Phenomena exhibited by the Passage of Polarized Light through Mica and Sulphate of Lime—The Coloured Images produced by Polarized Light passing through Crystals having one and two Optic Axes—Circular Polarization—Elliptical Polarization—Discoveries of MM. Biot, Fresnel, and Professor Airy—Coloured Images produced by the Interference of Polarized Rays—Fluorescence.

Such is the nature of polarized light and of the laws it follows. But it is hardly possible to convey an idea of the splendour of the phenomena it exhibits under circumstances which an attempt will now be made to describe.

If light polarized by reflection from a pane of glass be viewed through a plate of tourmaline, with its longitudinal section vertical, an obscure cloud, with its centre totally dark, will be seen on the glass. Now, let a plate of mica, uniformly about the thirtieth of an inch in thickness, be interposed between the tourmaline and the glass; the dark spot will instantly vanish, and, instead of it, a succession of the most gorgeous colours will appear, varying with every inclination of the mica, from the richest reds, to the most vivid greens, blues, and purples (N.211). That they may be seen in perfection, the mica must revolve at right angles to its own plane. When the mica is turned round in a plane perpendicular to the polarized ray, it will be found that there are two lines in it where the colours entirely vanish. These are the optic axes of the mica, which is a doubly refracting substance, with two optic axes, along which light is refracted in one pencil.

No colours are visible in the mica, whatever its position may be with regard to the polarized light, without the aid of the tourmaline, which separates the transmitted ray into two pencils of coloured light complementary to one another, that is, which taken together would make white light. One of these it absorbs, and transmits the other; it is therefore called the analyzing plate. The truth of this will appear more readily if a film of sulphate of lime, between the twentieth and sixtieth of an inch thick, be used instead of the mica. When the film is of uniform thickness, only one colour will be seen when it is placed between the analyzing plate and the reflecting glass; as, for example, red. But, when the tourmaline revolves, the red will vanish by degrees till the film is colourless; then it will assume a green hue, which will increase and arrive at its maximum when the tourmaline has turned through ninety degrees; after that, the green will vanish and the red will reappear, alternating at each quadrant. Thus the tourmaline separates the light which has passed through the film into a red and a green pencil; in one position it absorbs the green and lets the red pass, and in another it absorbs the red and transmits the green. This is proved by analyzing the ray with Iceland spar instead of tourmaline; for, since the spar does not absorb the light, two images of the sulphate of lime will be seen, one red and the other green; and these exchange colours every quarter revolution of the spar, the red becoming green, and the green red; and, where the images overlap, the colour is white, proving the red and green to be complementary to each other. The tint depends on the thickness of the film. Films of sulphate of lime, the 0·00124 and 0·01818 of an inch respectively, give white light in whatever position they may be held, provided they be perpendicular to the polarized ray; but films of intermediate thickness will give all colours. Consequently, a wedge of sulphate of lime, varying in thickness between the 0·00124 and the 0·01818 of an inch, will appear to be striped with all colours when polarized light is transmitted through it. A change in the inclination of the film, whether of mica or sulphate of lime, is evidently equivalent to a variation in thickness.

When a plate of mica, held as close to the eye as possible, at such an inclination as to transmit the polarized ray along one of its optic axes, is viewed through the tourmaline with its axis vertical, a most splendid appearance is presented. The cloudy spot in the direction of the optic axis is seen surrounded by a set of vividly coloured rings of an oval form, divided into two unequal parts by a black curved band passing through the cloudy spot about which the rings are formed. The other optic axis of the mica exhibits a similar image (N.212).

When the two optic axes of a crystal make a small angle with one another, as in nitre, the two sets of rings touch externally; and, if the plate of nitre be turned round in its own plane, the black transverse bands undergo a variety of changes, till, at last, the whole richly coloured image assumes the form of the figure 8, traversed by a black cross (N.213). Substances with one optic axis have but one set of coloured circular rings, with a broad black cross passing through its centre, dividing the rings into four equal parts. When the analyzing plate revolves, this figure recurs at every quarter revolution; but in the intermediate positions it assumes the complementary colours, the black cross becoming white.

