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systems of waves of equal intensity, and polarized in rectangular planes, differ in their progress of an undulation, the compound movement which they will communicate to each molecule, instead of being rectilinear, as in the two fasciculi considered separately, will be circular, and will be performed with uniform velocity. But if the difference of progress, instead of being an even or an uneven number of 4th of undulations, be a fractional number, the vibratory movements will be neither rectilinear, nor circular, but elliptical.

Here is an apparatus (fig. 13), contrived, I am informed, by Professor Wheatstone, which illustrates how two rectangularly polarized rays of light may influence each other. It consists of a series of rods disposed horizontally in an undulated form, so as to represent a system of plane waves. One end of each rod is rendered conspicuous by a white ball, and it will be seen, that, as now arranged, all the balls (which represent a line of etherial molecules) are in one plane, A. If now a block of wood, B, cut so as to represent a system of plane waves of equal size to those represented by the rods, be pressed against the balls, so that the two systems of waves act on each other in a rectangular direction, then, when the waves coincide, the plane, in which the balls lie, changes, and becomes diagonal, as in C; whereas, if the block be so applied to the balls, that the two systems of waves do not coincide, then the balls no longer remain in one plane, but become placed in a helicoidal manner, representing a circular or elliptical wave, as in D.

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With these remarks I finish the theory of light, and have now arrived at the subject of Coloured Polarization.




WHEN an excessively thin film of a doubly refracting crystal is placed in the polariscope, that is, between the polarizing and analyzing plates, the most gorgeous colour or colours appear, and when the analyzer is rotated on its axis they change to complementary tints. If the film be of uniform thickness, the colour is uniform; but if the film be of irregular thickness, different colours are perceived.

In order to produce colour, it is necessary to use, first, a polarizer, as a tourmaline, a doubly refracting prism, or a reflecting plate; secondly, a film of a doubly refracting crystal, called the depolarizer; and, thirdly, an analyzer or test, as a tourmaline, a reflecting plate, or a doubly refracting prism.

The office of the polarizer is indicated by its name; it polarizes the light. Without this no colour is perceived, for a reason which will be hereafter explained.

The doubly refracting film, called the depolarizer, receives the light thus polarized, and doubly refracts it. That is, a system of waves, constituting the incident ray, entering the crystalline film, is resolved into two systems of equal intensities within it. These form respectively the ordinary and extraordinary rays (fig. 14, O and E). They are polarized in planes +45° and-45° to that of the incident system, so that the plane of polarization of the ordinary system forms an angle of 90° with that of the extraordinary system.

Now, the two systems of waves thus produced traverse the crystal in different directions and with different velocities; but as the film or plate is excessively thin, they emerge superposed. One set proceeds through the crystal more slowly than the other; or, in the language of a distinguished writer on this subject, one set lags behind the other: so that at their emergence they are found to be in different phases of vibration.

By the analyzer each of the two systems (O and E) is resolved into two other systems (Oo Oe and Ee Eo), so that now four systems or two pairs are produced.

But the vibrations of these four systems are made in two planes : that is, two in one plane, and the other two in a second plane, which is rectangular to the first. Now, as the two vibrations which are made in the same plane, are not in the same phase (the one system having suffered a greater retardation than the other), the waves interfere and produce colour (if the incident light be white). But the two vibrations of the one plane conspire, while those of the other plane are opposed. Hence the tint or colour produced by the interference of the waves, in one plane, is com

plementary to that produced in the other plane. So that if the analyzer be a doubly refracting prism, both complementary colours are seen by transmission; but if it be a reflector, one is reflected and the other transmitted; whereas, if it be a tourmaline, one is transmitted, while the other is suppressed, extinguished or stifled.

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Production of Complementary Tints.

A. A ray of common or unpolarized light incident on B.

B. The polarizer (a plate of tourmaline).

C. A ray of plane polarized light incident on D.

D. The doubly refracting film or depolarizer.

E. The extraordinary ray} produced by the double refraction of the ray C.

O. The ordinary ray

G. The analyzer (a doubly refracting prism).

Eo. The ordinary ray

Ee. The extraordinary rav produced by the double refraction of the extraordinary

Oo. The ordinary ray

ray E.

