Fig. 27.Fig. 27.
Fig. 28.Fig. 28.
A moment's reflection will show that, if what is here stated be correct, on placing a second plate of tourmaline with its axis parallel to the first, the light will pass through both; but that, if the axes be crossed, the light that passes through the one plate will be quenched by the other, a total interception of the light being the consequence. Let us test this conclusion by experiment. The image of a plate of tourmaline (tt, fig. 27) is now before you. I place parallel to it another plate (t't'): the green of thecrystal is a little deepened, nothing more; this agrees with our conclusion. By means of an endless screw, I now turn one of the crystals gradually round, and you observe that as long as the two plates are oblique to each other, a certain portion of light gets through; but that when they are at right angles to each other, the space common to both is a space of darkness (fig. 28). Our conclusion, arrived at prior to experiment, is thus verified.
Let us now return to a single plate; and here let me say that it is on the green light transmitted by the tourmaline that you are to fix your attention. We have to illustrate the two-sidedness of that green light, in contrast to the all-sidedness of ordinary light. The white light surrounding the green image, being ordinary light, is reflected by a plane glass mirror in all directions; the green light, on the contrary, is not so reflected. The image of the tourmaline is now horizontal; reflected upwards, it is still green; reflected sideways, the image is reduced to blackness, because of the incompetency of the green light to be reflected in this direction. Making the plate of tourmaline vertical, and reflecting it as before, it is the light of the upper image that is quenched; the side image now shows the green. This is a result of the greatest significance. If the vibrations of light were longitudinal, like those of sound, you could have no action of this kind; and this very action compels us to assume that the vibrations are transversal. Picture the thing clearly. In the one case the mirror receives, as it were, the impact of theedgesof the waves, the green light being then quenched. In the other case thesidesof the waves strike the mirror, and the green light is reflected. Torender the extinction complete, the light must be received upon the mirror at a special angle. What this angle is we shall learn presently.
The quality of two-sidedness conferred upon light by bi-refracting crystals may also be conferred upon it by ordinary reflection. Malus made this discovery in 1808, while looking through Iceland spar at the light of the sun reflected from the windows of the Luxembourg palace in Paris. I receive upon a plate of window-glass the beam from our lamp; a great portion of the light reflected from the glass is polarized. The vibrations of this reflected beam are executed, for the most part, parallel to the surface of the glass, and when the glass is held so that the beam shall make an angle of 58° with the perpendicular to the glass, thewholeof the reflected beam is polarized. It was at this angle that the image of the tourmaline was completely quenched in our former experiment. It is calledthe polarizing angle.
Sir David Brewster proved the angle of polarization of a medium to be that particular angle at which the refracted and reflected rays inclose a right angle.[17]The polarizing angle augments with the index of refraction. For water it is 52½°; for glass, as already stated, 58°; while for diamond it is 68°.
And now let us try to make substantially theexperiment of Malus. The beam from the lamp is received at the proper angle upon a plate of glass and reflected through the spar. Instead of two images, you see but one. So that the light, when polarized, as it now is by reflection, can only get through the spar in one direction, and consequently can produce but one image. Why is this? In the Iceland spar as in the tourmaline, all the vibrations of the ordinary light are reduced to two planes at right angles to each other; but, unlike the tourmaline, both beams are transmitted with equal facility by the spar. The two beams, in short, emergent from the spar, are polarized, their directions of vibration being at right angles to each other. When, therefore, the light is first polarized by reflection, the direction of vibration in the spar which coincides with the direction of vibration of the polarized beam, transmits the beam, and that direction only. Only one image, therefore, is possible under the conditions.
You will now observe that such logic as connects our experiments is simply a transcript of the logic of Nature. On the screen before you are two disks of light produced by the double refraction of Iceland spar. They are, as you know, two images of the aperture through which the light issues from the camera. Placing the tourmaline in front of the aperture, two images of the crystal will also be obtained; but now let us reason out beforehand what is to be expected from this experiment. The light emergent from the tourmaline is polarized. Placing the crystal with its axis horizontal, the vibrations of its transmitted light will be horizontal. Now the spar, as already stated, has two directions of vibration, one of which at the presentmoment is vertical, the other horizontal. What are we to conclude? That the green light will be transmitted along the latter, which is parallel to the axis of the tourmaline, and not along the former, which is perpendicular to that axis. Hence we may infer that one image of the tourmaline will show the ordinary green light of the crystal, while the other image will be black. Tested by experiment, our reasoning is verified to the letter (fig. 29).
