refraction

Squaring the circle at Omotesando Koffee, Fitzrovia

Omotesando Koffee, Fitzrovia
The name “Omotesando” is represented solely by a square on a sign outside the shop. Is this a practical realisation of squaring the circle?

There was a lot of excitement late last year (2018) as the London branch of Omotesando Koffee opened just off Oxford Street. I watched as there were visits by Brian’s Coffee Spot, and Bex’s Double Skinny Macchiato and others, thinking that soon, I too would pop along. After all, it is a place that celebrates pour overs in central London. And yet, I went for the first time two weeks ago while meeting Sadiq of Amoret Coffee to discuss details of the first coffee and science evening being hosted in the Notting Hill branch of Amoret on the 11 June (more details and sign up page here).

On that first occasion, I had enjoyed a Rwandan by pourover and took in the minimalism and cubist geometry of the cafe but largely was too involved in discussing details of the event to think about the connections that the space prompted. And so a second visit was arranged. Again I found that the fold out chairs underneath the bench tables were a little too tall for me (though on the second occasion I didn’t fall off) but it did mean that, although I had a prime seat in front of the bar where they were preparing my pour over (a Burundi from guest roaster La Cabra), it was not easy to turn around to watch. It was however great to find that the cake menu at the order point at the front of the cafe clearly listed all the allergens in each of the cakes and so I was able to confidently enjoy a vegan banana cake with the coffee.

Omotesando Koffee, brownie with square revealed
Cubes and squares were a recurring theme inside the cafe

Omotesando offers a challenging space for a website built on the premise that any cafe offers an opportunity to explore connections to the wider world of physics if you just slow down, take in your surroundings and notice them. It is a space that seems to revel in minimalism. Most of the space is a fairly light coloured, mostly uniform wood. The bar is framed with a cube, a shape that seems to crop up all around Omotesando, even in some of the cakes. The fold out stools (circular) are made of the same colour of wood as the rest of the majority of the cafe (though there are a couple of exceptions to this which hint at the carpentry). Perhaps the idea is that we should focus on the coffee rather than the environment. And maybe that is where your mind enjoys wandering, but another thought suggested itself to my mind.

Sitting on the stool facing the window, wishing that I could turn around to watch the pour over being poured while remaining comfortable (there is a foot rest when facing forward), it struck me that sitting right in front of the bar did not help me when I wanted to use the glass of the window as a mirror to the inside of the cafe. The glass was perfectly transparent to my eye and reflected very little of the light behind me. The fact that the side of the (La Marzocco) espresso machine was transparent rather than metallic and revealed the pipework and wiring that enabled great espressos to be prepared (we also enjoyed an iced latte) briefly led me to consider why some materials are transparent and others not (and also how transparency varies as the frequency of light changes).

Banana bread and coffee with IoP bag
My pour over coffee, a banana bread and my IoP re-useable bag sitting on the table at Omotesando, Fitzrovia, London

But as I reflected further, I could see in my mind’s eye, the viewpoint of a deep sea diver looking up from the sea bed towards the sky. A circle of light, “Snell’s Window” opening above them. You can see images of Snell’s window where divers are framed by the effect in the photograph here. The effect is caused by the refraction of the light as it enters the water. Just as a straw (paper of course) appears bent as you view it through the glass of water, so light entering the sea will be bent by an amount given by Snell’s law. Even light entering at a grazing incidence will be refracted towards the ‘normal’ (the line perpendicular to the sea-air interface) and so if you work through the maths (there’s a good description here), you find that you will only see light from a cone of about 100 degrees around your view point.

Coffee reflections
What would you reflect on?

But although Otomesando has an entirely glass frontage, you do not feel you are in a gold fish bowl, nor can you only see a small window outside. The wide window instead offering plenty of opportunity for watching the office workers and builders scurry about outside. And, on writing this and looking through my photos of the cafe, I noticed that my photographs of the front of the cafe and of a coffee inside were both taken at shallow angles showing the reflections from the surface of the window and the coffee rather than the interior. An effect almost opposite to that of the deep sea diver. Omotesando Koffee offers a space where each cup offers further opportunities for reflection: more time for noticing the physics of the everyday. A great place therefore to spend some time thinking about, as well as enjoying, your coffee.

