Category Archives: physics

Magnet Mushroom

At the end of 2013 Sonya Hallett and I invented a game. We’re calling it Magnet Mushroom, and you can play it too if you have an iron or steel tray, a bunch of magnets and some small pieces made of iron or steel. We used a baking tray, a pack of polished magnetite from a museum shop and the leftover metal bits from some Ikea bookshelves.

Here are the rules:

  1. Each player gets an equal set of magnets and metal bits.
  2. Take turns to place a magnet, with as many bits of metal as you like, on the tray, or on something which is already on the tray.
  3. If any magnet touches the tray during your turn, you lose. The last player to place a piece wins.
  4. At the end of a round, collect back all your pieces.
  5. The winner starts the next round.

Some Magnet MushroomsThe most basic move is a simple mushroom: a magnet stood on an upright metal piece. Because the metal becomes instantly magnetised, the magnet sits on it quite stably, however unlikely the configuration might look.

In fact, it is possible to make a mushroom two or three pieces tall and only moderately unstable. You can also support a magnet on two or three pieces, making it more stable, or attach more metal to the top or sides for added interest.

The challenge of the game comes mainly from the fact that every magnet is attracted or repelled by every other magnet – if you place one mushroom too close another, those forces will pull them down in an instant. There is a surprising amount of strategy involved in leaving the board in a stable enough configuration not to fall down, but unstable enough to make things difficult for the next player. Much of the fun of the game also comes from the creation of beautiful and wildly improbable-looking structures.

Some Magnet MushroomsThe simplest version of the game uses similar magnets and identical metal pieces, but if you want to mix things up a bit – or you run out of the pieces you started with – you can open it up by using  more different pieces. Experiment with it! Let me know what you come up with.

Extended Magnet Mushrooms

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Ionic Bonding

What Ionic Bonding Is

Ionic bonding is the type of chemical bonding that binds non-metals with metals, and occasionally other things*, forming ionic compounds. An ion is just an atom (or sometimes a molecule) with an overall electric charge – many atoms and molecules have exactly as many electrons as they have protons, so the charges cancel out; when that doesn’t hold true, we end up with ions.

Metals are prone to losing electrons from their outside shell, leaving them with a positive charge; non-metals often pick up additional electrons from somewhere, filling up their outside shell and leaving them with a negative charge. Opposite charges attract, so electric forces tend to cause these positive and negative ions to stick together. Since those forces radiate out in all directions, you don’t just get one positive ion (or cation) bonding with one negative ion (or anion) – any more ions that happen by get pulled in, too. There’s always a sweet spot where the pushing and pulling of the ions balances out, allowing new ions to slot neatly into any existing structure. That neatness gives a very regular lattice-like pattern to the solid – in other words, ionic compounds form crystals.

Ionic bonding illustrated
A crystallisation of some of these ideas by the brilliant Sonya Hallett

What Ionic Bonding Isn’t

It’s worth saying something about some common misconceptions about ionic bonding. If you have learned about it before, you may have been told that an ionic bond is what you get when a metal ion donates an electron to a non-metal. This description has a pleasing simplicity to it, but it is really very misleading. For one thing, ionic bonding typically holds together many atoms at once. This is in contrast to the covalent bonds** that hold non-metals together, where the bonding is down to each atom sharing electrons with its neighbours, which leads to the formation of well-defined molecules. Ionic compounds are not really made of molecules at all, just big crystalline structures.

The other thing wrong with the electron-donation picture is that the ions have usually gained or lost electrons long before they ever meet – for many elements, like sodium and the other alkali metals, it is rare to find them any other way on Earth. Less reactive metals may have been exposed to ionising radiation, or lost an electron or two in a collision. Reactive non-metals have a tendency to pick up any free electrons they bump into, whatever the source, because they fit nicely into the geometry of their outside shells.

Ionic Compounds

Ionic compounds are characteristically hard, usually with high melting points, and very brittle. The hardness and high melting points are down to their crystal structure; as long as the lattice holds, they are solid and quite strongly bonded. However, since the crystal is made of alternating positive and negative ions, a knock that causes one layer to get out of alignment with the next will often lead to cations lining up with cations, and anions with anions, producing a repulsive force that tears the crystal apart – hence the brittleness. Metals, which also have a crystalline structure, don’t suffer from this problem, which is why they are much more malleable.

