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

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amounts of power; only 1 watt would be needed to maintain 100 m 2 in the ‘switched on’ condition. This makes them very attractive for use in pocket calculators for instance, especially those powered by small solar cells. One can easily detect the presence of polarisers in LCD displays by viewing them through another polaroid and rotating it: the screen darkens and lightens as would be expected. But the design of LCD displays is sometimes unfortunate: those used in the instrument panels of cars may not be aligned with polaroid sunglasses worn by the driver so that their apparent brightness is degraded and they can be completely blocked by a slight tilt of the head.

Chapter 4

Fields

Michael Faraday is widely regarded as the greatest experimental scientist ever. He not only showed great skill and ingenuity in the laboratory, he also brought deep insight to bear on the problems he studied. He was able, far more than most, to see what issues were worth studying and to persevere with them even when he met with persistent failure.

From 1820 to 1831, working at the Royal Institution in London, Faraday established the laws of electromagnetic induction: the relationship between magnetism and electricity which produced the electric motor, the dynamo and the transformer. He then took up the subject of electrochemistry in which he established some fundamental relationships between electricity and matter. From all this he came to believe that all physical forces and phenomena must be related, even interchangeable—he would have had great sympathy with modern attempts to find a ‘grand unified theory of everything’. In 1845 he wrote:

I have long held an opinion, almost amounting to conviction. . . that the various forms under which the forces of matter are made manifest have one common origin; or in other words, are so directly related and mutually dependent. . . this strong persuasion extended to the powers of light. . . and (I) have at last succeeded in magnetizing and electrifying a ray of light. . . . (his own italics)

After exhaustive tests over a long period with completely negative results, on 13 September 1845 he tested some samples of glass that he had made some years earlier under a contract from the Royal Society. He found that when light was passed through a piece of very dense

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Figure 4.1. Faraday magneto-optical rotation. A rod of very dense glass is placed along the axis of a magnetic field, here represented by the coil of an electromagnet. Polarised light passing along the rod is rotated as indicated by the vector arrows.

Figure 4.2. If the rotated beam of polarised light in figure 4.1 is reflected back down the glass rod, it is rotated further before emerging beside the source. This shows that it is the light itself that is influenced, not the material of the glass.

lead silico-borate glass along the direction of a magnetic field, then the direction of polarisation was rotated (figure 4.1). This effect is now universally known as Faraday magneto-optic rotation or simply the Faraday effect (although he discovered many other effects too).

He soon showed that the same effect was present, although to a lesser degree, in other materials, both solids and liquids. Its properties were that the rotation depended on the material used (a characteristic now known as the Verdet constant of the material), on the length of the material within the field and on the strength of the magnetic field itself. But the big surprise was that if the rotated beam was reflected back towards the source, the rotation was not reversed on the return trip and thus cancelled out, but occurred again so that the rotation was doubled (figure 4.2). This may seem paradoxical because light passing the opposite way in the same field is, of course, then being rotated the opposite way. But clockwise as seen from one direction is anticlockwise when seen from the other direction. So a ray whose polarisation has been rotated clockwise (say from 12 to 1 o’clock as seen from behind), and

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then reflected back by a mirror is now passing the other way and sets off vibrating at 11 o’clock as seen from behind; during the second passage through the glass it will be rotated anticlockwise, thus increasing the earlier rotation to end at 10 o’clock.

Michael Faraday had originally assumed that the magnetic field would somehow stress the atoms within the glass, in which case one would expect any effect on light to depend on its direction of travel and to be ‘unwound’ again on the way back. But the actual situation suggested that light itself must have some directional property across its line of travel. Faraday said it is as if the glass itself is somehow rotating in the magnetic field and carrying the light round with it. One must remember that the very nature of light was not at all well understood at the time but this discovery was clearly important in giving a new angle on it. Twenty years later, in 1865, James Clerk Maxwell of King’s College, London published the now famous Maxwell equations, for which he acknowledged the influence of Faraday and specifically the magnetic rotation of polarised light. The new theory described light as an electromagnetic wave and predicted a much larger class of such waves of other wavelengths. We now know of electromagnetic waves extending from radio, with some wavelengths of over a thousand kilometres, through microwaves, infrared, the visible light spectrum at less than 1 micrometre (µm), ultraviolet, x-rays and, finally, gamma-rays less than 10−14 m: a continuous range of over 20 orders of magnitude. All can be described as the same interaction of a magnetic and an electric field, and all propagate at ‘the speed of light’.

Faraday rotation is easy to demonstrate although the very dense glass that gives a large effect is extremely expensive. Figure 4.3 shows a homemade device using a ‘borrowed’ rod of density 6.63 g ml −1 (most glasses have a density of around 2.5 g ml −1). It is 1 cm in diameter and 5 cm long and is held in a plastic bobbin wound with thick wire, giving a resistance of half an ohm. A polaroid is fixed across one end and a rotatable polaroid cap on the other end is crossed with the first to give extinction of the light. Passing current from a 12 V lead–acid battery through a heavy-duty push button then allows light to shine through brightly. For demonstration to an audience, the device is put over a hole in a cardboard mask on the patten of an overhead projector. A very similar device, though not using polaroids of course, that was made by Michael Faraday himself is on display in the Faraday Museum at the Royal Institution in London.

