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

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Figure 6.4. A possible sunstone—a ‘natural’ polariscope made from a cordierite crystal. A screw bottle top with a hole cut in it supports the rough crystal within a short cardboard tube. The direction of polarisation in the crystal can be determined with a piece of polaroid and marked on the outside of the tube. The direction of the sun can then be found by pointing the tube at the sky and watching the crystal darken as the tube is rotated. Compare this device with the ‘synthetic’ version shown in colour plate 7.

the crystal rather than trying to see through it. The tube is then rotated until there is a noticeable darkening within the crystal and reference marks previously made on opposite sides of the tube will then point at the sun. Two such bearings from different parts of the sky show just where the sun is. This works surprisingly well even when the sky is overcast, as long as the cloud cover is not too thick and dark. It does not work nearly as well if the crystal is smooth and polished; greatest sensitivity seems to depend on the changing brightness of glints within the rough stone. It works rather better than the synthetic polariscopes described in chapter 2, and very much better than the simpler ones described in chapter 1 or a calcite dichroscope as shown in figure 3.6.

This arrangement may also help to understand an anecdote from Gudmund’s Saga. He was murdered and robbed and his sunstone was discarded on the beach as worthless, but later it was recovered. It seems most unlikely that a single rough crystal could ever be found again on a beach, but it might have been mounted in a tube, made perhaps of horn, for viewing the sky. This might have seemed of no value to an ignorant person but would have been instantly recognisable as a navigation instrument to anyone familiar with its use. This last bit is my own speculation, because such a device works for me, but I am greatly indebted to Jørgen Jensen of Skodsborg, Denmark, for telling me of these stories and for a stimulating correspondence.

Much more recently, sophisticated sky compasses were developed for transpolar aviation around the 1950s. Before satellite or inertial navigation, and when even radio beacons were scarce, polar navigation presented problems. The magnetic compass is unreliable near the poles,

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indeed it is useless near the magnetic poles, and there are extended periods of twilight when neither the sun nor the stars are visible. But the instruments called the Pfund and the Kollsman sky compasses were elaborate polariscopes that were used to observe the polarisation in the sky above the aircraft and so get a bearing on the sun. Apparently Kollsman sky compasses were used by SAS navigators on direct flights between Copenhagen and Anchorage. The great circle route between these cities passes quite close to the North Pole and even closer to the North Magnetic Pole.

Another application of sky polarisation is in the ‘polar clocks’ invented by Charles Wheatstone at King’s College, London and described by William Spottiswoode in 1874. The sky around the Pole Star is viewed through a polariscope such as a Nicol prism, with some retarder crystals to make the contrast sharper. The instrument is then rotated until it indicates the direction of sky polarisation, which of course rotates around the pole star during the day at 15 ◦ per hour, being horizontal at noon and vertical at 6am and 6pm (figure 6.3). In an ingeniously simple form (figure 6.5) with no moving parts, the original polar analyser is a sheet of glass blackened behind and mounted to view the polar sky at Brewster’s angle (see chapter 7). A fan of retarder crystals formed of slivers of selenite (gypsum) radiates across the view and the most strongly coloured crystal indicates the time without the need for any adjustment. Three such instruments are now displayed at the Science Museum, at the Old Greenwich Observatory and in King’s College, London, and there is another at the Royal Institution. A clock of this kind can easily be improvised with modern materials, using either reflecting glass or a piece of polaroid and a fan of cellophane slips as retarders.

The advantages of a polar clock over the conventional sundial were listed by Wheatstone as: (i) it always faces the same part of the sky and so is not affected by shadows of trees, buildings or mountains—indeed it can itself be mounted in permanent shade as long as it can see the northern sky, whereas a sundial must be exposed to the full arc of the sun’s path; (ii) it works for some time after sunset and before sunrise; (iii) it also works ‘when the sky is overcast, if the clouds do not exceed a certain density’. This last point supports my own experience with the cordierite polariscope used as a ‘sunstone’. A modern variant of the polar clock has been set up as a sculptural curiosity in Dornach, Switzerland.

Finally, the polarisation of scattered light is used in astronomy. For instance the corona around the sun is visible mainly because its

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Figure 6.5. Wheatstone’s polar clock. Light from the region of the sky around the Pole Star passes through a sheet of glass, parallel with the equator and bearing a radial ‘fan’ of selenite or mica crystals that act as retarders. It is then viewed after reflection at Brewster’s angle from a sheet of glass painted black underneath. This acts as a polar analyser (see chapter 7) and the time of day is indicated by which crystal appears most strongly coloured. The angles shown are appropriate for use at the latitude of London (51◦28 N).