Fig. 29.Fig. 29.
Fig. 30.Fig. 30.
Let us push our test still further. By means of an endless screw, the crystal can be turned ninety degrees round. The black image, as I turn, becomes gradually brighter, and the bright one gradually darker; at an angle of forty-five degrees both images are equally bright (fig. 30); while, when ninety degrees have been obtained, the axis of the crystal being then vertical, the bright and black images have changed places, exactly as reasoning would have led us to suppose (fig. 31).
Fig. 31.Fig. 31.
Fig. 32.Fig. 32.
Considering what has been already said (p. 114) regarding the reflection of light polarized by transmission through tourmaline, you will readily foresee what must occur when we receive upon a plate of glass, held at the polarizing angle, the two beams emergent from our prism of Iceland spar. I cause both beams to pass side by side through the air, catch them on a glass plate, and seek to reflect them upwards. At the polarizing angle one beam only is capable of being thus reflected. Which? Your prompt answer will be, The beam whose vibrations are horizontal (fig. 32). I now turn the glass plate and try to reflect both beams laterally. One of them only is reflected; that,namely, the vibrations of which are vertical (fig. 33). It is plain that, by means either of the tourmaline or the reflecting glass, we can determine in a moment the direction of vibration in any polarized beam.
Fig. 33.Fig. 33.
As already stated, the whole of a beam of ordinary light reflected from glass at the polarizing angle is polarized; a word must now be added regarding the far larger portion of the light which istransmittedby the glass. The transmitted beam contains a quantity of polarized light equal to the reflected beam; but this is only a fraction of the whole transmitted light. By taking two plates of glass instead of one, we augment the quantity of the transmitted polarized light; and by takinga bundleof plates, we so increase the quantity as to render the transmitted beam, for all practical purposes,perfectlypolarized. Indeed, bundles of glass plates are often employed as a means of furnishing polarized light. It is important to note that the plane of vibration of this transmitted light is at right angles to that of the reflected light.
One word more. When the tourmalines are crossed,the space where they cross each other is black. But we have seen that the least obliquity on the part of the crystals permits light to get through both. Now suppose, when the two plates are crossed, that we interpose a third plate of tourmaline between them, with its axis oblique to both. A portion of the light transmitted by the first plate will get through this intermediate one. But, after it has got through,its plane of vibration is changed: it is no longer perpendicular to the axis of the crystal in front. Hence it will, in part, get through that crystal. Thus, by pure reasoning, we infer that the interposition of a third plate of tourmaline will in part abolish the darkness produced by the perpendicular crossing of the other two plates. I have not a third plate of tourmaline; but the talc or mica which you employ in your stoves is a more convenient substance, which acts in the same way. Between the crossed tourmalines, I introduce a film of this crystal with its axis oblique to theirs. You see the edge of the film slowly descending, and, as it descends, light takes the place of darkness. The darkness, in fact, seems scraped away, as if it were something material. This effect has been called, naturally but improperly,depolarization. Its proper meaning will be disclosed in our next lecture.
These experiments and reasonings, if only thoroughly studied and understood, will form a solid groundwork for the analysis of the splendid optical phenomena next to be considered.
CHROMATIC PHENOMENA PRODUCED BY CRYSTALS IN POLARIZED LIGHTTHE NICOL PRISMPOLARIZER AND ANALYZERACTION OF THICK AND THIN PLATES OF SELENITECOLOURS DEPENDENT ON THICKNESSRESOLUTION OF POLARIZED BEAM INTO TWO OTHERS BY THE SELENITEONE OF THEM MORE RETARDED THAN THE OTHERRECOMPOUNDING OF THE TWO SYSTEMS OF WAVES BY THE ANALYZERINTERFERENCE THUS RENDERED POSSIBLECONSEQUENT PRODUCTION OF COLOURSACTION OF BODIES MECHANICALLY STRAINED OR PRESSEDACTION OF SONOROUS VIBRATIONSACTION OF GLASS STRAINED OR PRESSED BY HEATCIRCULAR POLARIZATIONCHROMATIC PHENOMENA PRODUCED BY QUARTZTHE MAGNETIZATION OF LIGHTRINGS SURROUNDING THE AXES OF CRYSTALSBIAXAL AND UNIAXAL CRYSTALSGRASP OF THE UNDULATORY THEORYTHE COLOUR AND POLARIZATION OF SKY-LIGHTGENERATION OF ARTIFICIAL SKIES.
