Файл: Pye D. Polarised light in science and nature (IOP)(133s).pdf

all of one kind, are collected; then seeds of the other stereoisomer are used and the resultant crystals discarded. By alternating in this way a high yield can be obtained with very low contamination. Seeds can be very small so a single crystal, once isolated, can be fragmented and multiplied quickly.

Sometimes a racemic mixture can be combined with one stereoisomer of another chiral compound; the two kinds of molecule thus formed will not be simply mirror images but will have quite different shapes. This means they will have different solubilities which makes them easier to separate by crystallisation before the wanted stereoisomer of the original substance is recovered by separation from its temporary partner. Pasteur managed to separate the stereoisomers of racemic acid in this way by first combining them with naturally chiral quinine.

Another naturally occurring, optically active substance is turpentine. This is a mixture of chemical substances obtained by ‘bleeding’ the trunks of various coniferous trees. The direction in which it rotates polarised light varies, depending on the species of tree from which it is derived; it is commonly laevorotatory but may be dextrorotatory. Either way, this forms a simple test for ‘genuine’ turpentine since the cheaper synthetic turpentine substitute is optically inactive.

One further occurrence of chirality must be mentioned—that found in certain crystals. One example is sodium chlorate (NaClO 3) where the molecules are not chiral so that a solution in water is optically inactive. But when crystals form, although they have simple shapes (generally cubic but under some conditions tetrahedral), their internal lattice structure may take either of two mirror-image patterns, so that any given crystal will be either laevorotatory or dextrorotatory.

Another example is quartz. In chapter 3 it was stated that crystals show no birefringence for light passing along their optical axes. This remains true for quartz but quartz crystals do show optical activity, rotating the direction of polarisation, for rays along their axes. Quartz is silicon dioxide and the SiO2 molecule itself is not chiral so that fused quartz is optically inactive (it is of course insoluble in water). But the lattice of quartz crystals consists of a complex mesh of interlocking helices (often, wrongly, called spirals), with each atom being incorporated in several helices with different axes. A helix is chiral and, once a crystal starts to grow, it must be consistent, so that quartz crystals come in two chiral forms which are mirror images of each other (figure 5.7) and show the opposite optical activity along their axes. So in

Figure 5.7. Quartz occurs in two chiral forms and in alpha quartz these can be distinguished on a macro scale by small facets; these facets are missing from beta quartz which is more difficult to characterise chirally. Polarised light passing along their optical axes is rotated in opposite directions in each kind so that they can be designated laevo and dextro quartz, here seen on the left and right respectively.

both quartz and sodium chlorate, the molecules themselves are not chiral and chirality is a property only of the crystal lattices.

Slices of quartz crystals cut normal to their optical axes are commonly used as elements in optical instruments (including some designs of sensitive polarimeters), often as leftand right-handed pairs side by side. Because different wavelengths are rotated to different degrees, a thick slice of quartz cut normal to its optical axis shows colours between crossed polarisers that change when either polariser is rotated—but not when the crystal itself is rotated. These ‘rotation colours’ are therefore quite distinct from the colours produced by the property of birefringence that retards light crossing the optical axis of the same crystals as described in chapter 3. Quartz crystals are much easier to identify, and may be much larger, than the tartrate crystals separated by Pasteur, but the matter is complicated because quartz occurs in two forms depending on the temperature at which it was originally grown. ‘Alpha’ quartz has a distorted lattice and small extra facets on the ‘shoulders’ of its column that make its chirality obvious (figure 5.7) but these are missing from the common ‘beta’ quartz. Also real quartz crystals are often distorted and seldom look quite like the pictures ‘in the books’. Only perfect alpha quartz is easily identified in this way.