Oe. The extraordinary ray} produced by the double refraction of the ordinary ray O.

To render somewhat more intelligible the cause of the colours being complementary, and, therefore, to explain what is meant by the conspiration and opposition of vibrations, let us suppose the vibrations of the polarized light (C, fig. 14) to be made in the plane, CP, fig. 15; and to give more precision to our ideas, let us further suppose that the molecule Ĉ is, at a given instant, moving from C towards P.

The doubly refracting film resolves this motion into two other motions, performed at right angles to each other, one in the direction CO, the other in the direction CE. The waves produced by the vibrations in the plane CO, we shall suppose to constitute the ordinary system, while those in the plane CE form the extraordinary system. But the plate is much too thin to` have produced between these two systems any sensible separation. Each of these motions is resolved, by the analyzer, into two others at right angles to each other. That is, the vibration CO is resolved into the vibrations C Oo and C Oe; while the vibra tion CE is resolved into the vibrations CEo and C Ee. Now, it is obvious, that the two motions C Oo and CEo act in the same direction, or, in other words, they conspire, or strengthen each other; while the motions C Oe and C Ee, though performed in the same plane, oppose or destroy each other.

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By rotating the analyzer the reverse happens: C Oo and C Eo oppose or destroy each other, while C Oe and CEe conspire, or strengthen each other, as in fig. 16.

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Thus, then, the original polarized ray(C, fig. 14) has been resolved into four rays, two polarized in one plane, and the other two polarized in a plane rectangular to this. The two rays which interfere and destroy each other, differ by half an undulation. The colour produced by the interference of the conspiring rays, corresponds to the difference of the routes of the two polarized rays in the plate or film, while that which results from the interference of the opposing rays, is that which is due to the same difference augmented or diminished by half an undulation. In the case above noticed, in which CO e and CEe (fig. 15) are opposed, the colour corresponds to the difference plus half an undulation.

But it may be asked, What is the use of the polarizing plate? What is the reason that no colour is perceived if the light which is incident on the double refracting film be common or unpolarized? To explain this, let us suppose that a ray of common or unpolarized light consists of two rays rectangularly polarized. Each of these rays will suffer the same series of divisions, subdivisions, and interferences as the former; but the tints produced by the one

ray will be complementary to those of the other; so that we shall thus obtain two pairs of complementary tints, and as the tints of each pair will emerge superposed, they will neutralize each other, and the resulting light will be of uniform whiteness.

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For red and green are complementary tints, and produce by their union white light, as I have already demonstrated.

The office of the doubly refracting film, called the depolarizer, is to doubly refract the polarized light. It prepares the rays for the changes which they have ultimately to undergo and by which colour is to be produced. The thickness of the film or crystalline plate determines the tint; but the actual thickness required to produce a given tint depends on the nature of the crystal. By this plate or film two rectangularly polarized systems of waves are produced, which traverse the plate in different directions and with different velocities, and emerge in different phases of vibration. Now as they are superposed, and as the retardation amounts only to a few undulations and parts of an undulation, it might be supposed that colour would be produced by their interference. But I have already stated that two rectangularly polarized rays do not interfere, so as to produce colour. In order, therefore, to make them interfere, their planes of polarization must be made to coincide; and to do this is the function of the analyzer.

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In order to assist us in comprehending how a polarized ray may be resolved into two others polarized in different planes, we may take, as an illustration, a stretched cord, fig. 17 A B, dividing at B into B C and B D, making a small angle with each other at B, and having either equal or unequal tension. Let us suppose the extremity A of the single cord to be made to vibrate regularly in either a horizontal or vertical plane; now, by means of two polished guiding-planes, EF and GH, inclined at different angles to the horizon, and making a right angle with each other, the horizontal vibrations of the cord A B, will give rise to two other vibrations, parallel respectively to E F

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