It is in vain to attempt to describe the beautiful phenomena exhibited by innumerable bodies which undergo periodic changes in form and colour when the analyzing plate revolves, but not one of them shows a trace of colour without the aid of tourmaline, or something equivalent, to analyze the light, and as it were to call these beautiful phantoms into existence. Tourmaline has the disadvantage of being itself a coloured substance; but that inconvenience may be obviated by employing a reflecting surface as an analyzing plate. When polarized light is reflected by a plate of glass at the polarizing angle, it will be separated into two coloured pencils; and, when the analyzing plate is turned round in its own plane, it will alternately reflect each ray at every quarter revolution, so that all the phenomena that have been described will be seen by reflection on its surface.

Coloured rings are produced by analyzing polarized light transmitted through glass melted and suddenly or unequally cooled; also through thin plates of glass bent with the hand, jelly indurated or compressed, &c. &c. In short, all the phenomena of coloured rings may be produced, either permanently or transiently, in a variety of substances, by heat and cold, rapid cooling, compression, dilatation, and induration; and so little apparatus is necessary for performing the experiments, that, as Sir John Herschel says, a piece of window glass or a polished table to polarize the light, a sheet of clear ice to produce the rings, and a broken fragment of plate-glass placed near the eye to analyze the light, are alone requisite to produce one of the most splendid of optical exhibitions.

Pressure produces remarkable changes in the optical properties of crystals. Compression, perpendicular to the axis, transforms a crystal with one optic axis into one with two. A slice of quartz and one of beryl, both cut perpendicularly to their axis, were compressed thus by MM. Moignot and Soleil. They found that the single system in the quartz, which is a positive crystal, was doubled in the direction of the compression, while in the beryl, which is a negative crystal, the duplication was perpendicular to the compression. In the quartz the axis of the double system coincided with the line of pressure, but in the tourmaline, which is a negative crystal, the line which joins the centres of the rings was perpendicular to the pressure.

If a positive crystal be compressed in the direction of its axis the tint of the rings descends, and that of a negative crystal rises. But if the crystals be dilated in the direction of their optic axis, the tints in positive crystals rise, and negative descend.

It has been observed, that when a ray of light, polarized by reflection from any surface not metallic, is analyzed by a doubly refracting substance, it exhibits properties which are symmetrical both to the right and left of the plane of reflection, and the ray is then said to be polarized according to that plane. This symmetry is not destroyed when the ray, before being analyzed, traverses the optic axis of a crystal having but one optic axis, as evidently appears from the circular forms of the coloured rings already described. Regularly crystallized quartz, however, forms an exception. In it, even though the rays should pass through the optic axis itself, where there is no double refraction, the primitive symmetry of the ray is destroyed, and the plane of primitive polarization deviates either to the right or left of the observer, by an angle proportional to the thickness of the plate of quartz. This angular motion, or true rotation of the plane of polarization, which is called circular polarization, is clearly proved by the phenomena. The coloured rings produced by all crystals having but one optic axis are circular, and traversed by a black cross concentric with the rings; so that the light entirely vanishes throughout the space enclosed by the interior ring, because there is neither double refraction nor polarization along the optic axis. But in the system of rings produced by a plate of quartz, whose surfaces are perpendicular to the axis of the crystal, the part within the interior ring, instead of being void of light, is occupied by a uniform tint of red, green, or blue, according to the thickness of the plate (N.214). Suppose the plate of quartz to be ¹/₂₅ of an inch thick, which will give the red tint to the space within the interior ring; when the analyzing plate is turned, in its own plane through an angle of 17¹/₂°, the red hue vanishes. If a plate of rock crystal ²/₂₅ of an inch thick be used, the analyzing plate must revolve through 35° before the red tint vanishes, and so on, every additional 25th of an inch in thickness requiring an additional rotation of 17¹/₂°; whence it is manifest that the plane of polarization revolves in the direction of a spiral within the rock crystal. It is remarkable that, in some crystals of quartz, the plane of polarization revolves from right to left, and in others from left to right, although the crystals themselves differ apparently only by a very slight, almost imperceptible, variety in form. In these phenomena the rotation to the right is accomplished according to the same laws, and with the same energy, as that to the left. But if two plates of quartz be interposed, which possess different affections, the second plate undoes, either wholly or partly, the rotatory motion which the first had produced, according as the plates are of equal or unequal thickness. When the plates are of unequal thickness, the deviation is in the direction of the strongest, and exactly the same with that which a third plate would produce equal in thickness to the difference of the two.

