Sun, sky and colour: the optics of weather

Its a lazy summer evening by the lake. The Sun melts from its usual yellow into a blazing red as you watch it set over the water. As the bottom of the Sun noses below the horizon, the whole sphere seems to enlarge and flatten, as if somebody were stretching it against the land Finally, the uppermost sliver of the Sun starts to disappear, and a twinkle of green light appears at the last second.

You've just seen the optics of the atmosphere at their most dramatic – and illusory. The Sun is actually neither yellow, nor red, nor green. It doesn't really expand as it sets; instead, the atmosphere bends and spreads sunlight to make it appear so. And by the time you saw the base of the Sun hit the horizon, the entire sphere was already below your line of sight; the atmosphere's bending of solar rays allowed you to watch the Sun even after it set. Like the reflections in a carnival fun house, the colour and light we see in the sky aren't always what they seem.

Blue skies, sort of

Several things happen to rays of light as they complete their eight-minute journey from the Sun and pass through our molecule-laden, particle-cluttered atmosphere. First and foremost, they get scattered. One way of visualizing a ray of light is as a series of waves, with peaks that are separated by a constant distance. The colour of the light depends on the distance between those peaks – a number known as the wavelength. Visible light includes wavelengths as low as 400 nanometres (violet) to as high as 700nm (red). A nanometer is one billionth of a metre, or about forty billionths of an inch.

In between these extremes are the other familiar colours of the rainbow: blue, green, yellow and orange, in order. Flanking the visible spectrum on either side are the invisible wavelengths of ultraviolet (less than 400nm) and infrared (greater than 700nm). With a little help from the atmosphere, this distribution of light explains why the sky is blue. If a ray of incoming sunlight hits a particle whose diameter is much smaller than the light's wavelength, the light gets scattered in all directions, including toward Earth, and the scattering is greatest for the shortest wavelengths. This is the case for nitrogen and oxygen molecules, which make up the bulk of the atmosphere. They're only a few nanometers across, a tiny fraction of the wavelengths of visible light. Thus, the bulk of the scattered light falls at the lower end of the visible spectrum. Violet has the shortest wavelength, but sunlight delivers much more energy in blue – the next colour up the spectrum – so blue is the overall colour we see scattered toward us when we look up on a clear day.

Of course, the rich indigo above a mountain meadow isn't the same as the copper haze above a polluted city. When the air is hazy or dirty, it's full of many more large particles than you find in clean, clear air. This means that more of the sunlight is scattered – not just the smaller violet and blue wavelengths, but other colours as well This pushes the blend of skylight away from a deep blue and toward paler, lighter shades. When soot and other visible particles are present, they add their own colour to the mix.

AU about rainbows

Since water and ice are ideally transparent, they allow light to do a whole host of interesting things. The mechanism behind the beauty of the rainbow was explained hundreds of years ago in a tag-team effort by Rene Descartes and Isaac Newton. Descartes, the French philosopher-scientist, theorized in 1637 that the rainbow was produced by sunlight reflected toward a viewer by raindrops. Descartes was on target as far as he went, but he couldn't correctly explain why the rainbow had colours. Newton, through his innovative experiments with glass prisms in 1666, showed how raindrops separate light into the familiar colours of the rainbow. The full spectrum of visible light is usually interpreted as seven bands, corresponding to seven wavelength regions – red, orange, yellow, green, blue, indigo and violet. Newton added indigo to the list largely for philosophical rather than perceptual reasons. Actually, rainbows have an indefinite number of hues. Through a cognitive process called metamerism, it seems we tend to clump the colours across this continuous spectrum into the rainbow bands we perceive.

The sunlight enters a raindrop, tiny variations in the entrance angle translate into a separation of hues as the light reflects and exits the drop. If conditions are right, the colours show up as a rainbow across the sky from the sun.

It's easy to know where to look for a rainbow: opposite the Sun, against a shower or thunderstorm. In the mid-latitudes, most rainbows occur in the late afternoon and evening, when the Sun is toward the west and the departing storm to the east. More rarely, a storm will approach in the early morning and trigger a rainbow in the western sky.