Chapter 6

Scattering

On the moon, the sky is black and the stars shine clearly even when the sun is high. But here on earth the clear daytime sky is blue and no stars can be seen through it. This was explained by John Tyndall, Director of the Royal Institution, in the 1860s as the scattering of sunlight in the upper atmosphere. He showed that small particles scatter light of short wavelengths more strongly than longer ones: blue more than red. That is why fine smoke and mist look blue. It is well known that distance, as depicted in a painting for example, involves a graded blue tinge. A. E. Housman asked ‘What are those blue remembered hills?’ and Thomas Campbell gave the answer ‘’Tis distance lends enchantment to the view, And robes the mountain in its azure hue’. Tyndall explained that even on clear days a very long propagation path will accumulate shorter wavelengths that have been scattered to form a blueish veiling.

Lord Rayleigh soon worked out the theory of it and calculated that even gas molecules in sufficient quantity will scatter blue light, so that air in the upper atmosphere looks blue without necessarily containing solid or liquid particles. For this reason molecular scattering is often called Rayleigh scattering. He found that for very small particles, smaller than the wavelength, the amount of light scattered is inversely proportional to the fourth power of wavelength, so that deep blue light of 420 nm is scattered ten times more strongly than deep red light of 750 nm. It follows of course that shorter wavelength ultraviolet (UV) light is scattered even more strongly, so the sky is very bright in the near-UV, even though UV is less strong than yellow light in sunlight itself. Many animals can see this near-UV although we humans cannot.

Tyndall scattering by small particles is very common in nature, and

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some familiar examples are the colour of blue eyes, the blue faces and rear ends of mandrills and some monkeys and the blue feathers of many birds such as tits and kingfishers. Wild-type green budgerigars combine Tyndall scattering with an overlying yellow filtering pigment to give their bright green colour. A genetic deficiency in producing the yellow screening gives the blue varieties, and a failure to develop the Tyndall scattering particles gives yellow birds. A similar combination is found in green tree frogs.

John Tyndall performed laboratory experiments on the scattering of light by smokes in air within a long glass tube, part of which is still on display at the Royal Institution. He found that the scattered light is polarised in a direction normal to the axis of the beam. In a horizontal beam of light all vertical components are scattered sideways (horizontally) and horizontal components are scattered upwards and downwards (vertically: figure 6.1). The degree of polarisation is greatest, nearly 100%, when viewed ‘side-on’ at 90 ◦ to the original beam and it becomes less as the angle of scattering decreases both forwards and backwards. All this was given a theoretical basis by Lord Rayleigh and it explained the fact that blue sky light is polarised, as had been observed by the Frenchman Franc¸ois Arago back in 1809. The actual degree of polarisation is always less than the ‘theoretical’ value, often markedly so, due to secondary rescattering of the light on its way to the observer. Blue eyes also show changes in brightness when viewed through a rotated polaroid. Irises of other colours have larger scattering particles and can show some polarising effect provided they are not too dark.

A beautiful demonstration of polarisation by scattering can be made with a column of water held above a bright halogen lamp (figure 6.2). A few drops of Dettol (or milk) disperse as very fine droplets to form a pale blue scatterer (colour plate 22), and a piece of polaroid shows that this light is polarised. If the polaroid is placed under the column, then the light is already polarised and can only be scattered strongly in two opposite directions and not at all at right angles. This is seen by the naked eye without the need for another polariser since the column itself acts as the second polariser. Also the polarisation, and therefore the brightness, is strongest for light that is scattered sideways at right angles to its own path; if the column is viewed at smaller angles to its axis, the polarisation is progressively weaker and dimmer as indicated in figure 6.1. Turning the polaroid then rotates the two scattered ‘beams’ round the room so that the intensity of scattering appears to wax and wane.

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Figure 6.1. Light passing through a suspension of fine particles, such smoke in air, becomes scattered. Light scattered at right angles is essentially 100% polarised with the direction of vibration normal to the path of the original beam (the scattered beam shown here will be polarised in a direction normal to the page). Light scattered in more forward or more backward directions is progressively less strongly polarised as indicated, although the predominant direction of polarisation remains the same (only a small scattering region is shown). At the right is a view along the column, showing the polarisation directions for light scattered at various angles around the axis.