In one of his papers, Faraday said that fused lead borate gave an

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Figure 4.3. A Faraday rotation device for demonstration on an overhead projector. As it draws about 25 A from a 12 V accumulator, the power can only be maintained briefly, so a push button is used instead of a switch. When ‘fired’ it allows a bright beam to pass through crossed polaroids, thus demonstrating an extremely important historical phenomenon. The effect is made more clearly visible if the device stands over a hole in a cardboard mask.

effect that was equal to the best heavy glasses he tried. Two of my colleagues kindly helped me to try this. John Cowley, a glassblower, made a rod of fused lead borate with materials and a mould supplied by Isaac Abrahams. This rod is 55 mm long and has a density of about 6.25 g ml−1. It is now mounted in its own coil (as in figure 4.3), using 500 g of enamelled copper wire 1.35 mm in diameter. It gives excellent results for direct viewing or for demonstration on an overhead projector, although the rod is coloured greenish rather than being clear.

The principle of the Faraday effect can be used to make a true one-way system for light—an optical isolator, invented by Rayleigh in 1885. The principle of this is shown in figure 4.4. Linearly polarised light is rotated by 45◦ by a magnetic field so that it passes through a second polariser orientated obliquely at the appropriate angle. But light passing in the opposite direction and starting with polarisation at 45 ◦ is then rotated further so that its exit polariser then appears crossed and extinction occurs.

Faraday rotation is not just a laboratory effect for it is used in astronomy to measure the strength of magnetic fields in the space between stars. Where it is possible to infer the original polarisation of

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Figure 4.4. The principle of a one-way optical isolator. The left polariser P1 is here set vertical; the light passing through it from A is then rotated clockwise by 45◦ by a Faraday rotator cell and passes freely through the right polariser P2, set obliquely at 45◦. But the lower beam of light entering from B is first polarised at 45◦ and then rotated to become horizontal so that it is blocked by the left polariser. The device is therefore transparent in one direction and opaque in the opposite direction. Large vector arrows show the setting of the polarisers, small ones show the polarisation of each light beam.

a light source (say when it is produced by scattering—see chapter 6), then any change in the direction of vibration during its journey to earth indicates the magnetic fields in the intervening space. In this way it has been shown that the interstellar magnetic field within our galaxy is about one-millionth of the strength of our own terrestrial magnetic field and is aligned along the spiral galactic arms.

Michael Faraday also tried to influence light with electric fields but he never succeeded. In the previous quotation, his use of the word ‘electrifying’ clearly refers to electric currents through the electromagnets used in some of his experiments, and not to a direct effect of electricity on light. It was not until 1875, 10 years after Maxwell’s theory and 3 years after Faraday died, that this was achieved by John Kerr. A Kerr cell (figure 4.5) consists of two sets of small plate electrodes immersed in nitrobenzene. They are set diagonally between crossed polaroids. An electrical pulse of several thousand volts then twists the direction of vibration so that the light can pass the second polaroid. Such a device, which is then sometimes called a Karolus cell, is used as the shutter for very high speed cameras because its action is extremely rapid. With a suitably short pulse of high voltage, the cell can be opened for as little as 1 ns (10−9 s), or one-thousandth of a millionth of a second. The light pulse that passes will then be only about 30 cm long—less than 1 foot! It may help to visualise such a short duration by saying that,

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Figure 4.5. A Kerr cell showing the electrodes that are connected together alternately in pairs and immersed in nitrobenzene. The electrodes are set at 45◦ to the vibration directions of two crossed polaroids. A momentary application of several kilovolts rotates the direction of polarisation so that the combination becomes transparent. It can be simply demonstrated on an overhead projector, using a piezo-electric gas-lighter as the high voltage source.

going the other way, 109 s is nearly 32 years. Such very short exposure times allow sharp pictures to be taken of extremely fast events such as the course of development of explosions.

In 1877 John Kerr also showed that when polarised light is reflected from the surface of iron or certain other metals, alloys and even some oxides, the direction of polarisation is rotated by the application of a magnetising field. This effect is therefore called the magnetic Kerr effect.

Both Faraday cells and Kerr cells can be used to modulate the intensity of light for communication through light fibres. The currently fashionable form is a Pockel cell which is like a solid state version of the Kerr cell that works in a crystal, often potassium dihydrogen phosphate, instead of in liquid nitrobenzene. The physical basis of this device is somewhat different in detail but the effect is virtually the same. It can vary the light entering the optical fibre so rapidly that up

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to 100 000 telephone calls or 100 television channels can be transmitted simultaneously down a single tiny fibre.

So Michael Faraday’s experiments in this area alone led to profound insights into the very nature of light, to a method for exploring features of the galaxy, to the fastest camera shutters and to the latest techniques for high-speed communications. There really is no way of knowing where a discovery may lead, no matter how ‘rarified’ it or the work leading to it may seem at the time.