We have this evening to examine and illustrate the chromatic phenomena produced by the action of crystals, and double-refracting bodies generally, upon polarized light, and to apply the Undulatory Theory to their elucidation. For a long time investigators were compelled to employ plates of tourmaline for this purpose, and the progress they made with so defective a means of inquiry is astonishing. But these men had their hearts in their work, and were on this account enabled to extract great results from small instrumental appliances. For our present purpose we need far larger apparatus; and, happily, in these later times this need hasbeen to a great extent satisfied. We have seen and examined the two beams emergent from Iceland spar, and have proved them to be polarized. If, at the sacrifice of half the light, we could abolish one of these, the other would place at our disposal a beam of polarized light, incomparably stronger than any attainable from tourmaline.
Fig. 34.Fig. 34.
The beams, as you know, are refracted differently, and from this, as made plain in §4, Lecture I., we are able to infer that the one may be totally reflected, when the other is not. An able optician, named Nicol, cut a crystal of Iceland spar in two halves in a certain direction. He polished the severed surfaces, and reunited them by Canada balsam, the surface of union being so inclined to the beam traversing the spar that the ordinary ray, which is the most highly refracted, was totally reflected by the balsam, while the extraordinary ray was permitted to pass on.
Letb x, c y(fig. 34) represent the section of an elongated rhomb of Iceland spar cloven from the crystal. Let this rhomb be cut along the planeb c; and the two severed surfaces, after having been polished, reunited by Canada balsam. We learned, in our first lecture, that total reflection only takes place when a ray seeks to escape from a more refracting to a less refracting medium, and that it always, under these circumstances, takes place when the obliquity is sufficient. Now the refractive index of Iceland spar is, for the extraordinary ray less, and for the ordinary greater, than for Canada balsam. Hence, in passing from the spar to the balsam, the extraordinary ray passes from a less refracting to a more refracting medium, where total reflection cannot occur; while the ordinary ray passes from a morerefracting to a less refracting medium, where total reflection can occur. The requisite obliquity is secured by making the rhomb of such a length that the plane of whichb cis the section shall be perpendicular, or nearly so, to the two end surfaces of the rhombb x, c y.
The invention of the Nicol prism was a great step in practical optics, and quite recently such prisms have been constructed of a size and purity which enable audiences like the present to witness the chromatic phenomena of polarized light to a degree altogether unattainable a short time ago.
(The two prisms employed in these experiments were lent to me by my lamented friend Mr. William Spottiswoode, and they were manufactured by Mr. Ahrens, an optician of consummate skill.)
Two Nicol prisms play the same part as the two plates of tourmaline. Placed with their directions of vibration parallel, the light passes through both; while when these directions are crossed the light is quenched. Introducing a film of mica between the prisms, the light, as in the case of the tourmaline, is restored. But notice, when the film of mica isthinyou have sometimes not only light, butcolouredlight. Our work for some time to come will consist of the examination of such colours. With this view, I will take a representative crystal, one easily dealt with, because it cleaves with great facility—the crystal gypsum, or selenite, which is crystallized sulphate of lime. Between the crossed Nicols I place a thick plate of this crystal; like the mica, it restores the light, but it produces no colour. With my penknife I take a thin splinter from the crystal and place it between the prisms; the image of the splinter glows with the richest colours. Turning the prism in front, these colours gradually fade and disappear, but, by continuing the rotation until the vibrating sections of the prisms are parallel to each other, vivid colours again arise, but these colours are complementary to the former ones.
Some patches of the splinter appear of one colour, some of another. These differences are due to the different thicknesses of the film. As in the case of Hooke's thin plates, if the thickness be uniform the colour is uniform. Here, for instance, is a stellar shape, every lozenge of the star being a film of gypsum of uniform thickness: each lozenge, you observe, shows abrilliant and uniform colour. It is easy, by shaping our films so as to represent flowers or other objects, to exhibit such objects in hues unattainable by art. Here, for example, is a specimen of heart's-ease, the colours of which you might safely defy the artist to reproduce. By turning the front Nicol 90 degrees round, we pass through a colourless phase to a series of colours complementary to the former ones. This change is still more strikingly represented by a rose-tree, which is now presented in its natural hues—a red flower and green leaves; turning the prism 90 degrees round, we obtain a green flower and red leaves. All these wonderful chromatic effects have definite mechanical causes in the motions of the ether. The principle of interference duly applied and interpreted explains them all.
