Corona gazing in cafes

interference patterns on coffee

There are many ways in which rainbows of colour are produced as light interacts with our coffee or in a cafe. Looking around yourself now, how many do you see? What physics underlies each?

As the nights grow longer and the days colder, we notice that windows steam up as the water vapour in the café condenses onto the cooler glass. Perhaps we see a similar thing on our glasses while we are drinking tea or on the windows of a bus. Initially we perhaps become frustrated at our inability to see what is going on outside but then we notice the colourful patterns around the lights of passing cars and of street lights. Haloes of coloured light around a central bright spot. What does this tell us and where else can we see it, either in a café or in life generally?

On a window pane, a large number of small droplets of water have condensed into what appears to us as a fog on the glass. As the light shines through from the car headlights, each droplet acts as an obstacle to the light and so bends it. You could see a similar effect with the waves on the sea going around stones or perhaps if you brew a large cup of coffee with the surface waves going around a spoon (let me know if you manage to see this bending in a coffee cup). The amount that the light bends is dependent on the wavelength of the light (look carefully at the waves going around obstacles in ponds to see this) and so different wavelengths (different colours) get bent by different amounts and interfere with each other at different points – a spectrum is produced. It is a phenomenon known as diffraction.

Not all beans are equal! How could you quickly distinguish between arabica and robusta beans?

This phenomenon means that we have a way of separating the frequencies (or wavelengths) of light. And so this means that we have a way of measuring the chemical composition of some substances as different chemicals absorb different frequencies and so have ‘fingerprints’ in the light they scatter. By passing the light scattered from a substance (such as arabica coffee beans compared to robusta) through a diffraction grating (which is an obstacle with a pattern of fixed size), we can separate the frequencies being scattered and see if any of them are ‘missing’ (ie. they have been absorbed by the material we’re studying). It would be  a bit like looking at that rainbow pattern in the café window and not seeing blue, its absence tells you something. This is one of the ways that robusta beans can be quickly found if they have been substituted for arabica beans in coffee trading.

Coffee Corona

Look carefully: Sometimes you can infer the existence of a thin (white) mist over your coffee by the corona pattern around reflected light fittings.

But it is not just its technological aspect that has interest for us surely? When gazing at the moon on a misty evening, the halo around the moon suggests the clouds between us and it. It is something that poets have remarked upon to evoke atmosphere, it is something that we can gaze at as we imagine the giant café window of our atmosphere. But the size, and distinctness of the lunar corona actually give us clues about the droplets making up the cloud. And then we look closer to home and to our own coffee and we see the same diffraction pattern again looking back at us from our coffee’s surface. Occasionally it is possible to see haloes on the coffee surface around the reflection of overhead lights in the café. A coffee corona! This reveals to us the fact that there are droplets of water above the surface of our coffee; an extra layer of hovering droplets. Something that we can sometimes see more directly in the dancing white mists.

Diffraction is a beautiful phenomenon that allows us to gaze and to contemplate how much we are able to deduce and how much we have yet to understand. How atmospheric our coffees and cafés are and the journey of understanding that we have taken to get to this point. Coffee gazing is a hobby that should be taken up by far more of us.

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Making a splash

You spilled your coffee, a terrible accident or an opportunity to start noticing?

Why do some droplets splash  while others stay, well, drop like? It turns out that there is some surprising physics at play here. When a drop of water, or coffee, falls from a height and onto a flat surface (such as glass), we are accustomed to seeing the droplet fracture into a type of crown of smaller droplets that form a mess over the surface. Visually spectacular, these splashing droplets have even been made into an art form (here).

Fast frame-rate photography reveals how each micro-droplet breaks away from the splashing drop:

Video taken from Vimeo – “Drop impact on a solid surface”, a review by Josserand and Thoroddsen.


So it perhaps surprising to discover that there are many things about this process that we do not yet understand. Firstly, if you reduce the gas pressure that surrounds the drop as it falls, it does not make a splash. In the extreme, this means that if you were to spill your coffee in a vacuum, you would not see the crown-like splashing behaviour that we have come to expect of falling liquids. Rather than splash, a droplet falling in low pressure spreads out on impact as a flattening droplet. This counterintuitive result was first described in a 2005 study (here) that compared the effect on splashing of droplets with different viscosities (methanol, ethanol, 2-propanol) falling through different gasses.

cortado, Brunswick House, everyday physics, coffee cup science

Don’t spill it!
But would a latte splash more or less than a long black?

The authors of the study ruled out the effect of air entrapment surrounding the droplet as it falls as high speed photography had not indicated any air bubbles in the droplet just before impact. Instead they considered that whether a drop splashes on impact – or not – depended on the balance between the surface tension of the falling liquid and the stress on the drop created by the restraining pressure of the surrounding gas. Calculating these stresses led to a second surprising result. Whether a drop splashes on impact or not depends on its viscosity (as well as the gas pressure and the speed of impact). But the surprising bit is that the more viscous the liquid, the greater the splash.

From a common-sense perspective (that may or may not have any bearing on the reality of the situation), an extremely viscous liquid like honey should not splash as much as a less viscous liquid like coffee. This suggests that there is an upper-limit in viscosity to the relation predicted in the 2005 study. After all, although the authors did change the viscosity of the liquids, the range of viscosity they studied was not as great as the difference between coffee and honey. This sounds like a perfect experiment for some kitchen-top science and so if any reader can share the results of their experiments on the relative splashes formed by coffee and honey, I would love to hear of them.


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.

Sun-dog, Sun dog

A Sun-dog in the clouds to the right of the setting Sun

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.