| A Tangle of Rainbows |
| Tuesday, 10 June 2008 | |
|
James Bullock unravels the mysteries of the rainbow Optical atmospheric phenomena can be stunning events that transform the sky. They are as varied as they are beautiful, impressing with both striking colour displays and their dramatic scale. Even simple clouds can grow to 19 kilometres tall and stretch across entire countries. It is not surprising then that these heavenly displays have been used as powerful metaphors in both religion and science. The magnitude of a rainbow lends itself easily to divine images whilst its artistic appeal prompted Keats to famously accuse Newton of "un-weaving" it, dispelling its mysteries and reducing it down to cold mathematics. Despite Keats' criticism, the rainbow in many ways unites the disciplines. Newton himself split the rainbow into seven colours through a belief that it should share the same number of divisions as a musical scale (hence the slightly dubious separation of 'indigo' and 'violet'). So what exactly is the science that "un-weaves" the rainbow? The answer evokes the simple principles of classical ray optics. Sunlight enters a rain droplet and slows down as it encounters a denser medium, as a result light is refracted and bent. The different wavelengths that make up white light are slowed by different amounts and the colours begin to separate. This dispersed light ray reflects from the back of the water droplet and exits as a rainbow spectrum over a narrow range of angles around 42º. This explains why the rainbow always appears in the direction opposite to the sun, as the brain sums up all the droplets into an arc of colour, projecting away from the raindrops. Each observer will therefore always see their own unique rainbow, which stays with them as they move (meaning that the pot of gold can never be reached). A secondary bow can also often be observed and is the result of a further set of reflections within the water droplet, flipping the colours around and exiting at a higher angle (52º). This gives a beautiful, if rather faint, band above the first. Following the same logic, higher order bows are also possible but they are increasingly faint and so are seldom seen.Nature always likes to play with simple designs and the rainbow has many variations. At sunset for example, when all but the red light has been scattered from the sky, an entirely red rainbow can be formed from the crimson light. On particularly bright nights, a pale 'moonbow' can form, appearing ghostly white due to the inability of our eyes to accurately observe colour in poor light. A further effect may occur with a large body of water around, where the sunlight can be reflected. This allows a second rainbow to take to the sky, appearing as if the first had split in two. All these phenomena can be explained by Newton's use of classical ray optics as detailed in his 1704 work, Opticks. However, although his approach generally predicts the correct results, it fails to explain several detailed features of the rainbow. In particular, it does not predict the supernumerary bows, which are faint rainbows observed inside the primary bow and the mysterious 'glory', a circle of colour emitted directly from the back of the raindrops (back in the direction from which the light has come). The search for an answer to these phenomena ended up inspiring one of the great breakthroughs of nineteenth century physics, wave optics. Originally proposed by Huygens in 1678 and later adopted by Young, wave physics could explain the supernumerary bows as a series of interference patterns produced by diffracting light waves. The final piece of the puzzle came with James Clerk Maxwell (University of Cambridge's first Clarendon Professor) and the immensely important theory of electromagnetism. This meant that by the end of the 1800s, light was no longer seen as a simple stream of 'corpuscular' particles, but also as a propagating electromagnetic wave. Finally, a set of tools was available with which to reveal the actual mechanisms behind the rainbow. An electromagnetic wave will not simply reflect from the raindrop as assumed by Newton, but will be scattered by it. In this process, the water droplet behaves somewhat like a magnet, interacting with the incoming light wave, removing energy from it and re-radiating it as a new wave (this is known as Rayleigh scattering). Maxwell's equations predict that the longer the wavelength, the less the light will be scattered. This explains why the sky is blue: atmospheric dust particles scatter the shorter, blue wavelengths of light across the sky, so this is the colour that reaches our eyes. But, at sunset, when the sun is low and the light is coming directly towards us, the blue light is scattered away, leaving only the longer red wavelengths. However, this model is a good approximation only when the water droplet size is much smaller than the wavelength of the incident light. If this is not so (for example in the droplets of rain or fog), the drop