An especially splendid effect is given if a retarder film of cellophane (see chapter 2) is put above the polaroid. The scattered light is then deeply tinged around the column, say blue in two directions, front and back, and the complementary orange at right angles to each side, where there was previously no scattered light. Again these effects are seen by eye alone, without another polariser. A different retarder film may give purple and green and so on (colour plate 23). These other colours also show that it is not only blue light that is scattered, although that is the predominant tinge when retarders are not used. Similarly the blue sky shows the whole spectrum when it is viewed through a spectroscope although the shorter wavelengths are brighter and so give the overall impression of being blue. Such impure blue is said to be unsaturated.

Another spectacularly beautiful demonstration was popular in the late 19th century and has been drawn to my attention by Sir Michael Berry. If the column is filled with a strong sugar solution and a polariser is placed below it, then scattering takes place but its direction is twisted along the tube by the chiral sugar (see chapter 5). Furthermore, different colours are twisted at different rates so that the scattering is coloured through the full spectral sequence along the tube (colour plate 24)—a

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Figure 6.2. A demonstration of scattering by fine droplets (e.g. Dettol or milk) dispersed in a column of water. A strong lamp (l) and heat filter (f) project light upwards into the column. If a sheet of polaroid (p) is placed beneath the column, the light can only be scattered strongly in two directions, say A–A. A retarder film (r) placed above the polaroid colours the scattered light and the complementary colours are then seen to be scattered sideways at right angles to each other: A–A and B–B. Turning the polaroid and the film together makes the colours rotate around the column. Above the column a white card is used to examine the colour of light that is not scattered.

rainbow-hued barber’s pole! Viewing at right angles around the axis, or rotating the polariser, shows that at every level each colour is replaced by its complementary colour. If the polariser is rotated slowly and steadily, then the sequence of colours appears to pass smoothly along the column. Quite a short column is adequate if the sugar solution is very strong. Fructose (fruit sugar available from health food shops) is especially effective because it has a much higher specific rotation than sucrose and it is also extremely soluble, so that the syrup can be made very strong.

To return to simple scattering, the properties shown above explain why the polarisation pattern of the blue sky is formed in rings around the sun, weakly near the sun itself but very strongly along the arc at

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Figure 6.3. Sunlight is scattered by the atmosphere and is polarised in rings around the sun/anti-sun axis. Near the sun the light is scattered forward and is weakly polarised; the arc at right angles to the sun scatters at 90◦ and is very strongly polarised, while backscattered light from near the anti-sun point is again weakly polarised. The patterns shown here are (left) noon at the latitude of southern England at the equinox and (right) sunset or sunrise. The arcs shown are at 30◦ intervals and the idealised values for their degree of polarisation are 14%, 60%, 100% and 60% again. Actual values would all be lower due to secondary scattering and there are additional effects, not depicted here, near the horizon. P labels the position of the Pole Star around which the polarisation pattern rotates daily.

right angles to the sun (and its rays) and then progressively weaker again towards the ‘anti-sun point’ (figure 6.3). The maximum degree of polarisation is rarely more than about 70–80% because some of the light becomes scattered again on its way down to the ground, especially if the air is hazy. Rescattering also adds some slight complexities to the pattern itself, especially near the horizon, but these are seldom significant. The demonstration in the scattering column can also simulate a red sunset. Adding more Dettol scatters more of the predominantly blue light so that what is left, emerging from the top of the column, is orange or red (colour plate 22). Similarly, light from the low setting sun has passed over the heads of people to the west and made their sky blue, so the remaining light is left richer in the longer red wavelengths. Enhanced effects are often produced when the atmosphere contains fine ash from

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distant volcanoes. It is also true, if rather unromantic, that some of the most spectacular sunsets nowadays occur in cities where scattering is enhanced due to pollution products in the atmosphere.

