of sundogs, the scatter in the plates' tilt is thought to be within a few degrees. But directly measuring the motion of crystals that wobble as they fall is hard, and differences by size and shape are still being studied.
- What crystals make the rarely seen halos? For some of the arcs that appear only rarely, opinions differ on which crystal shape and orientation cause them.
- Cirrus crystal shape and Earth's temperature. The shape of the crystals changes how much sunlight a cloud reflects. How to include cloud effects in climate predictions is still considered a major challenge.
So this article, too, is "an explanation within what is known today." The 22-degree figure is solid, but what form the ice crystals take as they drift in the sky still leaves room for investigation.
Links to textbooks (by level)
| Level | Subject and unit | Where in this article |
|---|---|---|
| Middle school | Science Year 1 "Refraction of light," Year 2 "How clouds form" | Light bending inside ice; high-altitude clouds being made of ice |
| High school | Physics "Refraction, dispersion and prisms" | Calculating minimum deviation; why red lies inside |
| High school+ | Advanced physics (rainbows, prism extrema) | Why light gathers at the minimum; the Bravais index |
| University | Optics, atmospheric optics, cloud physics | Classification of halos, the 46-degree halo, the parhelic circle |
| Research | Cloud physics, climate science | Scatter in crystal orientation; cirrus and climate |
| ― | Links to daily life | Watching the sky on winter mornings and evenings; thin cloud as a clue to changing weather |
- Wikipedia, "Sundog" (幻日)
- Wikipedia, "Halo" (暈)
- Walter Tape, "Atmospheric Halos", American Geophysical Union (1994)
- Robert Greenler, "Rainbows, Halos, and Glories", Cambridge University Press (1980)
- David K. Lynch, William Livingston, "Color and Light in Nature", Cambridge University Press
* This article is a general-audience science explainer. The figures given are rough guides to help you understand the mechanism. Never look directly at the Sun, or at the Sun through binoculars or a camera.