M. Biot has discovered the same properties in a variety of liquids. Oil of turpentine, and an essential oil of laurel, cause the plane of polarization to turn to the left, whereas the syrup of sugar-cane, and a solution of natural camphor, by alcohol, turn it to the right. A compensation is effected by the superposition or mixture of two liquids which possess these opposite properties, provided no chemical action takes place. A remarkable difference was also observed by M. Biot between the action of the particles of the same substances when in a liquid or solid state. The syrup of grapes, for example, turns the plane of polarization to the left as long as it remains liquid; but, as soon as it acquires the solid form of sugar, it causes the plane of polarization to revolve towards the right, a property which it retains even when again dissolved. Instances occur also in which these circumstances are reversed.

A ray of light passing through a liquid possessing the power of circular polarization is not affected by mixing other fluids with the liquid—such as water, ether, alcohol, &c.—which do not possess circular polarization themselves, the angle of deviation remaining exactly the same as before the mixture. Whence M. Biot infers that the action exercised by the liquids in question does not depend upon their mass, but that it is a molecular action exercised by the ultimate particles of matter, which depends solely upon the individual constitution, and is entirely independent of the positions and mutual distances of the particles with regard to each other. These important discoveries show that circular polarization surpasses the power of chemical analysis in giving certain and direct evidence of the similarity or difference existing in the molecular constitution of bodies, as well as of the permanency of that constitution, or of the fluctuations to which it may be liable. For example, no chemical difference has been discovered between syrup from the sugar-cane and syrup from grapes. Yet the first causes the plane of polarization to revolve to the right, and the other to the left; therefore some essential difference must exist in the nature of their ultimate molecules. The same difference is to be traced between the juices of such plants as give sugar similar to that from the cane, and those which give sugar like that obtained from grapes.

If chlorate of soda be dissolved in water, the liquid has no circular polarization; but if the solution be allowed to crystallize, some of the crystals turn the light to the right and others to the left. Now, if all those of one kind be gathered together and dissolved a second time, the liquid will have no circular polarization; but if crystals be allowed to form, some will turn the light to the right and others to the left, although only one kind was dissolved.^[11]

It is a fact established by M. Biot, that in circular polarization the laws of rotation followed by the different simple rays of light are dissimilar in different substances. Whence he infers that the deviation of the simple rays from one another ought not to result from a special property of the luminous principle only, but that the proper action of the molecules must also concur in modifying the deviations of the simple rays differently in different substances.

One of the many brilliant discoveries of M. Fresnel is the production of circular and elliptical polarization by the internal reflection of light from plate-glass. He has shown that, if light polarized by any of the usual methods be twice reflected within a glass rhomb (N.169) of a given form, the vibrations of the ether that are perpendicular to the plane of incidence will be retarded a quarter of a vibration, which causes the vibrating particles to describe circles, and the succession of such vibrating particles throughout the extent of a wave to form altogether a circular helix, or curve like a corkscrew. However, that only happens when the plane of polarization is inclined at an angle of 45° to the plane of incidence. When these two planes form an angle either greater or less, the succession of vibrating particles forms an elliptical helix, which curve may be represented by twisting a thread in a spiral about an oval rod. These curves will turn to the right or left, according to the position of the incident plane.