Omotesando is at 8 Newman Street, W1T 1PB

Tea Gazing

Milky Way, stars, astrophotography

The Milky Way as viewed from Nebraska. Image © Howard Edin (http://www.howardedin.com)

A recent opinion piece about last week’s announcement of the detection of gravitational waves at LIGO drew my attention to a quote from Einstein:

The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed.

Einstein was not the only scientist to have expressed such sentiments. Many scientists have considered a sense of wonder to be integral to their practice of science. For many this has involved gazing at the heavens on a clear night and contemplating the vastness, and the beauty, of the universe. Contemplating the twinkling stars suggests the universe outside our Solar System. Watching as the stars twinkle gives us clues as to our own planet’s atmosphere. Of course, it is not just scientists who have expressed such thoughts. Immanuel Kant wrote:

“Two things fill the mind with ever-increasing wonder and awe, the more often and the more intensely the mind of thought is drawn to them: the starry heavens above me and the moral law within me.“*

light patterns on the bottom of a tea cup

Dancing threads of light at the bottom of the tea cup.

The other evening I prepared a lovely, delicate, loose leaf jasmine tea in a teapot. I then, perhaps carelessly, perhaps fortuitously, poured the hot tea into a cold tea cup. Immediately threads of light danced across the bottom of the cup. The kitchen lights above the tea cup were refracted through hot and not-quite-so-hot regions of the tea before being reflected from the bottom of the cup. The refractive index of water changes as a function of the water’s temperature and so the light gets bent by varying amounts depending on the temperature of the tea that it travels through. Effectively the hotter and cooler regions of the tea act as a collection of many different lenses to the light travelling through the tea. These lenses produce the dancing threads of light at the bottom of the cup. The contact between the hot tea and the cold cup amplified the convection currents in the tea cup and so made these threads of light particularly visible, and particularly active, that evening. It is a very similar effect that causes the twinkling of the stars. Rather than hot tea, the light from the distant stars is refracted by the turbulent atmosphere, travelling through moving pockets of relatively warm air and relative cool air. The star light dances just a little, with the turbulence of the atmosphere, this way and that on its way to our eyes.

Marcus Aurelius wrote:

Dwell on the beauty of life. Watch the stars, and see yourself running with them.Ҡ

Marcus Aurelius of course didn’t have tea. Watch the dancing lights in the tea cup and see yourself sitting with it, resting a while and then watching while dwelling on the beauty in your cup.

*Immanuel Kant, Critique of Practical Reason

†Marcus Aurelius, Meditations

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.

Seeing things at a kopitiam (coffee shop)

Rocky, Bangsar, KL, Malaysia, koptiam

A kopitiam in Bangsar, Kuala Lumpur, Malaysia

One of the great things about travelling is exploring the different cafe and coffee cultures in different countries. Is it the coffee that is important? Or food, alcohol or maybe just the opportunity for socialising? In Singapore and Malaysia, the “kopitiam” (or coffee shop) is a familiar part of each neighbourhood. Each kopitiam serves local coffee (kopi) and a variety of foods which are usually prepared while you wait, from stalls around the edge of the kopitiam. The kopitiam provides a space for socialisation and meeting people over a bowl of steaming noodles. Inside electric fans are blowing continuously in an effort to lessen the heat. Frankly, the local coffee is not to my taste but there are plenty of other things to eat and drink in each kopitiam. A breakfast of “kueh” and black tea for example is a welcome change from toast at home! In many areas of Singapore, and to a lesser extent Malaysia, local kopitiams are closing to make way for the new style cafés which serve a range of freshly roasted, pour over or espresso based coffee. Not being Malaysian or Singaporean I do not want to comment too much on that, I guess it is similar to the decline of the “caffs” in the UK. Mourned by many in the community but welcomed by others for the improved quality of the coffee.

straw, water, glass

An everyday example of refraction. The water refracts the light to make the straw appear ‘broken’.

However, with so much going on in a kopitiam, the temptation to look at a kopitiam-physics review was too great, especially when I started to “see things” at the edge of the shop. Am I going mad? No, it was not that my imagination was playing with my mind; I saw the ingredients for a mirage. You see, at the edge of the kopitiam the hawkers will cook noodles, or rice dishes etc. and this creates heat. Above some stalls there will be clouds of steam rising as the noodles boil in a pan. The clouds appear white because of the scattering of light by reasonably sized water droplets (more info here and here). Above other stalls, there is no steam but the heat created by the cooking makes the air immediately above the stove warmer (and therefore less dense). This less dense air refracts light less than air at room temperature. It is refraction that causes that straw in your iced coffee to look as if it is broken as you look at it (see picture). In the kopitiam, it means that as you look through this region of warm air you see a wobbly or wavy type pattern as the light from outside is refracted by different amounts depending on the temperature of the air that it goes through. It is this that is the primary ingredient for seeing a mirage.

