Diffraction

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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Reflections at Store St Espresso, Bloomsbury

Store St Espresso, coffee, Bloomsbury, UCL, London

Store St Espresso, Bloomsbury

I finally got around to visiting Store St Espresso two weeks ago while visiting the nearby Institute of Making’s 3rd birthday science-outreach party. Although the café was crowded, we managed to find a place to perch while we enjoyed a soya hot chocolate, caffé latte and my V60. Beans are from Square Mile while the V60 and filter coffee options featured guest roasters. Despite the narrow frontage, there is actually plenty of seating inside and people were happy to share tables with other customers when it got particularly busy. The café is well lit with sunlight streaming in through the sky lights above (indeed, the extra electric lighting indoors seemed a bit unnecessary given the amount of sunlight coming through the windows on such a good day). On the walls of the cafe were pieces of artwork, including quite a large pencil/charcoal piece right at the back of the cafe.

I was meeting a friend for coffee before going to the science event and so thought it would be good to combine a cafe-physics review with a visit to the science. It is always interesting to hear other people’s observations of the same space that you are ‘reviewing’. In this case, I was taken by the floor which showed some very interesting crack structures but what fascinated my friend (who was enjoying her caffe-latte) was the way that the sound from the stereo was reflecting from the bare walls, floor and ceiling. While cracks and fracture processes can be very interesting, perhaps it is worth following her observations as it leads, in a round about way, back to the coffee that she was drinking.

latte art, hot chocolate art, soya art

A caffe latte and a soya hot chocolate at Store St Espresso

While studying for my physics degree, a lecturer in a course on crystallography told us an anecdote. The story concerned a physicist walking past an apple orchard. As he was walking past, he noticed that at certain points he could hear the church bells from a distant church. As he walked on, the sound of the bells faded, before suddenly, he could hear them again. The physicist went on to derive the laws of X-ray diffraction, a technique that is now used routinely in order to understand the arrangement of atoms in crystals (like salt, diamond or caffeine). X-rays are part of the electromagnetic spectrum (just like visible light) but they have a very short wavelength.  The orchard had been inspirational to the physicist because, just as a crystal is a regular array of atoms, so the apple orchard is a regular array of trees; as you travel past an orchard (on the train, in a car or on foot), there are certain angles at which you can see straight through the trees, they have been planted in a 2D lattice. The church bells could only be heard at certain angles because of the way that the sound was being reflected from the multiple layers of the trees. The effect occurs because the sound made by church bells has a similar wavelength to the spacing of the trees (eg. ‘Big Ben’ chimes close to the note E, which has a wavelength of approximately 1m). The distance between atomic layers in a crystal is similar to the wavelength of the X-rays (the wavelength of X-rays frequently used for crystallography = 1.54 Å, size of the repeating structure in a salt crystal: 5.4 Å, 1 Å = 1/100000 of the smallest particle in an espresso grind). The physicist realised that the orchard affected the church bells in exactly the same way that the atoms in a crystal, be it salt, diamond or caffeine, will affect the deflection of X-rays. Suddenly, it became possible to actually ‘see’ crystal structures by measuring the angles at which the X-rays were scattered from substances.

bubbles on a soap solution

Not quite a regular 2D lattice. By controlling the size of the bubbles and the number of layers, you can simulate the crystal structure of different metals. Seems I need more practice in making bubbles of a similar size.

We can perhaps imagine an apple orchard but what do crystals look like? Crystals can come in many forms, all they need to be is a repeating structure of atoms through the solid. Some crystals are cubic, such as salt, some are hexagonal, others form different shapes. Metals, such as that making up the shiny espresso machine in the cafe are often a certain form of cubic structure and to visualise it, we can return to my friend’s caffé latte (via some soap). Two people who were instrumental in understanding X-ray diffraction were the father and son physicists, William Henry and William Lawrence Bragg. While attempting to make a model of crystal structures, William Lawrence Bragg found that the bubbles that could be formed on top of a soap solution were a very good approximation of the sort of crystal structures observed in metals (his paper can be found here). As they form, the soap bubbles (provided they are of similar size) form a regular cubic structure on the surface of the soap solution held together by capillary attraction, a very good model for the sort of bonding that occurs in metals. By controlling the size of the bubbles, the number of layers and the pressures on the layers of the bubbles, all sorts of phenomena that we usually see in crystals (grain boundaries, dislocations etc) could be made to form in “crystals” formed from soap bubbles. Why not look for such crystal structures in the foam of your cafe latte, though be careful to see how the size of the bubbles affects the arrangement of the bubbles through the foam structure.

Sadly, I have never found a reference to the story of the physicist and the apple orchard and it may even have been apocryphal. The closest reference I can find is that W. Lawrence Bragg (after whom the laws of X-ray diffraction are named) had a “moment of inspiration” for how X-rays would ‘reflect’ from multi-layers of atoms while he was walking in an area called “The Backs” in Cambridge. If any reader of this blog does know a good reference to this story I would be very much obliged if they could tell me in the comments section (below). To this day, I have been unable to pass by an orchard (or even a palm oil estate in Malaysia) without thinking about crystal structure, X-ray diffraction and church bells!

It seems that taking time to appreciate how sound is reflected (or diffracted) from objects, either in Store St Espresso or in an apple orchard, could be a very fruitful thing to do. If you have an observation of science in a cafe that you would like to share, please let me know here.

Store St Espresso can be found at 40 Store St. WC1E 7DB

The physics of X-ray diffraction and some great bubble crystal structures can be found in the Feynman Lectures on Physics, Vol II, 30-9 onwards.

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.