The motion of the ethereal medium in elliptical and circular polarization may be represented by the analogy of a stretched cord; for, if the extremity of such a cord be agitated at equal and regular intervals by a vibratory motion entirely confined to one plane, the cord will be thrown into an undulating curve lying wholly in that plane. If to this motion there be superadded another similar and equal, but perpendicular to the first, the cord will assume the form of an elliptical helix; its extremity will describe an ellipse, and every molecule throughout its length will successively do the same. But, if the second system of vibrations commence exactly a quarter of an undulation later than the first, the cord will take the form of a circular helix or corkscrew, the extremity will move uniformly in a circle, and every molecule throughout the cord will do the same in succession. It appears, therefore, that both circular and elliptical polarization may be produced by the composition of the motions of two rays in which the particles of ether vibrate in planes at right angles to one another.

Professor Airy, in a very profound and able paper published in the Cambridge Transactions, has proved that all the different kinds of polarized light are obtained from rock crystal. When polarized light is transmitted through the axis of a crystal of quartz, in the emergent ray the particles of ether move in a circular helix; and when it is transmitted obliquely so as to form an angle with the axis of the prism, the particles of ether move in an elliptical helix, the ellipticity increasing with the obliquity of the incident ray; so that, when the incident ray falls perpendicularly to the axis, the particles of ether move in a straight line. Thus quartz exhibits every variety of elliptical polarization, even including the extreme cases where the excentricity is zero, or equal to the greater axis of the ellipse (N.215). In many crystals the two rays are so little separated, that it is only from the nature of the transmitted light that they are known to have the property of double refraction. M. Fresnel discovered, by experiments on the properties of light passing through the axis of quartz, that it consists of two superposed rays, moving with different velocities; and Professor Airy has shown that in these two rays the molecules of ether vibrate in similar ellipses at right angles to each other, but in different directions; that their ellipticity varies with the angle which the incident ray makes with the axis; and that, by the composition of their motions, they produce all the phenomena of polarized light observed in quartz.

It appears, from what has been said, that the molecules of ether always perform their vibrations at right angles to the direction of the ray, but very differently in the various kinds of light. In natural light the vibrations are rectilinear, and in every plane. In ordinary polarized light they are rectilinear, but confined to one plane; in circular polarization the vibrations are circular; and in elliptical polarization the molecules vibrate in ellipses. These vibrations are communicated from molecule to molecule, in straight lines when they are rectilinear, in a circular helix when they are circular, and in an oval or elliptical helix when elliptical.

Some fluids possess the property of circular polarization naturally, as oil of turpentine, the essential oils of laurel and lemon, sugar of grapes, and various liquids.

Elliptical polarization is produced by reflection from metallic surfaces. Mr. Baden Powell discovered it also in the light reflected from China ink, chromate of lead, plumbago, &c. Mr. Airy observed that the light reflected from the diamond is elliptically polarized; and Mr. Jamin has shown that this kind of polarization is generally produced by reflection from almost all transparent bodies, whatever their refractive power may be, especially from glass at angles very little different from the law of the tangents.

Water polarizes light circularly when between the points of maximum density and solidification; hence it becomes crystalline.

The coloured images from polarized light arise from the interference of the rays (N.216). MM. Fresnel and Arago found that two rays of polarized light interfere and produce coloured fringes if they be polarized in the same plane, but that they do not interfere when polarized in different planes. In all intermediate positions, fringes of intermediate brightness are produced. The analogy of a stretched cord will show how this happens. Suppose the cord to be moved backwards and forwards horizontally at equal intervals; it will be thrown into an undulating curve lying all in one plane. If to this motion there be superadded another similar and equal, commencing exactly half an undulation later than the first, it is evident that the direct motion every molecule will assume, in consequence of the first system of waves, will at every instant be exactly neutralized by the retrograde motion it would take in virtue of the second; and the cord itself will be quiescent in consequence of the interference. But, if the second system of waves be in a plane perpendicular to the first, the effect would only be to twist the rope, so that no interference would take place. Rays polarized at right angles to each other may subsequently be brought into the same plane without acquiring the property of producing coloured fringes; but, if they belong to a pencil the whole of which was originally polarized in the same plane, they will interfere.

