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

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Figure 7.5. Multiple reflections by more than one sheet of glass. Light reflected from the first face at Brewster’s angle is not bright but it is completely polarised; light refracted from this face meets the second face at Brewster’s angle for the denser medium and the reflection is again fully polarised. The ongoing light (heavy line) is therefore enriched in light polarised at right angles—within the plane of the diagram. A second and further plates repeat the process so that the emergent beam is bright and, in principle, becomes progressively more polarised. But all the reflected light does not necessarily leave the system because some of it is reflected again as shown by the finer lines, and some of this ‘unwanted light’ can re-enter the onward path to degrade the final degree of polarisation.

bright—approaching 50% of the incident intensity. Many textbooks say a high degree of polarisation is quickly achieved, by as few as eight plates, and calculations of simple repeated subtraction would seem to support this.

But in practice things are rather more complicated and less effective. The main problem is that if the successive plates are close together, the light reflected from each face does not leave the system but is reflected again by the adjacent plate. It will also be reflected internally within each plate. Both processes may be repeated many times for each ray and can only be avoided by quite elaborate design. Proper analysis shows that even 16 plates in a simple stack at Brewster’s angle can only achieve 74% polarisation. This theoretical performance is greatly degraded by dust or by imperfections on the glass surfaces. Adding more

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plates gives diminishing returns and begins to add serious loss due to absorption of the transmitted rays. Indeed a simple stack of thin glass plates does not even give the greatest polarisation at Brewster’s angle but at a much higher, near-grazing angle of incidence, as noted by Brewster himself in 1831. For most purposes, therefore, a plain stack of plates is not a practical solution despite its apparent simplicity. Nevertheless a sophisticated modern version can be made by building a layer of say 25 very thin films between the faces of two prisms; by adjusting the thickness of the films, all less than a wavelength, it is possible to achieve a high degree of polarisation up to 98%, at least over a narrow range of wavelengths.

Iridescent natural materials, such as some butterfly and beetle colours, some fish scales and feathers, and the mother of pearl in shells, are composed of multiple microscopic layers of material whose very many internal reflections interfere to produce different colours in different directions. The gemstone opal gives similar effects from a structure composed of an array of microscopic spheres of silica. As might be expected, the reflected coloured lights from these materials are sometimes quite strongly polarised, as can be seen when they are examined through a rotated polaroid. Most of the bright glints of hoar frost sparkling in sunshine are also strongly polarised in a direction depending on the angle of view; the few exceptions are presumably reflecting well away from Brewster’s angle and so remain bright when seen through a rotating polar.

Malus himself found that reflections from the surface of water are strongly polarised in just the same way as for shiny solids, with a Brewster angle of 53◦. This accounts for the usefulness of polaroid sunglasses. It is seldom that the actual brightness of light is distressing to the eye but rather the glare: unwanted light coming from below. Much of this is horizontally polarised, especially when reflected from wet roads but also quite strongly from most kinds of dry ground. Polaroid sunglasses are vertically polarised and so they greatly reduce glare even when the line of sight is not very near Brewster’s angle. (The downward looking parts of some insect eyes are sensitive only to vertically polarised light, presumably to achieve the same end when flying.) Polaroid glasses give a quite dramatic effect when one looks into still water, for reflections at the surface are reduced and at Brewster’s angle are effectively abolished. One can then see clearly into the depths, with details of the bottom, weeds and fishes that are normally obscured by reflection of the sky or clouds. The water surface may seem to disappear

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Figure 7.6. A sound in Bermuda photographed through a vertically orientated polaroid filter. The bather is sitting near the edge of the water which is very clear and quite still. When the polaroid suppresses surface reflections the water virtually disappears.

completely (figure 7.6) provided that there are no ripples.

The polarisation of light reflected from water is admirably exploited by the aquatic bug called the Water Boatman or Backswimmer (Notonecta). As its names suggest, this insect lies on its back at the surface of freshwater and rows itself around by means of greatly enlarged back legs (figure 7.7). But from time to time it flies off looking for a new pond or ditch. In 1935 it was noticed that just before plunging in, when less than a metre above the surface, the insect hesitates briefly and tilts itself upwards by nearly 20◦. This was explained only in 1984 by careful examination of the insect’s vision. The ventral facets of its compound eye each contain eight sensory cells of which two are sensitive to ultraviolet, one polarised vertically, the other horizontally. When swimming, these facets look up at the sky and would seem to be ideal polar analysers for sky compass orientation (chapter 6). But no facets of this kind look forwards—at all angles more than 35 ◦ from vertically below (figure 7.7) all the polarisation sensitive cells respond only to horizontal polarisation. In flight, these forward-looking facets

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Figure 7.7. The Water boatman (Notonecta): top, swimming on its back; below, side views of the head; left, in normal flight posture; and right, tilted up by 28 ◦ before plunging into water.

would be ideal for detecting the polarised light reflected from standing water because light that is horizontally polarised is more likely to be seen if all the visual cells are maximally sensitive to light polarised in that direction, although they would not be able to tell that it is, in fact, polarised. But during the final plunge, the upward tilt brings some downward-looking, analysing facets just up to Brewster’s angle. Maximum stimulation of some cells and loss of stimulus to the others would then confirm that the light does come from reflection off a liquid and the bug can safely complete its dive. In ingenious laboratory tests, bugs landed on upward-facing lamps but only if they emitted ultraviolet light that was polarised transversely to the line of approach, thus simulating light reflected from water.