Many ionic compounds are soluble in water. This is because water molecules are polar, in the sense that they have more positive charge on one side than the other. A negative ion will attract the positive ends of water molecules, and when it collects enough water molecules that way, their collective attraction can overcome its bonding with its ionic neighbours and carry the ion away. The positive ions dissolve much the same way. All these positive and negative ions allow a solution, to conduct electricity – distilled water is actually an electrical insulator, whereas salt water conducts extremely well. Molten salts and other ionic liquids conduct in the same way. There is a useful complication to the way ions in a liquid conduct electricity – because the charge is carried by two kinds of ions travelling through space, not just free-floating electrons like you get in a metal, they tend to separate over time – cations are attracted to cathodes, and anions to anodes. This process, known as electrolysis, makes it possible to extract the constituent elements of a salt; sodiumpotassiumcalcium and various other elements were first isolated in this way.

* Sometimes polyatomic cations, like ammonium, can play the part usually played by metal atoms.

**We should note here that there is not really a sharp distinction between covalent and ionic bonds. Many covalent bonds are polar, meaning that the electrons are shared unevenly between the atoms, so that one of the atoms acquires a positive charge, and the other a negative one – these bonds can be considered to be a bit ionic. Similarly, ionic bonds can be considered mildly covalent when electrons get shared between atoms, which they inevitably do. Metallic bonding is sometimes considered a form of covalent bonding, but sometimes not – the shared electrons are more like a sea than a set of pairs. Chemistry gets pretty messy when you look close enough.

References:

This piece also appears on Everything2.

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The Everyday Signs of Light Waves

Light, like all the basic constituents of our universe, seems to be made of waves. Waves that act a bit like particles, sometimes, but which spread out and interfere with each other just like other waves.

It’s about 200 years since physicists finally agreed that light behaves like a wave, after Poisson proved himself wrong with an ingenious experiment involving a surprising bright spot in the shadow of a disc. We could have come to that conclusion much sooner, if we had known what we were looking for, but nobody really thought about interference patterns very much in those days.

Francesco Maria Grimaldi coined the term ‘diffraction’ in the 1660s, to describe his observation that light spreads out when it passes through a small hole. If you put a piece of paper in the path of the light you see a bright disc surrounded by increasingly large and faint rings. It looks something like this (the outer rings are fainter in real life, though):

Those dark rings are where the light waves coming from one part of the hole interfere destructively with those coming from the other side – the peaks of one meet the troughs of the other. The bright areas are where the peaks meet and combine. Grimaldi didn’t quite figure all of that out, although he did come to something like a wave theory of light.

Hooke and Huygens both worked on mathematical theories of light waves around that time too, but Newton published a theory of optics based on light consisting of particles (or ‘corpuscles’). It more or less worked, and given the towering nature of Newton’s scientific achievements, it isn’t surprising that people just sort of went along with that until the early 19th century, when it was conclusively disproved.

Once we realise that light is wavy, it becomes possible to explain quite a few observations which are otherwise a bit mysterious. Here are some of the things you might have noticed in your life, which are all inexplicable if you don’t know that light is made of waves which can interfere with each other.

Iridescence

SlickThe colours that we see when oil floats on the surface of water come about because the film is thin enough, and close enough to a constant depth, that light reflected from the bottom interferes with light reflected from the top. Since different colours have different wavelengths, they interfere to different degrees depending on tiny variations in the thickness of the film, and the angle of the light. A related effect explains the iridescence of certain beetles and butterflies.

Supernumerary Rainbows

A sunset rainbow over LondonRainbows, and even double rainbows, can be explained by simple refraction – the light changing speed and direction as it passes through a medium, in this case water. That itself doesn’t prove that light isn’t a particle, but some rainbows have additional, narrower bands of colour inside the main bow – and those are entirely puzzling until you understand that they are caused by interference. The explanation is in the diffraction of light bouncing from fine raindrops, which creates a series of increasingly faint inner rings. The smaller the droplets, the bigger the spacing is between the rings, which is the general rule in all kinds of diffraction. This means that unless they are all much the same size, the effect gets smeared out with different rings overlapping, and we don’t see the supernumerary bows at all.

Corona

CoronaWhen the moon shines through thin clouds, or a layer of fog, there is often a bright area around it, fringed by bands of colour. Again, this only happens when the droplets of the cloud are particularly consistent in size – if the size varies from one part of the cloud to another we get a patchwork of colours referred to as iridescent clouds. With sunlight these effects tend to happen where the light is too bright to make out the colours, while with the moon, the light is too faint for our colour vision to work at full capacity. The best way to see these beautiful effects in their full glory is to wear sunglasses, and look at the thin clouds around the sun while blocking the sun itself from your view.