The manner in which the coloured images are formed may be conceived by considering that, when polarized light passes through the optic axis of a doubly refracting substance,—as mica, for example,—it is divided into two pencils by the analyzing tourmaline; and, as one ray is absorbed, there can be no interference. But, when polarized light passes through the mica in any other direction, it is separated into two white rays, and these are again divided into four pencils by the tourmaline, which absorbs two of them; and the other two, being transmitted in the same plane with different velocities, interfere and produce the coloured phenomena. If the analysis be made with Iceland spar, the single ray passing through the optic axis of the mica will be refracted into two rays, polarized in different planes, and no interference will happen. But, when two rays are transmitted by the mica, they will be separated into four by the spar, two of which will interfere to form one image, and the other two, by their interference, will produce the complementary colours of the other image when the spar has revolved through 90°; because, in such positions of the spar as produce the coloured images, only two rays are visible at a time, the other two being reflected. When the analysis is accomplished by reflection, if two rays are transmitted by the mica, they are polarized in planes at right angles to each other. And, if the plane of reflection of either of these rays be at right angles to the plane of polarization, only one of them will be reflected, and therefore no interference can take place; but in all other positions of the analyzing plate both rays will be reflected in the same plane, and consequently will produce coloured rings by their interference.

It is evident that a great deal of the light we see must be polarized, since most bodies which have the power of reflecting or refracting light also have the power of polarizing it. The blue light of the sky is completely polarized at an angle of 74° from the sun in a plane passing through his centre.

A constellation of talent almost unrivalled at any period in the history of science has contributed to the theory of polarization, though the original discovery of that property of light was accidental, and arose from an occurrence which, like thousands of others, would have passed unnoticed had it not happened to one of those rare minds capable of drawing the most important inferences from circumstances apparently trifling. In 1808, while M. Malus was accidentally viewing with a doubly-refracting prism a brilliant sunset reflected from the windows of the Luxembourg Palace in Paris, on turning the prism slowly round, he was surprised to see a very great difference in the intensity of the two images, the most refracted alternately changing from brightness to obscurity at each quadrant of revolution. A phenomenon so unlooked for induced him to investigate its cause, whence sprung one of the most elegant and refined branches of physical optics.

Fluorescence, or the internal dispersion of light, though far from possessing the beauty or extensive consequences of polarized light, is scarcely less wonderful. A variety of substances, such as canary-glass, a solution of sulphate of quinine, fluor-spar, and a great number of organic substances, have the property of diminishing the refrangibility of light by internal dispersion, consequently of increasing the length of the waves, and lowering the colour in the prismatic scale; it is therefore called degraded light, or fluorescence, because first discovered in fluor-spar.

If a piece of glass coloured by cobalt be fixed in a hole in a window-shutter of a dark room, a slab of white porcelain placed near it will appear blue; but if the slab be viewed through a yellow glass coloured by silver, it will appear to be almost quite black, because the yellow glass absorbs all the rays transmitted by the blue glass. If, however, a piece of canary-glass be laid on the slab while it is dark, every part of the canary-glass will shine as if it were self-luminous, and with so bright a light that anything written on the slab that was invisible before may now be distinctly read. Such is the singular phenomenon of internal dispersion, degraded light, or fluorescence. The brightness is by no means due to phosphorescence, because the canary-glass only shines when under the influence of the active or blue rays, whereas phosphorescent bodies shine by their own light—the latter has independent, the former dependent, emission; it is possible, however, that a connexion may hereafter be traced between them.