Dragonflies also have downward-pointing facets able to analyse the polarisation of either ultraviolet or of blue light. As before, these probably serve to detect the presence of water. It has also been suggested that, as the dragonflies fly over an expanse of water, the reflected light from all sides is predominantly horizontally polarised and could provide an ‘artificial horizon’ to help in maintaining a proper flight path. Such cues can sometimes be misleading, however, for recently it has been found that some mayflies are attracted in very large numbers to mate and lay their eggs on asphalt road surfaces, which is, of course, disastrous

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Figure 7.8. Two ray paths through raindrops that give rise to rainbows. The lower case involves a single reflection and gives the primary bow at 42 ◦ to the sun–antisun axis while the upper case involves two reflections and produces the secondary bow further out. In both cases the coloured rainbows are only chromatic fringes of larger areas of white reflective scattering which is strongly polarised in the tangential directions, around the bows.

for reproduction. It seems that roads not only resemble streams in their general shape, but even their reflected light is polarised to about the same degree as that from rippled water, which polarises light less effectively than a smooth surface.

Rainbows are another familiar source of strongly polarised light. It is often thought that rainbows result from the backscattering of sunlight by rain droplets, but actually the light is mainly returned by reflection within each drop. Figure 7.8 shows how light entering a spherical drop of water is first bent by refraction, then reflected from the back of the drop and finally refracted again as it leaves. Light can only be returned in this way up to an angle of about 42 ◦, resulting in a disc

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of reflected light whose edge is 42 ◦ from the anti-sun point. This is seldom actually noticed although it shows clearly when viewed against a dark background (colour plate 25). The actual familiar rainbow is just a coloured fringe at the outer edge of this disc. It occurs because refraction allows the longer red waves to be returned at a slightly greater angle than the shorter blue and violet waves, thus forming a narrow spectrum, about 2◦ wide.

About 8◦ further out, light is again returned after being reflected, this time twice within each water drop. The inner edge of this band forms the secondary rainbow, about 3◦ wide and with the colours reversed— red on the inner side and blue–violet outwards. In both rainbows, the angles of reflection inside the drops happen to be close to Brewster’s angle (37◦ or the cotangent of the refractive index for light within the denser medium) so that both kinds of rainbow are strongly polarised, the primary bow slightly more so (96%) than the secondary bow (90%). The direction of polarisation is tangential to the bows themselves, that is it runs around their curves, and this effect can easily be seen with a piece of polaroid. Segments of the bows themselves and the white regions bounded by them can be made to disappear when the polaroid is orientated in the radial direction.

When the sun is higher in the sky than 42◦, primary bows can seldom be seen because they would have to be below the horizon, but bows do appear if the droplets are not falling rain but dew drops on a lawn, or the spray from a garden sprinkler or from a waterfall (colour plate 25). These rainbows are easier to observe than those produced by rain showers because they are generally less transitory and do not fade just as one is getting interested in making observations! There are many other atmospheric phenomena that give rise to colours in the sky and these are often polarised too. They are called haloes and arise from various kinds of ice crystals in high clouds; they are described in detail in the book by Greenler listed in the bibliography. Curious things happen to the polarisation of rainbows that are reflected by standing water and these are discussed in the book by Konnen, also listed there. Unfortunately both topics are too complex to go into here.

Photographers often use linear polarising filters on their cameras, either to suppress reflections or to obtain striking contrasts between sky and clouds (chapter 6). But they are often puzzled when catalogues offer filters of ‘circular polaroid’. The reason is that many modern cameras have reflectors behind the lens that divert some light for automatic focusing or for automatic exposure control. These reflectors polarise

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Figure 7.9. Light reflected from dark metals such as blue steel may be strongly polarised, especially at near grazing incidence—as if the refractive index were very high. (a) The left half, being lit here by vertically polarised light, is dark and unreflective. Other metals may show some degree of polarisation unless they are very shiny and reflect nearly all the incident light. Polarised reflection is also shown for a razor blade (b) and a blue hack-saw blade (c) using the polariscope of figure 1.4.

this light at least partially, so that a linear polariser on the lens will affect the readings as it is rotated. To avoid this, the back of the filter is covered by a quarter-wave retarder that changes the emerging light from plane to circular polarisation (see chapter 8). Because the light is now radially symmetrical, rotating this filter makes no difference to any reflections and automatic readings within the camera. The circular polaroid is actually fitted ‘backwards’, not in the way that would be needed to respond, as the name suggests, to circular polarisation of the incoming light. This is just one example of the problems that can arise by reflection within optical instruments; it is an effect that can easily give rise to false readings in a wide range of instruments unless proper precautions are taken in the design.

