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duction 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 ali 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 doublyrefracting 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 vibra