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

Figure 8.10. Reflection of linearly polarised light at high, almost ‘grazing’ angles by shiny metallic objects produces eliptical or even circular polarisation as shown by the Cotton polariscope of figure 8.7. The incident light is linearly polarised at about 45◦ to both the plane of incidence and the plane of the reflector (shadowy reflections of the polaroid can be seen). The reflected light is right circular or left circular, depending which of the two possible directions the linear polarisation occurs—i.e. it can be reversed by rotating the linear polariser by 90 ◦. The two objects are a steel camper’s mirror and a stainless steel cake slice.

Figure 8.12 shows that two rotating vectors of equal length and speed of rotation add up to a linear vector. This means that linearly polarised light can be regarded as equivalent to two components of circularly polarised light of equal strength and wavelength. Normally this concept is not very helpful and is best ignored but, as figure 8.13 shows, a change in the relative timing of the two rotating vectors when they recombine twists the resultant linear vector to either left or right. Since circular birefringence delays one circular component with respect to the other, it provides this change of timing and the consequent twist.

Figure 8.11. Normal back-silvered mirrors cannot reflect at high angles of incidence due to refraction by the glass. Light incident at a large, grazing angle is bent so that it is actually incident on and reflected from the shiny surface at about 41◦. This is therefore the maximum angle of actual incidence and is insufficient to produce the circular polarisation seen in figure 8.10.

Figure 8.12. Two vectors of equal length, rotating in opposite directions at equal rates are exactly equivalent to one linear vector. This statement is summarised in the upper line and is demonstrated below by five instantaneous ‘snapshot’ figures at different times through half a rotation. As the two rotating vectors move apart, they add together to produce a single vertical vector that fluctuates in height and is normally summarised by the single arrow representing its maximum value in one direction only. The next half-rotation will restore the resultant to its original position and length. Dotted lines are for construction only.

This explanation was first put forward by Augustin Fresnel in 1822 and was proved by some ingenious measurements some 62 years later. A difference in refractive index means that rays will be bent to different degrees in a prism. The effect is quite small but a series of hollow prisms alternately containing left-handed and right-handed chiral solutions can

Figure 8.13. If one of the rotating vectors of figure 8.12 is delayed a little, they will meet up at a different point and so the resultant linear vector will be rotated. This shows that circular birefringence (when two circular vectors propagate at different speeds so that one of them is delayed) in sugar solutions rotates the direction of linearly polarised light as seen in the equivalent phenomenon of optical activity described in chapter 5.

actually be made to split linearly polarised light into two separate beams of circularly polarised light of opposite handedness.

Circular dichroism, sometimes called the Cotton effect, is where a material absorbs left-handed circularly polarised light more than righthanded, or vice versa, and transmits or reflects the remainder. It therefore forms a method of producing circularly polarised light from ordinary unpolarised light. Every fluctuating component of the light is resolved into two rotating vectors of which one is preferentially absorbed, leaving a net circularity in the opposite sense. This happens when the material contains asymmetrical molecules of one handedness. It also occurs in some liquid crystals (see chapter 3) and again depends on the presence of chiral molecules in which those of one handedness predominate, which often implicates a biological process somewhere in their origin.

An interesting natural case of circular dichroism is found in the wing cases and some other parts of certain brightly coloured or shiny chafer beetles, such as Cetonia (the rose chafer) and Plusiotis. These bright green insects absorb right-handed polarised light so that the colour they reflect is strongly left-handed. They look completely normal through a left circular polaroid but black through a right circular polaroid. This occurs because of a special structure in their external skeletons. These consist of birefringent layers of molecules that are all orientated in one direction within each layer. But successive layers are rotated steadily in a systematic helical arrangement, with the scale of the rotation being comparable with the wavelength of light (much larger

than the size of the molecules). The effect of this arrangement has been called ‘form dichroism’ to distinguish it from ‘molecular dichroism’. The phenomenon may be quite widespread as it is not visible to the eye and can only be detected by use of a circular (‘Cotton’) polariscope such as shown in figure 8.7. It emphasises the point that there is still much scope for scientific discovery based on simple observation, given some diligence and a little ingenuity.

Chapter 9

Seeing the polarisation

From all that has been discussed in the earlier chapters, it seems that nearly all the natural daylight we see is at least partially polarised. Polarisation is unavoidable because we never look directly at the sun and all the light that actually enters our eyes has been either reflected or scattered by something. It turns out that many animals are able to detect both the degree of linear polarisation and its direction, and they exploit this information in several ways. Such creatures include insects, crustacea, octopus and cuttlefish and some vertebrates but not, except in an insignificant way, ourselves and other mammals. Having already seen in this book what we are missing, it is pertinent to consider how other eyes respond to polarisation and why ours do not.