By this time you have learned that the word 'light' may be used in two different senses: it may mean the impression made upon consciousness, or it may mean the physical cause of the impression. It is with this cause that we have to occupy ourselves at present. The luminiferous ether is a substance which fills all space, and surrounds the atoms and molecules of bodies. To this inter-stellar and inter-atomic medium definite mechanical properties are ascribed, and we deal with it in our reasonings and calculations as a body possessed of these properties. In mechanics we have the composition and resolution of forces and of motions, extending to the composition and resolution ofvibrations. We treat the luminiferous ether on mechanical principles, and, fromthe composition and resolution of its vibrations we deduce all the phenomena displayed by crystals in polarized light.
Fig. 35.Fig. 35.
Let us take, as an example, the crystal of tourmaline, with which we are now so familiar. Let a vibration cross this crystal oblique to its axis. Experiment has assured us that a portion of the light will pass through. The quantity which passes we determine in this way. Let A B (fig. 35) be the axis of the tourmaline, and letabrepresent the amplitude of an oblique ethereal vibration before it reaches A B. Fromaandblet the two perpendicularsacandbdbe drawn upon the axis: thencdwill be the amplitude of the transmitted vibration.
I shall immediately ask you to follow me while I endeavour to explain the effects observed when a film of gypsum is placed between the two Nicol prisms. But, prior to this, it will be desirable to establish still further the analogy between the action of the prisms and that of the two plates of tourmaline. The magnified images of these plates, with their axes at right-angles to each other, are now before you. Introducing between them a film of selenite, you observe that by turning the film round it may be placed in a position where it has no power to abolish the darkness of the superposed portions of the tourmalines. Why is this? The answer is, that in the gypsum there are two directions, at right angles to each other, in which alone vibrations can take place, and that in our present experiment one of these directions is parallel to one of the axes of the tourmaline, and the other parallel to the other axis. When this is the case, the film exercises no sensible action upon the light. But now I turn the film so as to render its directions of vibrationobliqueto the two tourmaline axes; then, you see it exercises the power, demonstrated in the last lecture, of partially restoring the light.
Fig. 36.Fig. 36.
Let us now mount our Nicol prisms, and cross them as we crossed the tourmaline. Introducing our film of gypsum between them, you notice that in one particular position the film has no power whatever over the field of view. But, when the film is turned a little way round, the light passes. We have now to understand the mechanism by which this is effected.
First, then, we have a prism which receives the light from the electric lamp, and which is called thepolarizer. Then we have the plate of gypsum (supposed to be placed at S, fig. 36), and then theprism in front, which is called theanalyzer. On its emergence from the first prism, the light is polarized; and, in the particular case now before us, its vibrations are executed in a horizontal plane. We have to examine what occurs when the two directions of vibration in the interposed gypsum are oblique to the horizon. Draw a rectangular cross (A B, C D, fig. 37) to represent these two directions. Draw a line (ab) to represent the amplitude of the horizontal vibration on the emergence of the light from the first Nicol. Let fall from each end of this line two perpendiculars (ac,af,bd,be) on the two arms of the cross; then the distances (cd,ef) between the feet of these perpendiculars represent the amplitudes of two rectangular vibrations, which are thecomponentsof the first single vibration. Thus the polarized ray, when it enters the gypsum, is resolved into its two equivalents, which vibrate at right angles to each other.
Fig. 37.Fig. 37.
In one of these two rectangular directions the ether within the gypsum is more sluggish than in the other; and, as a consequence, the waves that follow this direction are more retarded than the others. In both cases the undulations are shortened when theyenter the gypsum, but in the one case they are more shortened than in the other. You can readily imagine that in this way the one system of waves may get half a wave-length, or indeed any number of half wavelengths, in advance of the other. The possibility of interference here at once flashes upon the mind. A little consideration, however, will render it evident that, as long as the vibrations are executed at right angles to each other, they cannot quench each other, no matter what the retardation may be. This brings us at once to the part played by the analyzer. Its sole function is to recompound the two vibrations emergent from the gypsum. It reduces them to a single plane, where, if one of them be retarded by the proper amount, extinction will occur.
