22 degree halo – Bean Thinking

What do you notice about this iced latte? The cup is rich with physics, but for this post, the important bit is the floating ice on top.

A coffee should be a time for relaxation, for reflection. As we come to the end of summer here in the northern hemisphere, we may want to enjoy one last iced coffee before we return to the warming coffees of winter. If on the other hand you are reading this from the southern hemisphere, the equatorial region, or some time after it was originally posted, you may be just starting to enjoy your iced coffees again. Either way, ice is remarkable and it is good to make some time to enjoy it. One of the things that makes it remarkable is what seems to be its very ordinariness: it floats.

Ice floats because the solid form of water is less dense than the liquid form. This is actually fairly unique to water. Most liquids get more dense as you cool them. As they transform into solids, they get denser still. This would mean that if you were to cool a liquid until it starts to solidify, the solid would sink, not float, on the liquid. If water were like most other liquids, all the ice in our iced-coffee would be at the bottom, not jiggling at the top. In addition to what would be an almost aesthetic problem for the coffee, this has consequences for life itself. When a lake or a pond freezes over, the fish and other aquatic life, can survive under the ice in the denser water. This odd property of water has helped life to evolve.

The reason for this strange behaviour lies in the way that water molecules bond together. Each water molecule can bond to a neighbour through a hydrogen bond. This optimises the structure to a layered form of well spaced hexagons (link here for an interactive model of water ice). Each corner of the hexagon is an oxygen atom. The size of the hexagon means that, if they weren’t arranged into a regular lattice, the water molecules could get closer together than they do in the solid phase. Which is another way of saying that the liquid can get more dense than the solid. Ice will float on water.

The layered structure of the ice crystals also means that each hexagonal face will tend to glide over the one below it or above it. It is this property of ice that means that we can determine the direction of glacial flow in centuries past. When fresh snow falls on top of a glacier, the density of the snow layer is about 50-70 Kg/m3. For comparison, the density of water is 1000 Kg/m3. Although each snow crystal is hexagonal, they have random orientation as they fall. As new snow falls, it pushes down on the old snow and compacts it until, about 80m down into the glacier, the density of the (now) ice is 830 Kg/m3. As the depth increases still further, the density increases to 917 Kg/m3 which is as dense as a glacier can be but is still much less than the density of water; a glacier would float. When the snow crystals are pressed down, the hexagonal layers of ice will glide past each other in the direction of push and the crystals will re-orienate. They will also grow as they merge with other crystals and as a result of the heat from the bedrock beneath them. This means that deep in the glacier, more of the crystals will be orientated in the direction of the push. Taking a vertical core of ice and looking at the orientation of the crystals in 0.5mm thick cross sections therefore reveals how they have been pushed as a function of depth. This in turn reveals which way the glacier has flowed in the past.

Sun-dog, Sun dog — A ‘rainbow’ of colour as seen in a ‘sun dog’ observed in central London. Note the order of the colours.

The structure of ice has one other surprise for those of us who are enjoying more coffee outside. Depending on the weather conditions, high up in the atmosphere, hexagonal ice crystals form. Because they are hexagons, they are, in effect, a section of a 60 degree prism. This means that light entering through one face, will be refracted twice to emerge from the crystal at 22 degrees relative to where it came from. If there are enough of these crystals high in the atmosphere, a bright circle will form around the Sun. For reasons that are probably obvious, it is known as the 22 degree halo. It seems fairly difficult to observe this halo. What is far more common to see are two bright regions of light at the 9 o’clock and 3 o’clock positions on the halo. In addition to being brighter than the rest of the light circle, these two regions often appear like a ‘rainbow’, but with the red on the inside of the halo and the blue on the outer edge. Known as “sun dogs” or parhelia, they too are a consequence of the ice crystals. As the ice crystals fall, they are more likely to fall flat so that each hexagonal face is horizontal. More of these ice crystals means that there is going to be more light refracted at the position horizontal to the Sun and so the light there is intense. They appear as separated colours for the same reason that the colours disperse with a prism: each wavelength of light has a very slightly different refractive index and so gets ‘bent’ by a slightly different amount. The ice crystals are bending the red a bit less than the blue.

This is a good time of year to keep an eye out for Sun dogs and haloes. And if we can do so while enjoying a well made iced coffee with the ice cubes floating at the surface, all the better.

