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Interferences of Light.—It is a law in dynamics, that the velocity produced by two joint forces, when they act in the same direction, will be as the sum of the forces. Hence if two waves, all of whose parts respectively coincide, meet, it is evident that their velocities will be doubled. Whether the vibrating medium be water, air (sound), or ether (light), this statement holds good: the intensity of the waves is doubled.

But the velocity of two joint forces, when they act in opposite directions, will be as their differences. Hence, if a wave (of water, air, or ether) be half an undulation behind another wave, the velocities of the two are mutually destroyed. When stones are thrown into a pond, and two groups of waves cross each other on its surface, there are points at which the water remains immoveable when the two systems are nearly of the same magnitude, while there are other places in which the force of the water is augmented by their concurrence. If two sonorous undulations differ a little from each other in frequency, they alternately tend to destroy each other, and to acquire a double, or, perhaps, a quadruple force; and the sound gradually increases and diminishes in continued succession at equal intervals. This alternate intension and remission is called a beat.

In the same way, the waves of the "' luminiferous ether interfere, and, mutu

al ally destroying each other, cause dark

l\ ness. This important fact, that under

I \ some circumstances, light added to light

/ 1 d causes darkness—a fact apparently fatal

"-.... / 1 _..-* to the projectile theory of light—was first "? established by Dr. Young. This distin

1 guished philosopher—whose attainments

\ and knowledge were insufficiently esti

■■riiniinai mated while he was living—passed a sun

\ beam through a hole (O) made with a

I fine needle in thick paper, and brought

\ into the diverging beam a slip of card

iff / (A B) one-thirtieth of an inoh in breadth, //*/ / and observed its shadow (E F) on a white 'Tf j screen, at different. distances. The ft I shadow was divided by parallel bands, but the central line (X) was always white. That these bands originated in the interference of the light passing on both sides of the card, Dr. Young demonstrated by simply intercepting the light on one side by a screen (C D), leaving the rays on the other side to pass freely. In this arrangement all the fringes which had before existed in the shadow immediately disappeared, although the light inflected on the edge (A) was allowed to retain its course. The same result took place when the intercepting body was at C D, before the edge B of the body.

By a series of wooden sliders, originally contrived by Young*, but put into a very convenient form for use in the lecture-room, by my friend Mr. Woodward, the interference of waves may be neatly illustrated. By this apparatus it will be seen that when the difference amounts to 2, 4, 6, or other even number of half undulations, the waves coincide and mutually augment their intensities; while, when the difference amounts to 1, 3, 5, or other odd number of half undulations, there is discordance and mutual destruction. Now it will be perceived, that these numbers coincide with those referred to by Newton, as expressive of his fits of transmission and reflection.

If two waves of homogeneous or monochromatic light interfere, the result will be an augmentation or diminution of brilliancy, or complete destruction. The light is augmented when the waves accord—but is lessened or destroyed when they are mutually opposed. Hence Newton's rings, seen by homogeneous light, are merely dark and light bands of one and the same colour.

But if two waves of heterogeneous or white light interfere, the result will be the production of vivid coloured fringes. Certain colours are destroyed, while others remain, or have their brilliancy augmented.

It is a law in dynamics, that a body acted upon by two forces united, will describe the diagonal of a parallelogram in the same time in which it would have described its sides by the separate action of those forcesf. Hence, if two waves, whose molecules are in the same phases of vibration, but whose planes of vibration are more or less angular, say rectangular, to each other, the only effect produced is an alteration of the plane of vibration.

This is an explanation of a fact discovered by Fresnel, and laid down by him as a law, that " two rays of light, polarized at right angles to each other, exhibit none of the phenomena of interference," that is, they produce no colours or fringes.

If both the forces act upon a body in such a manner as to move it uniformly, the diagonal described will be a straight line; but if one of the forces acts so as to make the body move faster and faster, then the line described will be a curve. Now this dynamical law explains how two plane luminous waves, whose molecules are vibrating in rectangular planes, by their mutual action, produce a circular or elliptical wave. For if two

* Lectures on Natural Philosophy, vol. i., p. 390, plate xxv., fig. 352 D. t This fact was demonstrated by a neat machine, invented by Mr. E. M. Clarke, of the Strand.

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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 ith 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.

Fig. 13.

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

LECTURE II.

3. 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, 0 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 (0 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

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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.

Fig. 14.

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Production of Complementary Tints.

A. A ray of common or nopolarized light incident on B.
H, The polarizer (a plate of tourmaline).

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

D. The doubly refracting film or depolarizer.

O. ThI orSnaryr'ayy "** } Ponced by the double refraction of the ray C.

G. The analyzer (a doubly refracting prism).

Bo. The ordinary ray \ produced by the double refraction of the extraordinary

Ee. The extraordinary ray / ray B.

o'e. The extraordinary ray } JTM*"** *T ** doaWe refaction 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, C P, fig. 15; and to give more precision to our ideas, let us further suppose that the molecule C 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 C 0, the other in the direction CE. The waves produced by the vibrations in the plane C O, we shall suppose to constitute the ordinary system, while those in the plane C E 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 C O is resolved into the vibrations C Oo and C Oe; while the vibration CE is resolved into the vibrations GEo and CEe. Now, it is obvious, that the two motions C Oo and GEo 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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