But here, as in the case of thin films, the different lengths of the waves of light come into play. Red will require a greater thickness to produce the retardation necessary for extinction than blue; consequently when the longer waves have been withdrawn by interference, the shorter ones remain, the film of gypsum shining with the colours which the short waves confer. Conversely, when the shorter waves have been withdrawn, the thickness is such that the longer waves remain. An elementary consideration suffices to show, that when the directions of vibration of the prisms and the gypsum enclose an angle of forty-five degrees, the colours are at their maximum brilliancy. When the film is turned from this direction, the colours gradually fade, until, at the point where the directions of vibration in plate and prisms are parallel, they disappear altogether.
(The best way of obtaining a knowledge of these phenomena is to construct a model of thin wood orpasteboard, representing the plate of gypsum, its planes of vibration, and also those of the polarizer and analyzer. Two parallel pieces of the board are to be separated by an interval which shall represent the thickness of the film of gypsum. Between them two other pieces, intersecting each other at a right angle, are to represent the planes of vibration within the film; while attached to the two parallel surfaces outside are two other pieces of board, which represent the planes of vibration of the polarizer and analyzer. On the two intersecting planes the waves are to be drawn, showing the resolution of the first polarized beam into two others, and then the subsequent reduction of the two systems of vibrations to a common plane by the analyzer. Following out rigidly the interaction of the two systems of waves, we are taught by such a model that all the phenomena of colour obtained by the combination of the waves, when the planes of vibration of the two Nicols are parallel, are displaced by thecomplementaryphenomena, when the planes of vibration are perpendicular to each other.)
In considering the next point, we will operate, for the sake of simplicity, with monochromatic light—with red light, for example, which is easily obtained pure by red glass. Supposing a certain thickness of the gypsum produces a retardation of half a wave-length, twice this thickness will produce a retardation of two half wave-lengths, three times this thickness a retardation of three half wave-lengths, and so on. Now, when the Nicols are parallel, the retardation of half a wave-length, or of anyoddnumber of half wave-lengths, produces extinction; at all thicknesses, on the other hand, which correspond to a retardation of anevennumber of halfwave-lengths, the two beams support each other, when they are brought to a common plane by the analyzer. Supposing, then, that we take a plate of a wedge form, which grows gradually thicker from edge to back, we ought to expect, in red light, a series of recurrent bands of light and darkness; the dark bands occurring at thicknesses which produce retardations of one, three, five, etc., half wave-lengths, while the bright bands occur between the dark ones. Experiment proves the wedge-shaped film to show these bands. They are also beautifully shown by a circular film, so worked as to be thinnest at the centre, and gradually increasing in thickness from the centre outwards. A splendid series of rings of light and darkness is thus produced.
When, instead of employing red light, we employ blue, the rings are also seen: but as they occur at thinner portions of the film, they are smaller than the rings obtained with the red light. The consequence of employing white light may be now inferred; inasmuch as the red and the blue fall in different places, we haveiris-colouredrings produced by the white light.
Some of the chromatic effects of irregular crystallization are beautiful in the extreme. Could I introduce between our two Nicols a pane of glass covered by those frost-ferns which your cold weather renders now so frequent, rich colours would be the result. The beautiful effects of the irregular crystallization of tartaric acid and other substances on glass plates now presented to you, illustrate what you might expect from the frosted window-pane. And not only do crystalline bodies act thus upon light, but almost all bodies that possess a definite structure do the same. As a generalrule, organic bodies act thus upon light; for their architecture implies an arrangement of the molecules, and of the ether associated with the molecules, which involves double refraction. A film of horn, or the section of a shell, for example, yields very beautiful colours in polarized light. In a tree, the ether certainly possesses different degrees of elasticity along and across the fibre; and, were wood transparent, this peculiarity of molecular structure would infallibly reveal itself by chromatic phenomena like those that you have seen.
Not only do natural bodies behave in this way, but it is possible, as shown by Brewster, to confer, by artificial strain or pressure, a temporary double refracting structure upon non-crystalline bodies such as common glass. This is a point worthy of illustration. When I place a bar of wood across my knee and seek to break it, what is the mechanical condition of the bar? It bends, and its convex surface isstrainedlongitudinally; its concave surface, that next my knee, is longitudinallypressed. Both in the strained portion and in the pressed portion of the wood the ether is thrown into a condition which would render the wood, were it transparent, double-refracting. For, in cases like the present, the drawing of the molecules asunder longitudinally is always accompanied by their approach to each other laterally; while the longitudinal squeezing is accompanied by lateral retreat. Each half of the bar of wood exhibits this antithesis, and is therefore double-refracting.