It appears from the analytical investigation of this phenomenon that the vibrations of the fluorescent substance are analogous to those of a sonorous body, as a bell or musical cord, which give the fundamental note and its harmonics. Now since there is a reciprocal action between the molecules of matter and light, when the light of the sun is absorbed by a substance capable of fluorescence, it puts the whole of its molecules into vibrations the same as its own, analogous to the fundamental note, while at the same time a certain number of molecules take more rapid vibrations exactly like the harmonics. The latter form new centres of light throughout the substance, which impart their vibrations to the ethereal medium around, and constitute fluorescence or degraded light. For example, in the experiment that has been described, the blue light imparted its own vibrations to all the molecules of the canary-glass, and also more rapid vibrations to a certain number of them. All of the blue rays were excluded by the yellow glass held before the eye; but it was pervious to the rays emanating in more rapid vibrations from the smaller number of molecules, which thus became really new centres of light, different from the sun’s light, though owing to it; the one celestial, the other terrestrial; and the latter vibrations being more rapid than those of the blue light, their refrangibility was less, and therefore their colour lower in the prismatic scale. Mr. Power computed from his formulÆ, that fluorescent light is produced by undulations which are a major or minor third below the pitch of the general vibration of the medium—that is to say, below the vibrations which the whole molecules of the body most readily assume.

Professor Stokes, of Cambridge, who made the preceding experiment, found that the chemical rays from a point in the solar spectrum produced, in a solution of the sulphate of quinine, light of a sky-blue colour, which emanates in all directions from the liquid, and that this blue fluorescent light contains, when analysed, all the rays of the spectrum; hence he inferred that the dispersive power or fluorescence had lowered the refrangibility of the chemical rays, so as to make them visible: and Sir David Brewster observes that the new spectrum, of all colours into which they were transformed, must possess the extraordinary property of being a luminous spectrum, either without chemical rays or full of them. The dispersion in the quinine solution is greatest near the surface, but the blue emanation proceeds from every part of the liquid; and Sir John Herschel, who discovered the fluorescent property in this liquid, and gave it the name of epipolic light, found that the remainder of the beam, when it issued from the solution, though not apparently different from the incident white light, is yet so much changed in passing through the liquid, that it is no longer capable of producing fluorescence, though still capable of common dispersion. The blue light from the solution of quinine, when examined, consisted of rays extending over a great part of the spectrum.

By passing a sunbeam through a bluish kind of fluor-spar, Sir David Brewster perceived that the blue colour is not superficial, as it appears to be, but that some veins in the interior of the crystal disperse blue light, others pink, and even white light; in short, he met with fluorescence in such a variety of substances, that he concludes it may prevail more or less in the greater number of solids and liquids.

Professor Draper, of New York, proved that the result is the same whether the incident light be polarized or not, and that the dispersed or degraded light is never polarized, but that it emanates in all directions, as if the substance were self-luminous; he made experiments with light from all parts of the solar spectrum, and with various substances, and always found that the refrangibility of the incident ray was diminished by internal dispersion, and that the colour was changed to suit the new refrangibility. Professor Draper has also shown that the law of action and reaction prevails in all the phenomena of the sunbeam, as in every other department of nature; so that a beam cannot be reflected, refracted, much less absorbed, without producing some change upon the recipient medium; and Mr. Power proved analytically that the solar rays can exercise no action upon any medium through which they are transmitted, without being accompanied by a diminution of refraction. He says, “The new light emanating from the fluorescent media is just like any other light of the same prismatic composition. In its physical properties it retains no trace of its parentage; it is of terrestrial origin, and its colour depends simply on its new refrangibility, having nothing to do with that of the producing rays, nor to the circumstance of their belonging to the visible or invisible part of the spectrum.” These phenomena can only be explained by the undulatory theory of light.