The fact that air at different temperatures refracts light by different amounts is the reason for mirages in the desert. Frequently, warm air is trapped at ground level by a layer of cold air above it. The light is bent as it travels through these layers (see diagram here) and so it may appear as if they sky is on the ground (which the brain will interpret as a pool of water on the ground). Conversely, if there is a layer of cold air trapped beneath a layer of warm air, the light is bent downwards and so objects that are usually below the horizon due to the curvature of the earth can be seen (illustrated by the diagram here).

Edmond Halley, Canary Wharf, Isle of Dogs, view from Greenwich

The view towards the Isle of Dogs (and Canary Wharf) from Greenwich. Things have changed a little since Halley’s time.

Back in 1694 Edmond Halley (who drank coffee with Isaac Newton at the Grecian) was investigating the evaporation of water as a function of temperature. He wanted to see if evaporation alone could explain the rainfall and the quantity of water in the river system. As he did so he noticed that, in still air, there was a layer of water vapour that formed above the bowl of evaporating water. He noticed this because it refracted the light in an unusual manner. At the time, there was reported to be an unusual phenomenon that occurred at high tide near Greenwich. It seems that cows used to graze on the Isle of Dogs in London. Ordinarily the cows could not be seen from Greenwich because they were too far away, but occasionally, at high tide, the cows would be visible. Putting together what he knew about the evaporating water Halley wrote “This fleece of vapour in still weather… may give a tolerable Account of what I have heard of seeing the Cattle at High-water-time in the Isle of Dogs from Greenwich, when none are to be seen at low-water (which some have endeavoured to explain by supposing the Isle of Dogs to have been lifted by the Tide coming under it.) But the evaporous effluvia of water, having a greater degree of refraction than the Common Air, may suffice to bring these Beams down to the Eye, which when the Water is retired, and the vapours subsided with it, pass above, and consequently the Objects seen at the one time, may be conceived to disappear at the other”*. I think that although he had the mechanism correct (in terms of refraction), the cause of this odd refraction was temperature inversion and a layer of cold air immediately above the Thames rather than water vapour but what do you think? Let me know in the comments section below.

 

* Punctuation and capitalisation kept as in original. Taken from Edmond Halley, “An Account of the Evaporation of Water, as It Was Experimented in Gresham Colledge [sic] in the Year 1693. With Some Observations Thereon” Phil. Trans. 18, 183-190, 1694″

Arepa and Co, Haggerston

Haggerston Canal

Arepa and Co are on the right hand side of this canal

Edmond Halley (of comet fame) was born in the London district of Haggerston in 1656. More recently, Arepa and Co a Venezuelan cafe located alongside the canal that runs through the district, has just celebrated its first birthday there. This cafe serves a variety of Venezuelan foods including the arepas of the name which are, apparently, a traditional corn cake that can be filled with a variety of fillings (more info here). There are seats both inside the cafe or outside, overlooking the canal. As it was the early afternoon and we’d already had lunch, we decided upon a coffee, a sugar cane lemonade and, to accompany it a plate of Tequenos de Chocolate. These unusual little pancakes filled with chocolate were delightful to enjoy with a cup of coffee and a view over the canal. Sitting back and enjoying this relaxing view, I noticed a tree on the roof of a building on the opposite side of the canal. Hanging on the tree were a number of glass shapes. As the wind blew, the different faces of the shapes caught the Sun. Looking towards these glass shapes, they appeared to change colour as the sunlight was refracted through them. A glinting rainbow array of light fell onto our side of the canal.

The story of the investigation of colour is a great example of how our preconceived ideas can influence the results that we think we see. Up until the seventeenth century, colour was viewed as a property of the surfaces of an object as opposed to “light” which was that which rendered objects visible. Therefore trying to explain how rainbows formed or light scattered from ornaments was a difficult task. Indeed, medieval philosophers (the term ‘scientist’ is a nineteenth century invention), considered that there were only seven colours: Yellow, orange, red, purple, green and black and white.