Nacreous clouds

Nacreous Clouds 1Far rarer than the corona and a good deal more spectacular, nacreous clouds are also the result of diffraction. The difference is that rather than droplets of liquid water, the light of nacreous clouds are diffracted through stratospheric ice crystals. Usually the stratosphere is too dry to form clouds at all, and not quite cold enough, but when it drops below about 85°C, and especially when moist air is lifted up from the troposphere by gales down below, great wave-shaped clouds of fine ice crystals can form, with amazing colours that are often at their most vivid just before dawn and just after dusk.

Glory

Balloon glory atmospheric opticsSpeaking of glory, if you ever get to look down at your shadow (or your aeroplane’s shadow) in mist or clouds of the right consistency, you will see something called a glory, which looks very much like a corona surrounding your shadow in the mist. Your shadow, meanwhile, is likely to take on an eerie shape known as Brocken’s spectre.

Net curtains

When net curtains, or umbrellas, are made with sufficiently thin and uniform fabric, it is quite common to see diffraction fringes around light sources. The shape of these is characteristic of a square diffraction grating, and closely analogous to some of the patterns seen in x-ray crystallography.

Water drops

abstract yellowIf you get the chance to look through a drop of water at an unfocused point of light somewhere behind it – through a window or a pair of glasses, for example – you are likely to see a caustic projected on the back of your eyeball. Around the edges and cusps, where the light is bent back on itself, we can sometimes see quite rich and occasionally colourful interference fringes.

Water droplets

A different but related effect is sometimes seen through a fine mist of water on a glass pane, or an eye that is covered with the right kind of gunk. There is a hazy ring around light sources, and then the darker and lighter fringes that are characteristic of diffraction. Occasionally the same effect can be seen in a dusty mirror.

Floaters

When we look at a bright, featureless area, it is common to see what look like translucent objects floating across our fields of vision. These are the shadows of loose cells and other tiny pieces of debris passing close to our retinas, and they are often on the right scale to show noticeable diffraction fringes around their edges.


Once you know what to look out for, the wave nature of light is easy to see. All these little oddities in the behaviour of light make perfect sense when you know that light – just like water waves and sound waves – bends when it passes from one medium to another, spreads out around barriers, and shows areas of greater and lesser intensity where waves reinforce or cancel each other out.

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Iron Noder

This November I posted 30 finished pieces of writing on Everything2, on whatever I felt like writing about at the time. By doing so I completed the Iron Noder Challenge, which has been running every November since 2008. This was the first time I took part in earnest – making the effort to write and re-write for an hour or two almost every day, in order to average at least one post a day that I could be happy with. Continue reading Iron Noder

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Ice and Frost

Slab of wonderI think most people don’t pay nearly enough attention to what they’re walking on, especially in cold weather. The richness of the patterns that ice forms is staggering, and provides an intriguing glimpse into the physical processes going on both at a molecular level and on a much larger scale. Some of the most fun shapes emerge when the temperature varies enough so that ice alternates with water, and flow patterns meet crystal dendrites.

Ice creaturesI have two theories about the sort of sideways icicles we sometimes see. Either they come from ice that has cracked and water has seeped through and refrozen, or they are caused by fingers of ice crystal which get a head start on the rest of the puddle for some reason – most likely, some facet of the surface they’re growing on just happens to provide a perfect nucleation point, and the crystals grow out from there because there’s nowhere else for them to get a foothold. Even though this starts at the level of water molecules forming neat little piles too tiny for any microscope to pick apart, in the right conditions these minuscule fingers of crystal just grow bigger and bigger…

Ice danceSome bubbles usually form in ice as it’s freezing. These are due to the presence of dissolved air in the water, which is no longer able to stay dissolved when it gets colder, so it migrates into pockets as the water freezes around it. Bubbles like these, trapped in the Antarctic ice core, tell us what the air on Earth has been like over hundreds of thousands of years, providing the strongest evidence that the temperature on Earth varies in proportion to the amount of carbon dioxide in its atmosphere. We know, for instance, that levels of carbon dioxide and methane are higher, and rising faster, than they have been in 800,000 years.