It is frequently stated that light reflected from metals is not polarised but once again reality is not quite so simple. Light reflected from dark metals such as tempered ‘blue’ steel may be very strongly polarised, especially at high angles of incidence (figure 7.9). Aluminium, copper and stainless steel also give quite strong polarised reflections at grazing angle (figure 7.10). It has also been long known that light that is emitted by white hot metals, either solid or molten, is strongly polarised when viewed at highly oblique angles. It was the absence of such polarisation in light from the ‘edges’ of the sun that showed it must be made of gas rather than solids. On the other hand a degree of polarisation in moonlight confirms that it shines by reflecting light from the sun.

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Figure 7.10. Light reflected by polished copper (bottom) is much more strongly polarised than light reflected from brass (top) which is brighter and more reflective overall. Both here and in figure 7.9, the polariscope has two pieces of polaroid each orientated at 45◦ to the line where they meet, so the reflected light is shown to be horizontally polarised.

Bright shiny metals reflect a very high proportion of the total incident light, so clearly this cannot be strongly polarised although there is a more subtle effect. Light vibrating in the direction normal to the surface (which would be suppressed by the Brewster effect with nonmetals) suffers a phase change with respect to any components vibrating at right angles. So if the incident light is already polarised, it may become circularly or elliptically polarised after reflection (again see chapter 8 for further details). This effect will not be evident when examined with linear polaroid and is therefore often overlooked. Light reflected by a back-silvered glass mirror shows little effect because refraction by the glass limits the effective angle of incidence: even a grazing angle at the surface of the glass is reduced to a much lower angle of incidence on the silvered back (maximum about 41 ◦, see figure 8.11).

A very interesting case is a crystal of germanium, a semiconductor that polarises light like a shiny non-conductor. Its refractive index has

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Figure 7.11. Reflection on a piece of glass as in figure 7.1 but with pictures laid beneath the glass. Here it is seen that where the light is vertically polarised, and so is not reflected, the glass becomes ‘transparent’ and objects below it are no longer obscured by reflections. Such an effect might help fishing birds to see through the surface of water.

the extraordinarily high value of 4 so that Brewster’s angle is 76 ◦ and complete polarisation occurs at an almost grazing angle. But the degree of reflection is about 40% which is almost metal-like since a polarised beam obviously cannot exceed 50% of the original unpolarised light.

The effect of polarisation can sometimes be seen without the aid of an artificial analyser. Colour plate 26 shows a lake called Bachalpsee above Grindelwald, Switzerland, photographed at dawn. The distinctive peaks of Schreckhorn and Finsteraarhorn show the view to the southsoutheast (the latter bearing about 155◦) and the shadows show the summer sun must be rising in the northeast over to the left. The striking feature is that the nearer part of the lake does not reflect the brilliant blue sky. The reason is that the clear sky 90◦ from the sun must be very strongly polarised vertically (see chapter 6); but the nearer water gives a line of view that approaches Brewster’s angle at which only horizontally polarised light can be reflected. So the lake is acting as an analyser ‘crossed’ with the sky’s polariser.

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Another example is seen in colour plate 27, looking due north at sunset, as shown by shadows on the dome and minarets. The nearer part of the reflecting pool does not reflect the clear sky although the Taj Mahal itself is reflected perfectly because it is not a polariser. This beautiful effect is often seen in photographs where the view combines light from the side, a clear sky and still water in the near foreground. But are there any depictions of the effect in art? I would be most grateful for any information helping to identify a good example of the effect being noted by a landscape painter.

Finally one might speculate about the implications of polarised reflections for fishing birds. If, as now seems probable, some birds are able to respond selectively to the plane of polarisation, they might gain the advantages of polaroid glasses as modelled in figure 7.11. It would be interesting to see whether herons and kingfishers, for example, attack their prey at Brewster’s angle of 53 ◦ where they would be able to see best into the water. Even if they do not respond directly to polarisation itself, they would still benefit by exploiting Brewster’s angle at right angles to the sun when the sky is blue, as we can ourselves. The advantage would be especially great in early morning and late afternoon if birds faced north or south rather than in other directions. Simple observations of the behaviour of such birds might be very useful and interesting.