Prism associated with Isaac Newton

A late C17th prism in the British Museum collection, © Trustees of the British Museum

Work understanding colour as a refracted component of white light started with Marci in his 1648 work Thaumantias (another name for Iris, the Greek goddess of the rainbow) and continued with Newton’s famous experiments with prisms. Newton showed that a glass prism refracted the different colours of light by different amounts (resulting in a spectrum). If two prisms were placed at right angles to each other, the rainbow of light from the first prism recombined into white light emerging from the second. With the change in mindset that this brought about, phenomena such as the rainbow could be more easily explained.

Grecian, Coffee House, London Coffee House

The Devereux pub now stands on the site of the Grecian coffee house, a former meeting place of the Royal Society

Which brings me back to coffee. Back in the eighteenth century cafes (or coffee houses) were not just places to have coffee but places to engage in the latest philosophical, political or scientific discussion and debate. Scientists of the day regularly gave public lectures and demonstrations in coffee houses both as a way of entertainment and of education. One scientist who participated in this was Stephen Demainbray (1710-1782). Demainbray demonstrated Newton’s experiments and theories on colour to a coffee drinking audience. The models that he used to explain the refraction of light are now on display in the Science Museum which is well worth a visit if you are in London. In the present day, there are still cafes and coffee houses that try to do a similar thing (of showing fun science to a coffee drinking audience), although perhaps sadly there are fewer now than there were then. Two movements that are trying to put the science back into coffee houses are Science Cafes and Cafe Scientifique. Although not always held in cafes, both movements have the aim of combining interesting science with a cup of coffee or glass of wine. Somewhat poetically the next Cafe Scientifique in London is to be held, on the 9th December, at the Royal Society. It is poetic because back in the time of Newton, discussions with the Royal Society president (Newton) and other society members took place at the Grecian Coffee House.

Both “Science Cafes” and “Cafe Scientifique” have events worldwide. It is worth taking a look at their websites to see if there is an event near you. Why not pop along and see what you can find out while having a cup of coffee?

 

Sources used:

The Rainbow Bridge, Raymond L Lee, Jr and Alistair B Fraser, Pennsylvania State University Press, 2002

The Nature of Light, Vasco Ronchi, Heinemann, 1970

London Coffee Houses, Bryant Lillywhite, George Allen & Unwin Ltd, 1963

Dappled with Dew

Part of my morning routine can involve a walk through a local park. Each day reveals how the seasons are affecting the plants, bird life etc. This morning on walking through the park, I was treated to the spectacle of a thick layer of dew, shimmering and spectacular, glinting in the sunlight.

dew, surface tension, everyday physics, slow morvement

The dew this morning

Taking out my phone, I tried to take a picture of the scene for later and yet, what came out in the image was not the brilliant scene before me but instead some blurry grass. The ‘immediacy’ of the sight struck home. As with so many of the gifts that nature provides, attempting to take a photograph of it somehow just doesn’t quite capture the beauty of the moment. There are some great photographs of sunsets or sunrises, but part of the attraction of the image is not the photograph itself but our memory of those brilliant sunsets that we have experienced. The photograph is suggestive of the beauty that the photographer saw but somehow, the fullness of that beauty has not translated into the photograph.

As we stop to enjoy the moment, rather than photograph it and rush off to our morning appointment, we can start to notice what it is about it that captivates us. From my viewpoint, the majority of the dew this morning formed a silver blanket on the grass. It was this that caught my eye initially. Yet as I observed the dew, individual droplets came into focus and, because of the angle at which I was viewing them, they appeared as blue, as a slightly different blue and then other different colours. The physics of the rainbow was being revealed before me, one metre away on the grass. If I moved, the clues to these mysteries would disappear.

It was a reminder to slow down and notice things, who knows what we’ll see.  Perhaps you will disagree and say that it is just my poor photography skills that are the problem.  Please disagree in the comments section below!  Alternatively, if you agree and want to share a moment of beauty and everyday physics, please also share that in the comments section below.  I’ll finish this post however with an excerpt from the thoughts of someone who obviously did stop, slow down and observe his world.  The excerpt is from “Inversnaid” by Gerard Manley Hopkins:

Dew, surface tension, everyday physicsDegged with dew, dappled with dew,
Are the groins of the braes that the brook treads through,
Wiry heathpacks, flitches of fern,
And the beadbonny ash that sits over the burn.

What would the world be, once bereft,
Of wet and of wildness? Let them be left,
O let them be left, wildness and wet;
Long live the weeds and the wilderness yet.