reflections

Reflections, deviations…. coffee

The reflections from the surface of a cup of coffee of a building opposite a central London cafe. Towards the edges of the cup, the coffee bends upwards, revealed by the lines bending that would be expected to be straight.

A “flat white” could be ordered from many a coffee shop. A “flat black” may be a physical impossibility. We can realise this by gazing contemplatively, or perhaps even longingly, at a long black while it cools. Notice that the surface of the coffee is ever so slightly curved. Leaving aside the white mists that you may see skipping across the coffee surface, the coffee is flat in the middle of the cup but rises towards the edges. If you have noticed this, it is most probable that you did so because of the different way the light is reflected over the surface of the coffee. It is most obvious if you can arrange the reflections on the cup to reflect something supposedly straight: a window frame or a beam of strip light for example. The reflection is fairly clear and fairly straight until about 5mm from the edge of the cup where suddenly it bends. You can see an example of this in the photograph on the right.

The reason for the curvature is of course surface tension, which is the same effect that makes droplets form into shapes that are close to spheres. First investigated by Agnes Pockels and Lord Rayleigh in the nineteenth century, surface tension is caused by the fact that molecules at the surface of the water (in the coffee) will feel a net attraction to the other molecules within the water. There being no molecules of water above the surface of the cup, the surface molecules are pulled back towards the liquid in the cup. At the sides of the cup something slightly different is happening. There, the molecules in the water will be pulled back towards the liquid but will also experience the uncompensated attraction (or repulsion) from the atoms in the mug material. Exactly analogous to surface tension, but in the solid, the interaction of the surface energy of the mug with the surface tension of the liquid will pull the liquid into different shapes. It is for this reason that highly waterproof surfaces, such as fresh oak leaves, will form spherical drops of water, but wettable surfaces, such as an oak leaf in autumn, will accumulate flatter, less spherical droplets on the surface.

coffee, red wine, wet coffee stain, coffee spill, coffee ring
The interaction between the surface tension of the water and the surface energy of the solid surface it sits on determines the shape of the droplet. These drops of coffee and wine on paper were for an experiment about coffee ring formation. The droplets are: Drops of coffee (left), soapy coffee (middle) and red wine (right)

We see the effects of surface tension too when a bubble, or a small bit of dust, sits on the surface of the coffee. Again, looking at the light reflections, we see how the coffee, or tea, bends near the floating object showing how un-flat the surface really is. Bubbles are usually large enough that we can see them directly. In the photograph on this page for example, you can clearly see the reflections from the surface of the bubble together with the bent reflections of light from the surface of the liquid. However in the case of the dust, sometimes the dust is small enough that the reason that we see it is because of the change of the path of the light reflected from the surface. For a similar reason, the insects that skate the surface of a pond are visible because of the light patterns they make rather than their intrinsic visibility. Each time we are using the deviation of the light from its expected path in order to deduce the presence and shape of an object hidden to our view.

A similar deviation of the expected path of light is seen in the phenomenon of gravitational lensing which has been used to infer the presence of black holes. Such a deviation even provided experimental evidence for Einstein’s (then) recently proposed General Theory of Relativity, just over 100 years ago on May 29, 1919. The idea that light had weight and would be deflected by a gravitational field was not new, indeed, even the Newtonian model of gravity predicted that light would be deflected as it went past a massive object*. The question was how much and, as an important secondary question, how to measure it. As Arthur Eddington later described in his book “Space, Time and Gravitation”*, according to Newton, any object thrown horizontally on the Earth’s surface would fall 16 feet (in his use of units, 4.88 m in SI) in one second. The same was true for light. However with Einstein’s theory, the predicted deflection of light was 32′ (9.75m). The difficulty for the experimentalist is that in the same second, the light would have travelled nearly 300 000 km. Detecting such a small deflection over such a large distance would be difficult, harder than seeing a grain of dust on the coffee surface. Which is where the light deflection comes in. Because if you watch as the light from a distant star travels past a massive and fairly large object, such as the Sun, you should be able to discern the small, but significant deflection. And on May 29th 1919 a total solar eclipse (which thereby blocked the extra and interfering light from the Sun) offered a perfect opportunity for Eddington and an expedition sent by the Royal Society and Royal Astronomical Society (to Brazil and West Africa) to attempt to measure such a deflection.

tea reflections, bubble on tea, surface tension, light bending
The way that light reflects off a surface of a cup of tea in this case, reveals the curvature of the tea surface. In this case the curvature is clearly due to the bubble in the centre. Sometimes you can see distortions on the surface caused by bits of dust which are difficult to see on their own.

Although the deflection was significant, working with large telescopes and photographic plates, the magnitude of the deflection of the light that they were looking for was still only 1/1500 of an inch on the photographic plate. Two groups at two different locations took multiple photographs of the eclipsed Sun and the stars around it in order to measure the position of the stars as seen behind the Sun and then compare that to the position of the stars when they had been photographed earlier in the year without the Sun between them and the Earth. Eddington describes the experiment:

“There is a marvellous spectacle above, and, as the photographs afterwards revealed, a wonderful prominence-flame is poised a hundred thousand miles above the surface of the sun. We have no time to snatch a glance at it. We are conscious only of the weird half-light of the landscape and the hush of nature, broken by the calls of the observers, and beat of the metronome ticking out the 302 seconds of totality.”

Finally after developing and comparing the images back in London, the team confirmed a deflection of 1″.98 +/- 0″.12 (Brazil) and 1″.61 +/- 0″.30 (W. Africa) for the stars closest to the Sun (NB. 1″ indicates 1 second of arc). Einstein’s theory had predicted a deflection of 1″.74, Newton’s theory had predicted 0″.87. The results of the light deflection were far more in agreement with Einstein’s new theory of General Relativity than with the classical Newtonian model.