It has long been suspected that some animals are sensitive to the direction of polarisation because that would explain some of the things they do. But early tests proved negative until some experiments were published by Irene Verkhovskaya in Moscow in 1940. She studied Daphnia, the small freshwater crustaceans popularly called ‘water fleas’, which migrate vertically over several metres in the water each day. She found that they are attracted to light and gather together where it is strongest. In several experimental arrangements, linearly polarised light was found to be two to three times more effective than unpolarised light in attracting the animals. At dawn, when they move towards the surface, the sky overhead is maximally polarised unless it is overcast, so this might increase the stimulus to migrate upwards. It was more than a decade later, however, before others showed that Daphnia are able to detect the actual direction of polarisation, since they align their bodies, and so direct their paths, at right angles to it.

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Very recently the preference of Daphnia for polarised light has been confirmed and has been linked to the tendency of these and other small invertebrates to avoid the vicinity of the shore. Light penetrating into deeper water is scattered (see chapter 6) and, so becomes horizontally polarised, much more than light falling onto shallows near the beach. So the animals are attracted away from the dangerous shallow regions until they are surrounded by safer deeper water. The two basic compound eyes of Daphnia are fused together to form a single median eye, with a total of 22 facets, that swivels rapidly around its axis within the head. The rotating eye presumably scans all possible directions of polarisation, perhaps to ensure that it detects the predominantly horizontal polarisation of its environment, as the animal swims along in varying attitudes. This would account for the apparently equal attractiveness of different directions of polarisation first seen in the original experiments.

The early experiments on Daphnia showed they are sensitive to the existence of polarisation but they were not the first animals shown to be able to detect the actual direction of polarisation. This was first demonstrated in bees by the great pioneer of animal behaviour studies and Nobel Laureate Karl von Frisch in 1948. He had already found that worker bees can communicate to other bees the direction and distance of a source of food, either nectar or pollen, by an excited dance performed repeatedly on the surface of the comb in the hive (figure 9.1). The direction is indicated by the ‘waggle run’ element of the dance in which the bee runs forward waggling her abdomen before turning alternately left and right to return to the start. The inside of most hives is completely dark, the combs are vertical and ‘upwards’ is regarded by the bees as representing the direction of the sun at the time; the waggle run then deviates left or right from the vertical according to the bearing of the food source to left or right of the sun itself (figure 9.1). As the sun moves across the sky through the day, so the waggle run for a particular direction gradually rotates appropriately, at 15 ◦ per hour or half the rate of the hour hand on a clock face.

When von Frisch experimentally abolished the vertical reference by arranging the combs horizontally, the waggle runs then pointed in the actual direction of the food source itself, but only if the bees could see the sun or part of the sky through a window in the roof of their hive. The bees could just cope when only 10–15% of the sky was visible to them, provided it was blue; when their field of view was covered by a cloud, or when their window was covered over, the dances immediately became

Figure 9.1. The waggle dance of the honey bee. Left: the pattern of the dance, turning alternately left and right with the waggle run up the middle. The angle of the waggle run from the vertical indicates the bearing of the food source with respect to the sun and the number of waggles gives the distance to the food. Right: the waggle run for a source 20◦ to the east (left) of the sun and the same two hours later when the sun has moved 30◦ westwards.

disorientated and random. The fact that a portion of blue sky provided a sufficient reference when the sun itself could not be seen was a major surprise but von Frisch suspected that the bees might be able to detect the sky polarisation pattern that is itself determined by the sun, as described in chapter 6. To test this he covered the window in the hive with a large piece of polaroid. When he turned the polaroid so that the polarisation of a patch of sky was altered in a controlled way, the bees’ dances rotated accordingly. The story has been vividly told in several popular books by von Frisch himself, translated into English, and it is well worth reading in greater detail.

In order to understand how the bees distinguish the direction of polarisation, it is necessary to know something about how their eyes work. The principal paired eyes of insects are of the type known as compound eyes and have a quite different action from the familiar simple or ‘camera’ eyes of vertebrates such as ourselves. In the latter, as in a camera, a single lens (generally combined with refraction by the curved cornea) focuses an image on the retina, which is a screen of light sensitive cells. Nerve fibres connect each point of the retina with the brain and thus transmit a detailed representation of the image. By contrast a compound eye consists of a convex array of separate facets or optically independent units, about 5500 in each eye of a worker honey bee, all pointing in different directions. Each unit, called an ommatidium, has its own lens which is hexagonal in outline so that they pack together to collect all the available light (figure 9.2). Behind