The polarisation of the blue sky can be very important in nature. Fifty years ago Karl von Frisch was studying the navigation abilities of bees and discovered the way in which they can ‘tell’ other worker bees where there are rich sources of food. In both cases bees refer to the position of the sun. When a bee flies out to forage, it notes the position of the sun in the sky and uses the reciprocal bearing to find its way back to the hive afterwards. Due allowance is made for the fact that the sun moves across the sky during the day. When food is scarce, a bee may fly as much as 5–10 km from the hive and be away for up to 4 hours, during which the sun moves 60◦, yet the insect still makes a ‘bee-line’ home. It then performs a ritual dance in the hive in which the direction of a good food source is indicated to other bees, again by reference to the direction of the sun.

But von Frisch found that when the sun is hidden by a cloud or behind a mountain or trees, the bees carry on normally. As described in more detail in chapter 9, he found that they are able to detect and use the pattern of polarisation in the sky. We now know that for bees and many other insects the ‘sun compass’ is actually less important than the ‘sky vault compass’, formed by to the pattern of sky polarisation which is, however, centred on the sun itself.

In fact the sky polarisation is generally sensed by insects in the near ultraviolet part of the spectrum. Those facets in the dorsal rim region of a bee’s compound eye face upwards or forwards (figure 9.5) and so look at the sky. They are also the facets that are sensitive both to ultraviolet and to polarisation. So to a bee the sky must look very different indeed from the sky that we see; instead of being plain blue it must be very bright in the ultraviolet and have a highly structured pattern of polarisation. More details of the sensitivity to polarisation in the eyes of bees and other insects are given in chapter 9.

In recent years it has even been suggested that migrating birds might use sky polarisation as an aid to navigation. Long flights often start around dusk, and for some time after sunset both the band of maximum polarisation and the direction of vibration stretch overhead across the sky in a north–south direction (figure 6.3). As this fades, the stars come out and birds are certainly known to use star patterns as a sky compass.

The sky compass has also been used by man for navigation. The Vikings were intrepid voyagers across the North Sea and northern

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Atlantic as much as two centuries before the magnetic compass became available. Between about 860 and 1010 AD they colonised Iceland, discovered and colonised Greenland and even visited both North America and Spitzbergen. Yet the magnetic compass almost certainly did not reach Europe until about 1200 AD. It is widely accepted that the Vikings used the sun and stars in their navigation but cloud would have been a problem. In the sagas there are passing mentions of a ‘sunstone’ by which the pilot could determine the position of the sun even through clouds. Admittedly the evidence is slim and it has been criticised because it would be of no use without also knowing the time of day, which can itself be measured from the sun only if one knows its direction. But the circularity of this argument can much too readily be used to dismiss the sunstone hypothesis. The passage of time is entirely predictable and can be estimated fairly accurately by the body’s ‘internal clocks’. Although wind and wave directions are often used to sail a constant course, they may change quite quickly and unpredictably and the use of a sunstone could have drawn attention to this. Any additional estimate of direction, even if not very accurate, might be very useful in an otherwise featureless environment.

Furthermore, the long expeditions to the west and back took many months, so the voyages must have begun as soon as winter was safely over and may not have ended until it was closing in again. At the high latitudes involved, in spring and autumn there would have been virtual twilight for most of the 24 hours with little or no actual sighting of the sun even in fine weather. The sky vault polarisation pattern would have had much to offer at such times, even under clear skies. The sunstone story is also rejected by many authors on the grounds that it would not work at all when the sky was generally overcast. The claim in Rodulf’s Saga, in the Flateyarbok, that the sun was thus located during a snowstorm is probably a romantic exaggeration—or even bluff as it was done at royal command with no possibility of verification or contradiction—but the technique can be made to work under quite thick cloud cover as the following can show.

It is suggested that the sunstone might have been the pleochroic crystal cordierite or possibly andaluzite, epidote or tourmaline, all of which occur in Scandinavia. It would certainly not work adequately with calcite (Iceland spar) as has sometimes been assumed. A rough, unpolished cordierite crystal mounted in a short tube (figure 6.4) forms an excellent polariscope for observing sky polarisation. The tube shields the crystal from all but one region of the sky and the user should look at