Larger bubbles also form under ice when it starts to melt from beneath, forming a space between the frozen layer and the water underneath. This process is dominated by the formation of liquid water, dripping and surface tension coming to the fore, so rather than the complex, angular crystals associated with freezing, we see the air forming in great bubbles and voluptuous curves.

Cold, hard cashThe patterns formed by frost depend on a number of factors – the relative temperature of the air and the ground and how much they vary, the speed of the wind and the level of moisture, and so on. Another factor is the nature of the surface the frost forms on – sometimes frost closely follows the lines of the surface, and sometimes it forms much more quickly in some spots than others, where imperfections in a smooth surface get the crystallisation process started. The patterns formed can give us insight into hidden features of the surface below, the subtleties we see speaking of deeper subtleties beyond our perception…

a quickr pickr post

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Caustics

I have been fascinated by caustics for a long, long time. I still remember the first time I noticed them – a bright, ethereal form dancing in the shadow of my mother’s wine glass. I was entranced by the way the light moved when the wine swished in the glass, and disappointed when my usually all-knowing mother wasn’t able tell me anything much about them.

Many years later, a friend asked me if I happened to know anything about caustics; I had never heard of them, so she explained that she was talking about the shifting patterns of light made by rippling water, the curves of light you see at the bottom of mugs, and so on. Finally I had a name for these patterns that had enchanted me since my infancy; when I got home I looked up the word, wondering what these things might have to do with caustic soda or holocausts.

Most caustics are quite harmless, but if you have ever used a magnifying glass to focus the light of the sun into a tight point to make smoking holes in things, you have witnessed their potential destructive power; this is where they get their name. Archimedes is famously said to have used a giant parabolic mirror to set fire to Roman ships using reflected sunlight, during the siege of Syracuse in 212 BC. In modern times, the Olympic Torch is similarly lit by a large parabolic mirror focusing the sun’s rays on a single point.

Caustics can occur whenever light leaves a curved surface; most often that means it has been reflected or refracted. Refraction caustics, caused when light rays are bent by passing through something, tend to show less extreme distortion than reflection caustics, but often show subtle colour variations like light from a prism, because shorter wavelengths of light are refracted more than longer ones.

'city (dawn reflections) rooftop' courtesy of suchstuffEither kind of caustic can hugely amplify tiny imperfections or very subtle curvature into striking patterns, the effect increasing with distance from the surface. For example, very few windows are truly flat, and it is common to see cross-like shapes or mottles reflected on the walls opposite, when the sun is low in the sky.

caustics in motionStrictly speaking a caustic is the entire envelope of light which leaves a curved surface; the patterns of illumination we usually see are just the intersection of that three-dimensional structure with another surface. Something of the 3D nature of caustics comes out when the distance to the illuminated surface varies, with some features getting washed out with distance while others become ever more prominent. See this short video clip for an example; there’s a much longer film, with music, linked here.

We’d notice very quickly if they weren’t there – simulating realistic caustics is an important issue in computer graphics mainly for this reason, and an otherwise convincing scene will seem oddly flat and unreal if it is missing caustics that should be there. Mostly, though, caustics are one of those kinds of things which quietly make life that much more pretty while they just sit in the background, beneath our threshold of conscious attention – but which often reveal truly striking beauty when we pay them a bit of attention.

Additional photos courtesy of Reciprocity, SEngstrom and suchstuff; see more in the Caustics pool on Flickr. You might also like to play about with my interactive caustics-simulation animation, Zoobie.

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Skywatching

AweI recently finished reading The Cloudspotter’s Guide (see review), and have concluded that it is one of my all-time favourite books. I have made skywatching a hobby for as long as I can remember, but the book has raised my awareness of the skies above us to new heights. As it happens, this has coincided with some absolutely pheomenal skywatching weather in Edinburgh, warm seas and sunshine feeding vast Cumulus clouds, weather fronts dropping stunning Cirrus squirls from the heavens, fascinating layers on layers of different clouds.

I’ll return to the book later; for now I just wanted to share the results of just two day’s skywatching…

The first of those days found me sitting in Holyrood Park one fine, sunny-cloudy afternoon after work, with my camera and a copy of The Cloudspotter’s Guide, with nothing to do but read about, watch and record the sky. The weather was as good as perfect for it – strange ice clouds high above, brooding storm clouds just far enough away not to alarm, and enough sunshine to keep us warm and illuminate the early-autumnal haze with lovely crepuscular rays.