Figure 6.6. Viewing the solar corona during a total eclipse of the sun when direct sunlight is blocked by the moon. Light scattered at right angles by the corona (A) is strongly polarised. The strong obscuring glare of sunlight scattered forwards by space dust (B) is not polarised and can, in principle, be separated by the careful use of polar filters (not drawn to scale).

clouds of electrons scatter sunlight towards us (and its spectrum shows a clear inverse fourth power relation to wavelength). But sunlight coming directly towards earth is also scattered forwards by space dust (figure 6.6) and this largely obscures the corona, just as the glare around the headlights of an oncoming car in fog obscures objects behind it. However, the corona light is mainly scattered towards earth at right angles to its orignal path and is therefore strongly polarised whereas the forward scattered light is not (nor does its spectrum show the inverse

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fourth power relationship because the dust is much larger). During total eclipses, astronomers use polarising filters to subtract one component from the other so that a clearer picture can be obtained of the ‘true’ or K-corona.

Another astronomical application has been the analysis of the clouds that surround the planet Venus and completely hide its surface from our view. The polarisation of light scattered by these clouds was first studied in 1922, and in 1971 a very ingenious analysis was able to establish the following facts: most of the cloud particles are spherical and their mean diameter is close to 2 µm; their refractive index at a wavelength of 550 nm (yellow–green) is 1 .45 ± 0.02 so that they cannot consist of pure water or ice; and they float high in the atmosphere where the pressure is only about 50 mbar. That is an impressive body of information to obtain from observations of polarised light by telescopes here on earth and it depends almost entirely on the polarisation produced by scattering.

Chapter 7

Reflection

One afternoon in 1808 a French scientist called Etienne-Louis Malus discovered something remarkable about light reflected from transparent materials. From his home in the rue d’Enfer in Paris, Malus examined the sunlight reflected from a window in the Palace of Luxembourg, just over 1 km away to the north-northeast. Looking through a birefringent crystal, he expected to see two images of equal brightness (see chapter 3) but instead he found that if he rotated the crystal around the line of sight, each image from the window was dimmed in turn every 90 ◦. As night was drawing on, he continued his observations with candlelight reflected by glass (as in figure 7.1) and also when reflected in the surface of a bowl of water. He found that the effect was most marked when the angles of incidence and reflection were around 55 ◦, though slightly more for glass than for water.

The details of this important story often vary in the telling: sometimes it is said a calcite crystal was used, sometimes a quartz, and even the date is quite often misquoted. Malus’ early papers on the subject (from December 1808) do not seem to relate the original circumstances, which were anecdotally recounted only in 1855 by his friend Francois Arago, in a posthumous appreciation of Malus commissioned by the Academie des Sciences. Arago only referred to the use of ‘a doubly refracting crystal’, but he was also discussing calcite in detail in adjacent paragraphs. The use of quartz is usually much trickier because the two images overlap so much (see chapter 3) and therefore might seem less likely. On the other hand the glint from a window 1 km away is quite small and could give separated images through a quartz crystal, although a candle flame would probably be too large a source in a domestic room.

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Figure 7.1. Polarisation by reflection in a sheet of glass. A vertical light box (a backlit translucent screen) has a piece of polaroid propped against its lower right, with the polarisation direction vertical. Light from the screen reflects well from a horizontal sheet of clear glass and also passes quite well through the polaroid. But light from the polaroid is not reflected in the glass because it is incident at around Brewster’s angle at which only horizontally polarised light can be reflected.

The Palace of Luxembourg housed the Senate as it still does today. The garden, which is open to the public, now has tall plane trees and there are tall buildings near the Passage d’Enfer that would almost certainly obscure the view, even from the top floor. But one can get a splendid bird’s eye view of the whole area from the top of the 200 m high Montparnasse Tower, a little more to the west and a comparable distance from the Palace. From there I found that a small quartz column easily resolves glints from the Palace as double images. A visit to the Palace garden also showed that the windows open on hinges, thus allowing the possibility of being set at a reflecting angle, although the building itself is arranged exactly north–south. But the sun must have been low that day in 1808 for its reflection to be seen at a distance over level ground, so the event must have started late in the day. In mid-summer the setting sun, as reflected to the Passage d’Enfer by a suitably opened window, would have an angle of incidence within about 7 ◦ of Brewster’s angle (see p 74)—close enough to give a high degree of polarisation since the maximum effect is not at all critical.

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Those seemingly simple observations have been hailed as a great turning point in our understanding of optics and the nature of light. At that time there was great puzzlement over the two rays produced from a single source by a birefringent crystal (see chapter 3). When two similar crystals are superimposed, the two rays may be split into four; but as one of the crystals is turned, the four become two and at one point (provided the two crystals are equally thick) even fuse to become one. This was thought to be a curious and inexplicable property of the crystals themselves, but Malus now showed that the nature of the light itself is different in the two rays. Light reflected from glass or water was clearly unusual in some way since it could form either of the beams normally produced by a birefringent crystal, depending on the orientation of the crystal. This light must therefore have some characteristic of its own that is expressed at right angles to its path.

This new way of producing polarised light by reflection very soon led a number of investigators to develop the first explanations both of double refraction and of the nature of polarisation itself. In 1808 the Academie des Sciences in Paris had offered a prize for a theory of double refraction in crystals and it was awarded to Malus in 1810; he died in 1812 aged only 37. Polarisation by reflection has also proved to be of great practical importance because in all optical devices every surface, including those of lenses, introduces some reflection and therefore some polarisation, and this may affect their operation, as discussed in detail later.