Chapter 5

Left hand, right hand

Some chemical solutions rotate the direction of vibration of polarised light despite the fact that their constituent molecules are randomly orientated and are continually jostled by thermal agitation. There is no trace of a regular lattice in this case and there is no need for a permeating field. All that is necessary is that the molecules of the dissolved substance (the solute) can exist in both ‘left-handed’ and ‘right-handed’ forms and that one of them predominates in the given solution. Just as gloves, and hands, come in mirror image pairs (a left and a right), some molecules come in leftand right-handed forms and their property of handness is called chirality. The word chiral comes from the Greek cheir ≡ hand.

The explanation of the effect of molecular handedness on polarised light began with another brilliant piece of mid-19th century research, this time by Louis Pasteur who was originally a chemist, although perhaps better known later as a pioneer of microbiology and vaccination. In 1848, when he was only 26 years old, he studied the chemistry of tartaric acid (a salt of which is cream of tartar) which had been produced from wine residues (or tartar) and was known to rotate polarised light in solution. Another acid, called racemic acid, that had been discovered in 1820, was found to have the same formula, C 4H6O6, as tartaric acid and its other properties were also identical except that it did not rotate polarised light at all. Tartaric acid was said to be ‘optically active’ and ‘dextrorotatory’ (twisting polarised light to the right—or clockwise as seen from in front) whereas racemic acid was optically inactive. Indeed when tartaric acid is heated in water it slowly loses its optical activity without any apparent change in molecular structure

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Figure 5.1. A crystal of sodium ammonium tartrate (left) which is laevorotatory

(L) and its mirror image (right) which is dextrorotatory (D). Pasteur showed that equal numbers of each kind are found in sodium ammonium racemate which is therefore optically inactive. (There has been much confusion over the proper shapes of these crystals and different shapes are often depicted; these patterns are copied from Pasteur’s own paper although one authority has declared that Pasteur never published any figures of the crystals he described!)

and becomes racemic acid. The two substances were even thought (in this case wrongly as it turned out) to produce identical crystals which made it even more puzzling.

But Pasteur found that there were tiny differences in the crystals. When he took racemic acid and prepared crystals of the salt sodium ammonium racemate, he noticed that half of them were actually mirror images of the rest (figure 5.1), and one of these matched the crystals of sodium ammonium tartrate. Although they were all very small, Pasteur carefully sorted the racemate crystals into two piles, using a magnifying glass and tweezers. When he dissolved them separately in water, both were optically active; one solution rotated polarised light to the right like the corresponding tartrate, while the other rotated it to the left. The latter was something not known before: a left-handed or ‘laevorotatory’ tartrate. The amount of rotation was equal in each case and when the solutions were combined they counteracted each other exactly to produce the typical optically inactive racemate. Pasteur then surmised that optical activity must be related to the fact that the crystals were mirror images. Furthermore, since optical activity persisted when the crystals were dissolved in water, then even the molecules of tartaric

acid and its salts must themselves exist in two forms which are mirror images of each other. We now call such pairs of molecular structures stereoisomers and an optically inactive mixture of the two is said to be racemic.

So surprising was this result that Pasteur, then so young and inexperienced, was invited to repeat his procedure under the supervision of an eminent old scientist called Jean Baptiste Biot who had himself discovered optical activity in liquids 30 years before. All went well and Pasteur’s reputation was established with a discovery that was to have immensely important consequences for the understanding of molecular structures. But it might easily have turned out very differently. Sodium ammonium racemate only forms two different kinds of crystal at temperatures below 26–28 ◦C; above that (like most other chiral salts, including other tartrates) the two stereoisomers form combined, or racemic, crystals that are quite different in their appearance and properties. It seems that Pasteur did not know this at the time, and if there had been a heatwave when he repeated the experiment it might not have worked, which would have been disastrous to his reputation. Indeed in hot weather he might not have made his original discovery at all.

Although Pasteur deduced that mirror image crystals must represent a handedness in the shape of their constituent molecules, the details eluded him. Twenty-six years later, in 1874, two chemists called van’t Hoff and Le Bel independently explained how some molecules that contain carbon atoms can exist in two forms that are optically active mirror images of each other. For a molecule to be chiral it must contain at least one atom that is joined to four different atoms or groups (figure 5.2) to form a three-dimensional structure (it does not work if they happen to be all in the same plane); then there are two possible configurations, or stereoisomers, that are mirror images and cannot be superimposed, one on the other. Now a carbon atom makes four links to other atoms as if they were attached to the corners of a tetrahedron, so chiral molecules are quite common in organic chemistry and therefore in living materials and natural products.

When only one of the stereoisomers is present (or when one predominates) in a solution, then it acts to twist the vibration direction of polarised light passing through it. The amount of rotation depends on the characteristic ‘specific rotation’ of the substance, on the concentration of the solution, on the temperature and on the length of light path through the solution. Shorter wavelengths of blue light are generally rotated more than the longer wavelengths of red light. If the rotated beam is