Let us now repeat this experiment with a bar of glass. Between the crossed Nicols I introduce such a bar. By the dim residue of light lingering upon the screen, you see the image of the glass, but it has no effect upon the light. I simply bend the glass bar with my finger and thumb, keeping its length oblique to the directions of vibration in the Nicols. Instantly light flashes out upon the screen. The two sides of the bar are illuminated, the edges most, for here the strain and pressure are greatest. In passing from longitudinal strain to longitudinal pressure, we cross a portion of the glass where neither is exerted. This is the so-called neutral axis of the bar of glass, and along it you see a dark band, indicating that the glass along this axis exercises no action upon the light. By employing the force of a press, instead of the force of my finger and thumb, the brilliancy of the light is greatly augmented.
Again, I have here a square of glass which can be inserted into a press of another kind. Introducing the uncompressed square between the prisms, its neutrality is declared; but it can hardly be held sufficiently loosely in the press to prevent its action from manifesting itself. Already, though the pressure is infinitesimal, you see spots of light at the points where the press is in contact with the glass. On turning a screw, the image of the square of glass flashes out upon the screen. Luminous spaces are seen separated from each other by dark bands.
Fig. 38Fig. 38
Every two adjacent spaces are in opposite mechanical conditions. On one side of the dark band we have strain, on the other side pressure, the band marking the neutral axis between both. I now tightenthe vice, and you see colour; tighten still more, and the colours appear as rich as those presented by crystals. Releasing the vice, the colours suddenly vanish; tightening suddenly, they reappear. From the colours of a soap-bubble Newton was able to infer the thickness of the bubble, thus uniting by the bond of thought apparently incongruous things. From the colours here presented to you, the magnitude of the pressure employed might be inferred. Indeed, the late M. Wertheim, of Paris, invented an instrument for the determination of strains and pressures, by the colours of polarized light, which exceeded in accuracy all previous instruments of the kind.
And now we have to push these considerations to a final illustration. Polarized light may be turned to account in various ways as an analyzer of molecular condition. It may, for instance, be applied to reveal the condition of a solid body when it becomes sonorous. A strip of glass six feet long, two inches wide and a quarter of an inch thick, is held at the centre between the finger and thumb. On sweeping a wet woollen rag over one of its halves, you hear an acute sound due to the vibrations of the glass. What is the condition of the glass while the sound is heard? This: its two halves lengthen and shorten in quick succession. Its two ends, therefore, are in a state of quick vibration; but at the centre the pulses from the two ends alternately meet and retreat from each other. Between their opposing actions, the glass at the centre is kept motionless: but, on the other hand, it is alternately strained and compressed. In fig. 38, A B may be taken to represent the glass rectangle with its centre condensed; while A' B' represents the same rectanglewith its centre rarefied. The ends of the strip suffer neither condensation nor rarefaction.
If we introduce the strip of glass (ss', fig. 39) between the crossed Nicols, taking care to keep it oblique to the directions of vibration of the Nicols, and sweep our wet rubber over the glass, this is what may be expected to occur: At every moment of compression the light will flash through; at every moment of strain the light will also flash through; and these states of strain and pressure will follow each other so rapidly, that we may expect a permanent luminous impression to be made upon the eye. By pure reasoning, therefore, we reach the conclusion that the light will be revived whenever the glass is sounded. That it is so, experiment testifies: at every sweep of the rubber (h, fig. 39) a fine luminous disk (O) flashes out upon the screen. The experiment may be varied in this way: Placing in front of the polarizer a plate of unannealed glass,you have a series of beautifully coloured rings, intersected by a black cross. Every sweep of the rubber not only abolishes the rings, but introduces complementary ones, the black cross being, for the moment, supplanted by a white one. This is a modification of a beautiful experiment which we owe to Biot. His apparatus, however, confined the observation of it to a single person at a time.
Fig. 39.Fig. 39.