We now know that the two beams from a birefringent crystal are polarised in opposite ways and that Malus’s observation of alternate dimming of the beams shows that light reflected by shiny, non-metallic surfaces is itself polarised. The direction of such polarisation is at right angles to the plane of the incident and reflected rays and this gives a simple way (as promised in chapter 1) to find which way any given piece of polaroid is aligned. Look through it at a reflection from any horizontal, shiny surface (water, glass, polished wood or gloss paint) and rotate the polaroid until the reflection dims. The direction of polarisation for transmission through the polaroid is then vertical and can be marked in one corner.

Malus soon showed that any light reflected from a piece of glass at an incidence of 57◦ can be reflected again from another, parallel piece (thus also at 57◦), but when the second piece is rotated around the incident axis (figure 7.2) its reflection is extinguished twice in every turn. At angles of incidence other than 57 ◦ the dimming is less effective.

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Figure 7.2. Malus’s experiment. Two parallel glass sheets reflect light at an angle of incidence of 57◦. But when the upper one is rotated around the vertical axis, the emergent beam fades twice as it swings round in a circle. The plates act as polariser and analyser, or second polariser.

The same effects were seen when light was reflected from glass and water in turn. Then in 1814 David Brewster realised that this ‘best’ angle of incidence is the one whose tangent is equal to the refractive index of the reflecting material. This is now known as Brewster’s angle, at which reflected light is fully polarised. Thus the Brewster angle for glass is 57◦ because its tangent is 1.54 and that is the refractive index for glass. Brewster’s angle also has the property that the reflected ray and the refracted ray entering the material are at right angles to each other (figure 7.3).

At Brewster’s angle, only around 15% of the incident light is reflected but as it is very nearly 100% polarised, a simple reflector can be used as a very cheap polariser of wide aperture. As Malus found, a second reflector can act as a second polariser or polar analyser, reflecting the light to a varying degree, depending on its orientation to the direction of polarisation from the first reflector. This then completes a simple but very effective home-made polarising apparatus. The reflectors are best made from black perspex (plexiglass) but clear perspex will do perfectly well if the back face is painted black (without the paint there

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Figure 7.3. Brewster’s angle. At the surface of a transparent material a beam of light is partly reflected and partly refracted. At high incidence (left) the two ongoing beams form an obtuse angle and at low incidence (centre) an acute angle. They are exactly at right angles to each other (right) when the tangent of the angle of incidence is equal to the refractive index (57◦ for glass in air). The reflected light is then virtually 100% polarised, in a direction normal to the plane of the diagram.

are distractions due to both transparency and double reflection). Glass is even cheaper but it is fragile. The plates, say about 10 cm × 15 cm, must be mounted in rectangular cardboard frames so that they lean across the axis at 34◦ (i.e. 90◦ −56◦ for perspex, or 33◦ = 90◦ −57◦ for glass, to be rather unnecessarily precise). A hole cut in the cardboard wall completes the optical pathway (figure 7.4). A sheet of clear perspex or glass, placed on top of one frame, can then support the other and also the objects to be examined. Relative rotation around the vertical axis allows the polarisers to be set parallel or crossed as required. With a little ingenuity the whole apparatus can be made to fold flat when the reflectors are removed so that it can all be stored in a shallow box.

This very simple device, or variants of it, can be used to demonstrate most of the vivid effects described in chapters 2 and 3 without the expense of large sheets of polaroid. Indeed until the 1930s reflection from glass was the only way to obtain large polarisers since both Nicol prisms and tourmaline crystals were necessarily small. A pair combined as shown in figure 7.4 was called a reflecting polariscope. It does have two drawbacks, however. First, the effectiveness is somewhat degraded towards the edges because the incident light and the line of view cannot be strictly at Brewster’s angle across the whole field, especially if source and viewer are nearby. Second, the reflection is rather weak (at most

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Figure 7.4. A reflecting polariscope made with two perspex sheets in cardboard stands. Left: a section showing how light is reflected twice at Brewster’s angle giving the bright field effect of parallel polarisers. Right: a view of the device with the top rotated to give the dark field effect of crossed polarisers.

only about 15% of the incident light is reflected at the first surface) but this can easily be compensated for by using a bright source such as a small halogen lamp.

One way in which the brightness can be increased is to use a stack of parallel, transparent plates and take either the reflected or the transmitted light, usually the latter. At Brewster’s angle the light reflected from one surface is dim but very strongly polarised. So the remaining light that passes onwards through the plate will be partially polarised by the subtraction. This light then meets the second face of the plate at Brewster’s angle (due to refraction the angle is now different from the original incidence but it matches Brewster’s angle exactly since in a denser medium it is the cotangent, not the tangent, that is equal to the refractive index). Light reflected back into the plate, therefore, is again totally polarised and the light passing on into air is a little more polarised (figure 7.5). So it would seem that passing this light through other, parallel transparent plates will reflect away more and more of the light polarised in one direction, making the remainder progressively more polarised. If the plates are very clear, this ongoing beam may be very