Snell’s law – Bean Thinking

Squaring the circle at Omotesando Koffee, Fitzrovia

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

Bend it like sugar at Muni, Fulham Road

Muni Coffee, near Chelsea and Westminster hospital — Muni Coffee on Fulham Road

The area around Fulham Road and Chelsea & Westminster hospital is one that has long been fairly empty of speciality coffee establishments. Then, in June this year, Muni opened up on Fulham Road (just over 200 m from the main entrance of the hospital, in case you are visiting and looking for a good café nearby). Muni’s website emphasises its social mission, knowing the farmers they trade with by name and introducing Filipino coffee to the UK. Inside, there are plenty of tables (with more outside if you are visiting in warmer times). There is a menu on the wall behind the counter to your right as you enter, but I missed the listing of the Pandan iced tea (which would have been very interesting to try) as I was obviously not paying enough attention and instead opted for my default trying-a-new-cafe coffee, a black Americano.

My sometimes companion in these reviews had a soya hot chocolate while I was very confident to enjoy one of the (lovely) salted caramel brownies because Muni lists all the ingredients for all of their cakes on a tablet device at the counter and so I was encouraged to double-check the ingredients list to see that there was nothing vaguely nut-related in it. A very good feature and this cafe definitely gets a tick in the “cafes with good nut knowledge” category on the right (as well as the new allergy-friendly category). As mentioned, the coffee is imported directly from the farmers in the Philippines, and roasted by Muni in North London. The black Americano I tried was fruity and flavoursome, while the beans I purchased and prepared later using a V60 produced a sweet and floral brew, perhaps with blueberry notes (but with no tasting notes on the packet, I’d be interested to see if others agree with me on this, please let me know in the comments section below).

coffee cake Muni — Coffee and nut-free salted caramel brownie at Muni

On the ceiling, wooden beams had cracked and aged creating a lovely aesthetic and taking me on a thought trail that involved aeroplane engines and heat process treatments. But then I noticed something else. As it was getting dark, the cars passing by on the busy Fulham Road were mostly using their headlights and this meant that, every so often, the edges of the windows around the door changed these headlights into a spectrum of colour. Flashes of blue, red and green as each car passed. It reminded me of Newton’s experiments in which he used a prism to first separate sunlight into its various colours before recombining it with another prism into white light. An effect that led me to think about an instrument that has been advertised as a tool to creating better coffee: the coffee refractometer.

Some of the same physics links Newton’s prism with the coffee refractometer. Perhaps you remember “Snell’s law” from school. The equation describes how much deviation light experiences as it passes from one medium (air) to another medium (glass or coffee). Light travels at different speeds through different media and the refractive index can be thought of as an indicator of the degree to which each medium slows down the light.

The window at the side of the door at Muni. Rainbows of colour were produced by the headlights of cars as they went by.

For the prism, the important detail is that light is composed of many colours (which means in this context, many wavelengths) and not all wavelengths are slowed to the same degree. This means that the refractive index of the glass prism is slightly different for red light than it is for blue. Consequently, the spectrum opens up as the white light travels through the prism.

For the coffee refractometer, the important point is slightly different. Water containing dissolved solids has a slightly different refractive index than pure water. Measuring the deviation of a light beam through a drop of coffee therefore gives an idea of the concentration of “total dissolved solids” and so a guide to the extraction of coffee from the grind that you have achieved. The difference in refractive index is however quite small, if the measurements here can be relied upon, while water has a refractive index of 1.333 (at 20ºC), a well extracted coffee showed a refractive index of 1.335. We can calculate how much difference this makes to the angle that the light is deflected: Assuming light enters the drop at an angle of 30º, the angle that light is refracted in water is 22.03º, while in the coffee it is 22.00º. A small effect that would be quite difficult to measure unless you had a refractometer.

However, there is an ingredient in some people’s coffee that bends light enormously: sugar (though I do hope that no one reading this uses it in the quantities needed for the experiment below). The refractive index of water is very dependent on the total concentration of dissolved sugar it contains. Therefore you can do a really cool experiment in which a sugar solution (which has more concentrated sugar at the bottom than the top) can be seen to bend the path of a laser beam. All the equipment can be easily found at home (or purchased for not too much from hardware/office equipment shops). Let me know if you try the experiment how you get along (and if you decide to try using a refractometer to enhance your coffee brewing experience). The video was shared on youtube by the Amateur Astronomical Spectroscopy group (CAOS).

Muni coffee is at 166 Fulham Road, SW10 9PR. Just around the corner on Drayton Gardens, is the blue plaque for Rosalind Franklin who used to live at an address there.