Bodies are usually expanded by heat and contracted by cold. If the heat be applied with perfect uniformity, no local strains or pressures come into play; but, if one portion of a solid be heated and another portion not, the expansion of the heated portion introduces strains and pressures which reveal themselves under the scrutiny of polarized light. When a squareof common window-glass is placed between the Nicols, you see its dim outline, but it exerts no action on the polarized light. Held for a moment over the flame of a spirit-lamp, on reintroducing it between the Nicols, light flashes out upon the screen. Here, as in the case of mechanical action, you have luminous spaces of strain divided by dark neutral axes from spaces of pressure.
Fig. 40.Fig. 40.
Fig. 41.Fig. 41.
Let us apply the heat more symmetrically. A small square of glass is perforated at the centre, and into the orifice a bit of copper wire is introduced. Placing the square between the prisms, and heating the wire, the heat passes by conduction to the glass, through which it spreads from the centre outwards. You immediately see four luminous quadrants and a dim cross, which becomes gradually blacker, by comparison with the adjacent brightness. And as, in the case of pressure, we produced colours, so here also, by the proper application of heat, gorgeous chromatic effects may be evoked. The condition necessary to the production of these colours may be rendered permanent by first heating the glass sufficiently, and then cooling it, so that the chilled massshall remain in a state of permanent strain and pressure. Two or three examples will illustrate this point. Figs. 40 and 41 represent the figures obtained with two pieces of glass thus prepared; two rectangular pieces of unannealed glass, crossed and placed between the polarizer and analyzer, exhibit the beautiful iris fringes represented in fig. 42.
Fig. 42.Fig. 42.
But we have to follow the ether still further into its hiding-places. Suspended before you is a pendulum, which, when drawn aside and liberated, oscillates to and fro. If, when the pendulum is passing the middle point of its excursion, I impart a shock to it tending to driveit at right angles to its present course, what occurs? The two impulses compound themselves to a vibration oblique in direction to the former one, but the pendulum still oscillates ina plane. But, if the rectangular shock be imparted to the pendulum when it is at the limit of its swing, then the compounding of the two impulses causes the suspended ball to describe, not a straight line, but an ellipse; and, if the shock be competent of itself to produce a vibration of the same amplitude as the first one, the ellipse becomes a circle.
Why do I dwell upon these things? Simply to make known to you the resemblance of these gross mechanical vibrations to the vibrations of light. I hold in my hand a plate of quartz cut from the crystal perpendicular to its axis. The crystal thus cut possesses the extraordinary power of twisting the plane of vibration of a polarized ray to an extent dependent on the thickness of the crystal. And the more refrangible the light the greater is the amount of twisting; so that, when white light is employed, its constituent colours are thus drawn asunder. Placing the quartz plate between the polarizer and analyzer, this vivid red appears; and, turning the analyzer in front from right to left, the other colours of the spectrum appear in succession. Specimens of quartz have been found which require the analyzer to be turned from left to right to obtain the same succession of colours. Crystals of the first class are therefore called right-handed, and of the second class, left-handed crystals.
With profound sagacity, Fresnel, to whose genius we mainly owe the expansion and final triumph of the undulatory theory of light, reproduced mentally the mechanism of these crystals, and showed their action tobe due to the circumstance that, in them, the waves of ether so act upon each other as to produce the condition represented by our rotating pendulum. Instead of being plane polarized, the light in rock crystal iscircularly polarized. Two such rays, transmitted along the axis of the crystal, and rotating in opposite directions, when brought to interference by the analyzer, are demonstrably competent to produce all the observed phenomena.
Fig. 43.Fig. 43.
I now remove the analyzer, and put in its place the piece of Iceland spar with which we have already illustrated double refraction. The two images of the carbon-points are now before you, produced, as you know, by two beams vibrating at right angles to each other. Introducing a plate of quartz between the polarizer and the spar, the two images glow with complementary colours. Employing the image of an aperture instead of that of the carbon-points, we have two coloured circles. As the analyzer is caused to rotate, the colours pass through various changes: but they are always complementary. When the one is red, the other is green; when the one is yellow, the other is blue. Here we have it in our power to demonstrate afresh a statement made in our first lecture, that although the mixture of blue and yellow pigments produces green, the mixture of blue and yellow lights produces white. By enlarging our aperture, the two images produced by the spar are caused to approach each other, andfinally to overlap. The one image is now a vivid yellow, the other a vivid blue, and you notice that where these colours are superposed we have a pure white. (See fig. 43, where N is the end of the polarizer, Q the quartz plate, L a lens, and B the bi-refracting spar. The two images overlap at O, and produce white by their mixture.)