Figure 9.2. The compound eye of the honey bee. Left: the outer surface showing part of the array of hexagonal lenses, each of which faces outwards in a slightly different direction. Right: below one lens (at greater enlargement) showing the arrangement of the eight main light sensitive cells in cross section. The arrow within each cell shows the polarisation direction to which it is most sensitive. The two cells marked by stars respond best to ultraviolet light and the rest to either blue or green light.

each lens there are essentially eight light-sensitive cells (figure 9.2) in an octagonal pattern, each connected to the brain by a nerve fibre. This little set of cells does not qualify for the term retina and is called a retinula or ‘little retina’. Clearly with such limited attributes one ommatidium cannot form and analyse an effective image and the visual field is only represented by the combined action of the whole array of such units.

Now von Frisch imagined that each of the eight light sensitive retinula cells might somehow be sensitive to one direction of polarisation so that one ommatidium would be able to analyse polarisation in terms of four components 45◦ apart (figure 9.3). This idea was correct in principle although the details turned out to be slightly different. Actually four of the eight cells are potentially most sensitive to one direction of polarisation while the other four are most sensitive to light polarised at right angles to this, giving simultaneous analysis into two orthogonal components (figure 9.2). The position is complicated, however, by the fact that the same cells also serve for colour vision which, as in our eyes is achieved by comparing the excitation of three kinds of cells with different spectral responses: in the bee retinula four of the eight cells are most sensitive to green, two to blue and two to ultraviolet (figure 9.2).

Figure 9.3. Karl von Frisch imagined the main eight sensitive cells of a bee’s ommatidium might be sensitive to four directions of polarisation. He made a model from pieces of polaroid which makes a very good polariscope as shown in this replica. The actual polarisation sensitivities as determined by later, physiological studies, are shown in figure 9.2.

In common with most other insects, bees have no red-sensitive cells. It is the ultraviolet cells that are most responsive to the direction of polarisation although an additional short ninth cell, also an ultraviolet unit and tucked in among the bases of the other eight, may be the most polarisation sensitive of all in most ommatidia.

The basis of this polarisation sensitivity is that in these eyes the light absorbing process is inherently dichroic. The visual cells of all animals detect light when it is absorbed by special receptor molecules that are thereby changed in shape by a photochemical reaction; this initiates a chain of events that culminates in messages to the brain via nerve fibres. The sensitive molecules, of substances called visual pigments, are elongated and absorb light most readily when the direction of polarisation is aligned with their long axis, or at least with a series of carbon=carbon double bonds within the molecules. In the light sensitive retinula cell of an insect compound eye these pigment molecules are all orientated in the same direction. They are held in the membranous walls of minute parallel tubular pockets called microvilli, that are tightly packed together and run from the wall of the cell across the light path (figure 9.4). Thus all the absorbing molecules lie across the light path and, with their axes all more or less parallel, the system as a whole is dichroic, like some crystals. Light polarised in one direction is strongly absorbed, leading to excitation of the cell, while light polarised at right angles is not absorbed and has no effect.

One final complication in the bee’s eye concerns twisting of the

Figure 9.4. The sensitive cells of the eyes of a bee and many other invertebrate animals contain tiny tubes called microvilli that lie across the light path (arrows). The membranous walls of the microvilli contain the light sensitive pigment molecules (represented as dashes) which are all orientated in the same direction. This almost crystal-like regularity makes the light absorbing process dichroic so that the cell is inherently most sensitive to light polarised along the axes of the microvilli.

group of retinula cells. In the system described earlier, there could be an ambiguity between colour and polarisation: both are detected by the brain comparing the excitation of different cells within the ommatidium, but differences of response may equally be due to the colour of the light or to its polarisation. In order to avoid this problem, the bundles of sensitive cells in most ommatidia are twisted along their length by more than 180◦, like strands of a rope, clockwise in some ommatidia and anticlockwise in others. Thus the axis of dichroicity rotates so that light not absorbed in the outer part of a cell may well be absorbed when it passes further down. This improves sensitivity because the total light capture is increased, but although the membranes with their visual pigment molecules are actually dichroic, the twisted cell as a whole is not, or it has greatly reduced susceptibility to polarisation. This may explain why the short ninth cell is often the most sensitive to polarisation, because its very shortness means it is never twisted enough to destroy its inherent dichroicity. The non-dichroic cells, however, are ideal for unambiguous colour analysis because differences in their excitation can only be due to differences in their spectral responses.

However, there is a band of about 150 specialised ommatidia that lie in the dorsal region of the eye and so face upwards. They are called the