Please do share any photographs you have of coffee with 22 degree haloes or sun dogs, either here or on Facebook or Twitter.

What haloes and crowns reveal about your coffee

Coffee Corona — Look carefully around the reflected white light. Do you see the rainbow like pattern?

Several weeks ago I had been enjoying some very good black coffee at OJO in Bangsar, KL. As is fairly typical for me, I had been trying to observe the white mists that form just above the coffee. White mists are fascinating, tissue-like clouds that you can often see hovering above the coffee. They form, tear suddenly and then reform into a slightly different pattern. As I was photographing my coffee, I noticed what seemed to be interference patterns on the mists (see picture), just like oil on water, a rainbow-like shimmering over the coffee surface. Yet that explanation did not make sense; interference patterns form because the layer of oil on water has approximately the same thickness as the wavelength of visible light (see more info here). The water droplets that make up the white mists are a good 15 times thicker than the wavelength of light. It is not possible that these mists are producing interference effects, it has to be something else.

Then, last week and back in London, I was walking towards the setting Sun one evening when I saw what looked like a rainbow in a cloud. What caused this and how was it related to what I had seen earlier in my coffee? A short trip to the library later and it was confirmed. What I had seen in the clouds was most likely a Sun-dog. Formed by the refraction of sunlight by ice crystals in the atmosphere, Sun-dogs manifest as bright regions of rainbow. The Sun-dog appeared in cirrus clouds because these are made from the sort of ice crystals that produce brilliant Sun-dogs. These ice crystals are flat and hexagonal so they refract sunlight exactly as does a prism. Just like a prism, red light and blue light will be refracted by differing amounts and so they will appear at different places in the sky. The minimum angle of refraction produces the most intense colouration and, for hexagonal platelets of ice, this occurs at 22º away from the light source.

I do not find degrees a particularly helpful way of thinking about distance but what helped me is that, in terms of the sky, if you hold your outstretched hand out at arms length, the distance from your thumb to the tip of your finger is, approximately, 22º. Hence, if you see a halo around the Sun at about that distance, it is most likely a refraction effect due to ice crystals in the sky and if you see an intense rainbow roughly parallel to the elevation of the Sun, it is very likely to be a Sun-dog.

What does this tell us about the colours in the mists above the coffee? Well, clearly the mists are not made of ice crystals but neither is the ‘rainbow’ colouring as far as 22º from the light source (a light bulb reflected in the coffee). Also, the rainbow is less vivid and, if you look closely, inverted from the rainbow in the clouds. In the cloud, the inner edge of the arc was red and the outer edge blue, in the coffee, the outer edge is more reddish, while the inner is more blue-ish. This is another clue. On the same evening as I had seen the Sun-dog, there was a full moon and around the Moon was a glowing ring, tinged slightly reddish on the outside. The ring was far closer to the Moon than the Sun-dog had been to the Sun. This Moon-ring, and the coffee colouring are the same effect, they are examples of ‘corona’ (literally crown) and they are caused by diffraction of light rather than refraction.

straw, water, glass — It is refraction that makes the straw appear broken in this glass of water.

Refraction we are all quite familiar with, it is the bending of a straw in a glass of water as you look through the glass. Diffraction is a little more tricky, but it is a consequence of how the light moves past an object. It can be understood by thinking about how water waves pass objects in a stream (or by playing with the simulation here). The amount that the wave is diffracted depends on both the size of the object and the wavelength of the wave. As blue light has a much shorter wavelength than red light, the blue will be diffracted by a different amount to the red. If the objects diffracting the light are of a similar size (as water droplets in white mists are going to be) a spectrum, or a rainbow of colour will appear around the light source. The more uniform the droplet size, the more vivid the spectrum in the corona. The thin cloud around the Moon that evening was made up of many different sized droplets and so the rainbow effect was very subtle. In contrast, around the reflection of the light bulb in the coffee, the water droplets in the white mist are a fairly similar size and so the spectrum is more vividly seen.

Seeing rainbow effects in the sky (or in the coffee) therefore gives us many clues as to what is in the sky or indeed, levitating above the coffee. Please do send me any pictures you have of coronae around light source reflections in your coffee, or indeed sun dogs if you are fortunate enough to see them*.

* Sun dogs are in fact apparently fairly common, it is more that we have to be attentive to see them.