Cirrocumulus lacunosus undulatusWith the help of the Guide I was able to identify this unusual net-like formation with some confidence as a Cirrocumulus lacunosus undulatus – that is, a collection of high, icy cloudlets forming a layer punctuated by holes – lacunas, if you like. Granted, that doesn’t tell us much of any real use, but still, it’s always nice to be able to put a name to something that’s been puzzling you.

Puny HumansThe banks of Cumulus congestus dwarfed the Salisbury Crags, which in turn dwarfed the people climbing them. I knew that it would rain on us sooner or later, but I had time to capture a series of pictures to turn into a highly amateur time-lapse film, so that I could watch those beautiful convection cells in action later. There’s a small version of this here, but if your computer can take it I recommend the full 2-megabyte version. I could have saved myself a lot of work later if I’d had a tripod with me – and a timer would help – but I didn’t have anything fancy to hand, so I just balanced the camera on my knees and took a picture every few seconds for a couple of minutes – compressed here into a couple of seconds.

A few weeks later the skies around Edinburgh were dominated by vast, looming, ever-growing Cumulus congestus and Cumulonimbus: puffy, dramatic and often deceptively solid-looking rain clouds, pouring down their loads even as they burgeon with freshly condensed droplets, up-wellings of warm, moist air racing to refresh them before they rain themselves out. I was staggered to end up avoiding the rains entirely, though it can’t have been more than a mile or two away at any point in the afternoon.

That day’s convection clouds came accompanied by a smattering of Cirrus clouds streaming out of a subtle Cirrostratus, showing that the air was moist right up to the highest reaches of the troposphere – to the tropopause, where the weather stops. Their ice crystals refracted the sunlight in a stunning range of displays; I have been watching out for such things for years, but had never seen such a range of ice halo phenomena in one day.

There were striking sun dogs (also known as parhelia, or mock suns) – the most obvious of the halo phenomena, these appear more than once a week in northern Europe, but most people still fail to notice them. They are created by horizontally-aligned plate-like ice crystals; the sunlight passes through one side of these transparent hexagons and out of another, making a bright, coloured patch of sky 22° or so away from the sun – about the distance from thumb to little figure of an outstretched hand at arm’s length. The colours are not always obvious, but when they are you can see that the sun dog is reddish towards the sun, and bluish on the other side – sometimes with a long, not entirely un-doglike tail.

The exact same kind of ice crystals produce the circumzenith arc, a ‘sky smile’ in vivid rainbow colours, going part-way around the top of the sky, above the sun. As on that day, these are therefore likely to be seen at the same time – although they are not seen as often as sun dogs, partly because they only appear when the sun is quite low in the sky. In their case, the bright colours – which at their best can out-do any common-or-garden rainbow – are the result of light entering the top of the ice-plates and leaving through the sides.

Accompanying these, less spectacular but undeniably still pretty, I was unsurprised by the appearance of a 22° halo, the most common halo effect produced by Cirrostratus; these are made by columnar ice crystals, like tiny pencils, which are randomly oriented, and they appear almost one day in three. When these crystals have smooth, flat ends (which they rarely do) they can also produce a 46° halo, much fainter and much larger than their cousin. When the columnar crystals are roughly horizontal, they can also produce a tangent arc, somewhat resembling a giant dove made of pure light. If my judgement is on, I was privileged to see both that afternoon.

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Salt Forms

The salt bin grinsThe salt bin opposite my flat provides me with a suprising amount of intrigue. Somewhere down the line, it filled up with water enough to become distended – or became distended enough to fill with water – so now it sits there and forever grins invitingly, like some kind of fat plastic crocodile.

It’s permanently full up with water now – intensely saline water, of course, which does some pretty interesting things when it’s stagnant… when someone dumped an old paperback in there, for example, it quickly became encrusted with those characteristically square salt crystals, like the ones you can buy at fancy delicatessens (‘fleur de sel‘)… although not so appetising.

Jagged salt spike layerLater, days of intense, steady sunshine led to some fascinatingly rich crystal formations around the borders of the salt bin, as an inch or two of the water evaporated.

Then, most recently, a combination of wear and tear with hot, hot sun and heavy rains have led the bin to start cracking at the sides, sweating its saline drips in waves to leave a story of the weather inscribed on its sides.

I suppose this would be a good place to write about the way crystals derive their shapes from the way their component molecules stack together, or about the echoes of geological forms in small-scale emergences like this.

…maybe some other time.

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