The ‘wobble’ of a few of the stars on the photographic plates had confirmed a prediction of the theory of Relativity. Which could lead to the question: What do you see, or not, as the light dances off of your coffee?

*”Space, Time and Gravitation: an outline of the General Theory of Relativity”, Sir Arthur Eddington, Cambridge University Press, first printed 1920, 1968 edition.

Reflections on physics and coffee

BeanThinking started as a way of slowing down and appreciating connections, often between a coffee and the physics of the wider world but also in terms of what can be noticed in any café. Perhaps, for this first post of 2017, it’s worth spending five minutes looking at your coffee while you drink it to see what you notice. Here are a few coffee connections that occurred to me recently:

reflections, surface tension

Reflections on a coffee.

Parallel lines and surface reflection: The parallel lines on the ceiling of a café were reflected in a long black. Surface tension effects on the coffee meant that the reflections were curved and not at all parallel. A piece of dust on the surface of the coffee was revealed in the reflection by the curved reflections of the ceiling. Astronomers can use similar effects (where images of a star appear in a different location to that expected) to infer the presence of dark objects between distant stars and their telescope. This gravitational lensing can be used to detect quasars or clusters of galaxies.

 

 

 

layering of coffee long black

Layers of coffee

Layering of crema as the coffee is consumed: The coffee stain effect and this layering of the crema suggests a connection between a coffee cup and geology. It used to be my habit to take a mug of tea with me when I taught small groups of undergraduates. In the course of one of these tutorials, a student (who had been observing similar layering in my tea mug) said, “You drink your tea faster when it is cooler than when it is hot”. Full marks for observation, but not sure what it said about his attention during my tutorials! Similar observations though can help geologists estimate the age of different fossils.

 

interference patterns on coffee

Bubbles in coffee

Bubble reflections: An old one but the interference patterns caused by bubbles on the surface of the coffee are full of fascinating physics. The fact that the bubbles are at the side of the cup and seem to be grouped into clusters of bubbles may also be connected with surface tension effects (although there is a piece of weather lore that connects the position of the bubbles to the weather. If anyone ever does any experiments to investigate this particular lore, I’d love to hear about them).

 

 

Coffee, Van Gogh

Art in a coffee cup

Van Gogh’s Starry Night: The effects of vortices and turbulence caused the crema of a black coffee to swirl into patterns reminiscent of this famous painting by Van Gogh. As a result of posting this image on Twitter, @imthursty sent me a link to this preprint of a paper submitted to the arxiv: the connections between Van Gogh’s work and turbulence. A great piece of coffee combining with art and science.

 

So many connections can be made between tea, coffee and science and the wider world, I’d love to see the connections that other people make. So, if you see some interesting physics, science or connections in your coffee cup, why not email me, or contact me via FB or Twitter.

 

Rain drops at Notes, Covent Garden

Notes Covent Garden, rain, puddles

No one wanted to sit outside when we visited Notes at Covent Garden

It was a cold and wet afternoon in early January when I finally had the opportunity to try Notes (Covent Garden branch). Inside, there were plenty of places to sit while warming up and drying off enjoying a coffee. Although it seems small from the outside, inside, the branch feels quite open, with the bar immediately in front of you as you come through the door. One of the attractions of Notes to me, was the fact that I knew that they served different single estate brewed coffees. I think I tried a “La Benedicion” coffee, or at least that is what I seem to have scribbled in my notepad. We took a stool-seat at the window to look out at the rain as my coffee arrived in a 0.25L glass jar. It is always nice to try different single estate coffees and generally, if I know that a café serves single estate coffees I will seek them out to try them for the Daily Grind.

The reflection of the Notes sign board in a cup of tea

The reflections in a cup of tea

Watching the rain form puddles outside, my thoughts were turned to the reflections bouncing off the water in the puddle. It struck me that the appearance of puddles depends on the water molecules behaving both as individual molecules and as molecules within a group. The rain creates ripples in the puddle which can only occur because each molecule is (weakly) attracted to the other water molecules in the puddle, forming a surface tension effect. A ripple is a necessarily collective ‘action’. On the other hand, the reflection of the lights from the street is the response of each individual water molecule to the incoming light. The reflected image is made from the response of many individual molecules. Reflection is more of an individual molecule thing.

Warning sign, train, turbulence

Such turbulence should be familiar to anyone who has stirred a cup of coffee.

I continued thinking about this when I got home where it occurred to me that there was another connection between rain and coffee. It is often said that “rain helps clear the air”, or something similar. Yet this is not quite true. If you have a coffee in front of you at this instant, take a moment to drag a spoon through it. Note the vortices that form behind the spoon. Such vortices form around any object moving through a fluid. In the case of the coffee it is the spoon through the water. For the rain, as the rain drop falls through the air it creates tiny vortices of air behind it. Just as with the coffee spoon, the size of these vortices depend on the speed and size of the falling drop. These vortices pull and trap the atmospheric dust bringing it down to earth more quickly than rain alone could do. The air is cleaned more by this ‘vacuum cleaner’ action than by the ‘wet mop’ of the rain itself.

I’m sure that there are many other coffee-rain connections that you can make if you sit in a café as I did on a rainy day. Let me know your thoughts on this or indeed, on anything that you notice and think interesting while sitting in a café. There is so much to notice if we just put down the phone or close the laptop while enjoying our brew.

Edited to add: Sadly, this article was posted just as Notes Covent Garden was closing down. Notes still has branches at Trafalgar Square and in Moorgate and is opening new branches in Kings Cross and Canary Wharf in February I believe. Hopefully they will all serve single estate brewed coffee and have good window seats from which to observe the rain when it falls.