Rainbows and Their Cousins

Here at PVL we do love atmospheric optical phenomena! I can report that, more than once, we were headed somewhere as a group and got delayed by particularly impressive parahelia, arcs or other interesting effects. While they often go unnoticed, such effects are more common than you might imagine. Robert Greenler, author of the lab-favourite "Rainbows, Halos and Glories" estimates that you can see at least one of the effects Alex describes below on about one day in three. So the next time you are outside: look up, fair reader, and take a glance a few tens of degrees from the sun! You might be surprised and impressed with what you find.

By Alex Innanen

It’s pride month, which means everything is decked out in rainbows from street corners to store shelves, and also I’ve been thinking about rainbows all month. So for your education and enjoyment some pictures of rainbows and other pretty atmospheric optics, and some of the science behind them.

 
A quick overview about the visible light spectrum: We all know that white light is made up of the colours of the visible spectrum which spans from red to violet. When Newton performed his experiments with prisms he identified seven colours – the classic ROYGBIV – but in truth the spectrum is continuous, and in fact those whose languages have fewer colour terms will actually perceive the divisions between colours differently (this is really really cool and unfortunately outside the scope of this post, and also I’m not a psychologist but there’s a nifty paper on it). IF you’ve ever listened to Pink Floyd or possibly performed an elementary school science experiment, you know that passing white light through a prism splits it up into the rainbow. This is because light refracts, or bends, when it goes from one medium to another such as air to glass. When light encounters the glass of a prism it moves slower, and the angle that it refracts is based on both the index of refraction of the material and the specific wavelength. Red has the greatest wavelength and is refracted at a smaller angle than blue. If the differences in angles of refraction are large enough, the different colours will ‘spread out’, or disperse.

The windows in the Pioneer Village subway station at York disperse light quite nicely, and I used to look out for rainbows on the stairs back when I did things like take the subway.

The refraction and dispersion principles above apply to meteorological rainbows – just within a water droplet as opposed to a glass prism. When light enters the droplet, it is refracted. Some of the light is then reflected off the back of the droplet and passes back out of the droplet. If we add these angles together, we get a concentration of rays emerging at about 42° from the droplet. Wikipedia has a helpful diagram of this: 

You can see that red light is at about 42°, but violet light, which has a greater angle of refraction, emerges from the droplet at an angle of about 40° – this dispersion gives us the rainbow. The rainbow at the top of this post – taken by my mum – shows another nifty property of rainbows. The sky inside the bow appears lighter than the sky outside – this is because 42° is the maximum angle for single reflection, but light is getting reflected out at angles lesser than that, just not as concentrated as it is at this maximum. 

I say single reflection – you’ve probably seen what’s commonly called a ‘double rainbow’ (see the gorgeous picture my friend Lizzie took of a desert rainbow below). The secondary rainbow, outside the primary, is always there but is often too faint to see. You’ll also notice that the order of the colours is reversed, with red on the inside and violet on the outside. The secondary rainbow is due to double reflection in the rain droplet; as light reflects more, more light is able to escape, hence the secondary rainbow being fainter than the primary. The reversal of the colours also creates the phenomenon known as Alexander’s Band, the darker band between the two bows, the same mechanism that makes the inside of the primary bow brighter also makes the ‘outside’ of the secondary bow brighter. The band between the two, consequently, is unlit by reflected light.

Rainbows aren’t the only way the atmosphere plays with light. Cloud droplets or small ice crystals can colour the clouds themselves – an effect called cloud iridescence, similar to iridescence from oil on water, or irisation, named for the Greek goddess of rainbows. It’s caused by the droplets or ice crystals diffracting sunlight, and unlike a rainbow, which is viewed in the sky opposite the sun, it occurs within a few tens of degrees to the sun.

 

 An iridescent cloud I saw in summer of 2018. I’ve turned up the saturation a smidge to show the colours better from my quick cell-phone picture.

Larger ice crystals can create their own host of atmospheric wonders. Water-ice crystals in high, wispy cirrus clouds can act like tiny prisms, refracting light into all sorts of configurations. The picture below is of a halo my friend Kayla captured.

The most common halo has an angular radius of 22° around the sun or moon and is produced by hexagonal ice crystals in random orientations. When light passes through a prism, it refracts by some deviation angle, which for a hexagonal water-ice crystal has a minimum of 22°. Similarly to the concentration of reflected rays at 42° for a rainbow, we get a concentration near this minimum angle for randomly oriented crystals. Also similarly to the rainbow, red light deviates less than other wavelengths. This gives the reddish inside edge of the halo you can see in Kayla’s picture. We don’t, however, get the rest of the spectrum like we do with a rainbow. As we move further from 22°, the colours overlap more, giving us a white outer ring. 

If 22° halos have more-or-less randomly oriented ice crystals, what happens if many crystals align in a certain way? If rod-shaped hexagonal crystals have their long axis aligned horizontally, you get what are called upper and lower tangent arcs, arcs which touch the top or bottom of the 22° halo but have different curvatures (I don’t have any pictures but look them up – they’re nifty). The curvature is dependent on the angle that the sun is above the horizon, and sometimes you can even have the tangent arcs curve around and enclose the halo in a kind of squashed ring – called a circumscribed halo –  touching the halo only at the top on bottom. 

If we take flat, plate hexagonal crystals, as they fall through the air, they tend to orient themselves horizontally, like a piece of paper falling. When light refracts from these oriented plates, as opposed to from crystals at a variety of orientations, we see brighter spots at the sides of the halo, or sometimes just these spots alone. These are known as sun dogs, or parhelia. 

 

My dad captured these sun dogs on New Year’s Eve several years ago.

The sun dogs, like the halo, are red on the inside, progressing through to a white streak which you can see on the left-hand sundog where the colours overlap. 

Oriented plate crystals can also reflect light leading to streaks of light appearing to extend vertically from a light source, known as light pillars, or, when caused by the sun, sun pillars. An observer sees sunlight reflected off many crystals either above or below the sun, which appear to be a column, getting wider and more disperse the further it is from the sun. You can see this in my final image below – taken from out back of the Bergeron Centre at York one late winter exam evening. 

 

There are so many more optical phenomena which could probably fill several blog posts (Brittney has already talked about Heiligenschein, if you want to scratch that scattering effect itch), and a lot of the effects I discussed are fairly common. So keep looking up, or if you’re craving a quick rainbow, the garden hose works nicely.