If you imagine an arrow going from the Sun directly through your head and onward, it would point to the imaginary centre of a rainbow's arc. The angle from that line to the arc itself is always 42°. To explain that number, you have to look inside a raindrop. When sunlight enters a raindrop, some of it bounces off the back of the drop and re-emerges on the same side it entered, but at an angle. This angle is a little different for each entrance point, but a good deal of the existing light is clustered around an angle of 42° from the entering light. The wavelengths that produce the colours of the main or primary rainbow each emerge at slightly different angles close to 42°, thus yielding the familiar bands, with red always at the top.

A careful rainbow-watcher will notice several quirks that can be easily explained Rainbows tend to be brighter along their legs, near the ground, than at the top of their arcs; this is a result of the shape of raindrops. As we'll see in the Rain section, most large raindrops don't actually resemble teardrops. Since these squashed drops are flatter than they are tall, the reflections in the vertical dimension (which produce the top of the rainbow) are less focused than those in the horizontal (which produce the rainbow's feet). The brightness and crispness of the entire rainbow depends on the density and character of the raindrops, as well as the clarity of the atmosphere in between rainbow and viewer.

Sometimes a rainbow has a twin, a fainter arc well above the main bow. This outer or secondary rainbow is produced by light that's reflected not just once, but twice, within different drops than the ones that produce the main rainbow. The secondary rainbow is always angled at 51° from the imaginary centre point discussed above. Because of the extra reflection that turns each ray of rainbow light more than 180°, the secondary rainbow's colours are reversed: red appears at the bottom, violet at the top.

Much white light gets reflected toward the violet side of a rainbow. Thus, you may notice that the sky beneath a bright single rainbow is noticeably lighter than the sky above it Likewise, the sky above a secondary rainbow is slightly brighter than the sky between the bows. The in-between region is called Alexander's dark band, after the sharp-eyed Alexander of Aphrodisias.

In theory, at least, the rainbow family extends beyond twins. Light that's reflected three times within a drop should produce a third rainbow – but it would appear across the sky from its siblings, around the Sun itself. Since this third rainbow would be even fainter than the first two to begin with, the chances of seeing it amid sunlight are basically nil. Only a handful of sightings have ever been reported.

Haloes and glories

Rainbow-like features paint the sky in several other ways. When the Sun or Moon is behind a thin sheet of cirrus cloud, it may be encircled by a halo, typically reddish-yellow at its inner edge and whitish beyond. Like rainbows, haloes are produced by light passing through airborne water, but in this case the water is frozen. The ice clouds that produce most haloes are made up of six-sided plates and pencilhaped crystals. Light that enters these crystals departs at a variety of angles, and the crystals themselves may be oriented randomly. Still, there's a concentration of light close to a 22° angle from the Sun or moon. As with rainbows, haloes can occur at other angles, too.

The plate-shaped crystals aren't always mixed up grab-bag style; larger ones fall nearly flat. In this case, the visible reflections occur mostly along a horizontal line passing through the Sun. These are sun dogs – small, bright patches, often in rainbow colours, that flank the Sun on either side at a 22° or greater angle. Since they're formed by a more organized array of crystals than those that produce haloes, sun dogs can feature more well-defined colours, although they don't normally approach the brilliance of rainbows.

Some very different rings of light – the glory – may be one inspiration for what artists have placed around the heads of spiritual icons for centuries. When a plane flies above a cloud bank on a sunny day, a small, roughly circular ring – usually in very pastel shades of red – may form around the plane's shadow. It's caused by diffraction: the interactions of sunlight at various wavelengths and angles hitting the faintly obscured area around the plane's distinct shadow. Even though the shadow reduces the total amount of light, cloud droplets can return some of the remaining light and, ironically, make this region brighter and more colourful than the areas in direct sun. The width of a glory depends on the size of the water droplets within the cloud; some glories are concentric. Halo-painting artists may also have been inspired by the more common heiligenschein, a bright light seen immediately around the shadow of your sunlit head on a variety of wet and dry surfaces.

Long before airplanes existed, glories were created by people perched on mountaintops. If you stand on a peak with the Sun at your back and a cloud bank below, you might see a huge-looking, elongated shadow of your body on the cloud, with a ring of glory surrounding your head. It's easy to believe that myth-makers drew on this spectacular effect in depicting the holiness of Christian angels, Greek gods and Indian icons.