This brings us to a point of our inquiries which, though rarely illustrated in lectures, is nevertheless so likely to affect profoundly the future course of scientific thought that I am unwilling to pass it over without reference. I refer to the experiment which Faraday, its discoverer, called the 'magnetization of light.' The arrangement for this celebrated experiment is now before you. We have, first, our electric lamp, then a Nicol prism, to polarize the beam emergent from the lamp; then an electro-magnet, then a second Nicol, and finally our screen. At the present moment the prisms are crossed, and the screen is dark. Iplace from pole to pole of the electro-magnet a cylinder of a peculiar kind of glass, first made by Faraday, and called Faraday's heavy glass. Through this glass the beam from the polarizer now passes, being intercepted by the Nicol in front. On exciting the magnet light instantly appears upon the screen. By the action of the magnet upon the heavy glass the plane of vibration is caused to rotate, the light being thus enabled to get through the analyzer.
Fig. 44Fig. 44
The two classes into which quartz-crystals are divided have been already mentioned. In my hand I hold a compound plate, one half of it taken from a right-handed, and the other from a left-handed crystal. Placing the plate in front of the polarizer, I turn one of the Nicols until the two halves of the plate show a common puce colour. This yields an exceedingly sensitive means of rendering visible the action of a magnet upon light. By turning either the polarizer or the analyzer through the smallest angle, the uniformity of the colour disappears, and the two halves of the quartz show different colours. The magnet produces an effect equivalent to this rotation. The puce-coloured circle is now before you on the screen. (See fig. 44, where N is the nozzle of the lamp, H the first Nicol, Q the biquartz plate, L a lens, M the electro-magnet, with the heavy glass across its perforated poles, and P the second Nicol.) Exciting the magnet, one half of the image becomes suddenly red, the other half green. Interrupting the current, the two colours fade away, and the primitive puce is restored.
The action, moreover, depends upon the polarity of the magnet, or, in other words, on the direction of the current which surrounds the magnet. Reversingthe current, the red and green reappear, but they have changed places. The red was formerly to the right, and the green to the left; the green is now to the right, and the red to the left. With the most exquisite ingenuity, Faraday analyzed all those actions and stated their laws. This experiment, however, long remained a scientific curiosity rather than a fruitful germ. That it would bear fruit of the highest importance, Faraday felt profoundly convinced, and present researches are on the way to verify his conviction.
A few more words are necessary to complete our knowledge of the wonderful interaction between ponderable molecules and the ether interfused among them. Symmetry of molecular arrangement implies symmetry on the part of the ether; atomic dissymmetry, on the other hand, involves the dissymmetry of the ether, and,as a consequence, double refraction. In a certain class of crystals the structure is homogeneous, and such crystals produce no double refraction. In certain other crystals the molecules are ranged symmetrically round a certain line, and not around others. Along the former, therefore, the ray is undivided, while along all the others we have double refraction. Ice is a familiar example: its molecules are built with perfect symmetry around the perpendiculars to the planes of freezing, and a ray sent through ice in this direction is not doubly refracted; whereas, in all other directions, it is. Iceland spar is another example of the same kind: its molecules are built symmetrically round the line uniting the two blunt angles of the rhomb. In this direction a ray suffers no double refraction, in all others it does. This direction of no double refraction is called theoptic axisof the crystal.
Hence, if a plate be cut from a crystal of Iceland spar perpendicular to the axis, all rays sent across this plate in the direction of the axis will produce but one image. But, the moment we deviate from the parallelism with the axis, double refraction sets in. If, therefore, a beam that has been renderedconicalby a converging lens be sent through the spar so that the central ray of the cone passes along the axis, this ray only will escape double refraction. Each of the others will be divided into an ordinary and an extraordinary ray, the one moving more slowly through the crystal than the other; the one, therefore, retarded with reference to the other. Here, then, we have the conditions for interference, when the waves are reduced by the analyzer to a common plane.
Placing the plate of Iceland spar between the crossedNicol prisms, and employing the conical beam, we have upon the screen a beautiful system of iris-rings surrounding the end of the optic axis, the circular bands of colour being intersected by a black cross (fig. 45). The arms of this cross are parallel to the two directions of vibration in the polarizer and analyzer. It is easy to see that those rays whose planes of vibration within the spar coincide with the plane of vibration ofeitherprism, cannot get throughboth. This complete interception produces the arms of the cross.