behaves instead as a 'multipole' (imagine a magnet with several norths and souths). There results a more complicated interaction, described by Mie scattering, which produces several new waves. These all interfere with each other, giving bright bands of colour at certain angles-the rainbow. The supernumerary bows mentioned above correspond to secondary bands occurring at larger scattering angles than the primary bow. The glory is a further result of Mie scattering, and is predicted by a complex mathematical argument. In essence, further reflections within the drop guide light along the air-water boundary, giving rise to yet another electromagnetic wave, which travels along the surface of the drop. This can be seen experimentally as a shining ring of light around the water drop's exterior. This travels along the drop and exits as a backscattered cone of rainbow light. As it is seen from the top of the clouds (where the sunlight hits), rather than underneath as for rainbows, an observer must be between the sun and the cloud to see it. This is most commonly the case from the side of a mountain or a plane, but has even been observed from space. The very first occurrence of this was recorded on 23 January 2003 by the MEIDEX instrument of the doomed space shuttle Columbia. It was named the 'Astronaut's glory', in honour of the lost crew. The glory appears as small, bright circles of colour surrounding the head of the observer's shadow projected onto cloud or fog. This halo effect created the legend of the Brocken spectre, named after the peak in the Harz Mountains of Germany where it was often observed. A mountaineer emerging from the mist below him would turn to see a ghostly figure, its head gleaming with a brightly coloured halo. The glory is a far more complicated effect than the rainbow. Whereas the rainbow was easily explained by ray optics and waves, the glory has no precise physical explanation save through the detailed mathematics of Mie theory, a set of analytical solutions to Maxwell's equations. As a result, the glory is still an active area of research. For example, in a 2004 paper by Bernhard Mayer and colleagues from the German Aerospace Centre, they discussed the potential of glories in determining the molecular-scale properties of their parent clouds. The optical properties, droplet radii, and even the size distribution of drops can all be inferred remotely from observations of the angular size of the glory. Available computer algorithms can even simulate a glory given these parameters. Last year, Anatoly Nevzorov of the Russian Central Aerological Observatory even suggested that the presence of certain glories could confirm the discovery of a special phase state of water known as 'amorphous water' in cold clouds, although this finding has recently been disputed. Rainbows and glories are also far from being the only atmospheric spectacles, another particularly elegant example being the nacreous clouds of the polar winter. These stratospheric clouds exhibit a subtle yet striking mother of pearl effect, and their height allows them to stay illuminated with light diffracting through ice crystals to produce the colour. The clouds themselves are formed in a rather unusual way, and feature strongly in the scientific debate over the ozone layer depletion in the 1980s. As temperatures drop over the polar winter, steep differences between northern and southern temperatures develop. As in all weather systems, this difference causes a pressure imbalance, resulting in a stable vortex as the wind rushes in. However rather than restoring equilibrium, the vortex isolates the air inside it and temperatures drop even further. Below -78ºC the air becomes cold enough to condense and then freeze the small amount of water vapour and nitric acid available and the polar, stratospheric clouds form. The clouds provide a large surface area upon which reactions take place, liberating CFC halogens from their otherwise stable forms. As the gaseous nitric acid is frozen inside the clouds, it cannot react with the halogens, removing an essential pathway back to stability. As the sunlight returns, photons enable the reaction cycles between the halogens and ozone. Ozone depletion then continues until the temperature becomes warm enough to break up the polar vortex and the clouds disperse, explaining the seasonal change in the Antarctic ozone layer hole. The rainbow has, since its early description by Aristotle, borne witness to many of man's greatest scientific works - from Newton's ray optics to the wave-particle duality of light and Maxwell's electromagnetism. It has inspired art and literature, religion and science and somehow symbolises an important respect for Nature. It will also never fail to attract the attention of mountain climbers, astronauts or simply passers-by, who are just lucky enough to be in the right place at the right time. James Bullock is a PhD student in the Department of Zoology |
| < Prev | Next > |
|---|
News Archives
| News Archives |
