Discoveries and Inventions of the Nineteenth Century

hollows of the other set; so that along these lines the surface would be smooth, while along C C the crests would have double the height. Now, if light be due to undulation, it should be possible to obtain a similar effect—that is, to make two sets of luminous undulations destroy each other’s effects and produce darkness: in other words, we should be able, by adding light to light, to produce darkness! Now, this is precisely what is done in a celebrated experiment devised by Fresnel, which not only proves that darkness may be produced by the meeting of rays of light, but actually enables us to measure the lengths of the undulations which produce the rays. Fig. 213. In Fig. 213 is a diagram representing the experiment of the two mirrors, devised by Fresnel. We are supposed to be looking down upon the arrangement: the two plane mirrors, which are placed vertically, being seen edgeways, in the lines, M O, O N, and it will be observed that the mirrors are placed nearly in the same upright plane, or, in other words, they form an angle with each other, which is nearly 180°. At L is a very narrow upright slit, formed by metallic straight-edges, placed very close together, and allowing a direct beam of sunlight to pass into the apartment, this being the only light which is permitted to enter. From what has been already said on reflection from plane mirrors, it will readily be understood that these mirrors will reflect the beams from the slit in such a manner as to produce the same effect, in every way, as if there were a real slit placed behind each mirror in the symmetrical positions, A and B. Each virtual image of the slit may, therefore, be regarded as a real source of light at A and at B; thus, for example, it will be observed that the actual lengths of the paths traversed by the beams which enter at L, and are reflected from the mirrors, are precisely the same as if they came from A and B respectively. 410The virtual images may be made to approach as near to each other as may be required, by increasing the angle between the two mirrors, for, when this becomes 180°, that is, when the two mirrors are in one plane, the two images will coincide. If, now, a screen be placed as at F G, a very remarkable effect will be seen; for, instead of simply the images of the two slits, there will be visible a number of vertical coloured bands, like portions of very narrow rainbows, and these coloured bands are due to the two sources of light, A and B; for, if we cover or remove one of the mirrors, the bands will disappear and the simple image of the slit will be seen. If, however, we place in front of L a piece of coloured glass, say red, we shall no longer see rainbow-like bands on the screen, but in their place we shall find a number of strips of red light and dark spaces alternately, and, as before, these are found to depend upon the two luminous sources, A and B. We must, therefore, come to the conclusion that the two rays exercise a mutual effect, and that, by their superposition, they produce darkness at some points and light at others. These alternate dark and light bands are formed on the screen at all distances, and the spaces between them are greater as the two images, A and B, are nearer together. Further, with the same disposition of the apparatus, it is found that when yellow light is used instead of red, the bands are closer together; when green glass is substituted for yellow, blue for green, and violet for blue, that the bands become closer and closer with each colour successively. Hence, the effect of coloured bands, which is produced when pure sunlight is allowed to enter at L, is due to the superposition of the various coloured rays from the white light. Let us return to the case of the red glass, and suppose that the distance apart of the two images, A and B, has been measured, by observing the angle which they subtend at C, and by measuring the distance, C O D, or rather, the distance C O L. Now, the distances of A and B from the centre of each dark band, and of each light band, can easily be calculated, and it is found that the difference between the two distances is always the same for the same band, however the screen or the mirrors may be changed. On comparing the differences of the distances of A and B in case of bright bands, with those in the case of dark ones, it was found that the former could be expressed by the even multiples of a very small distance, which we will call d, thus: 0, 2d, 4d, 6d, 8d, ... 411while the differences for the dark bands followed the odd multiples of the same quantity, d, thus: d, 3d, 5d, 7d, 9d, .... These results are perfectly explained on the supposition that light is a kind of wave motion, and that the distance, d, corresponds to half the length of a wave. We have the waves entering L, and pursuing different lengths of path to reach the screen at F G, and, if they arrive in opposite phases of undulation, the superposition of two will produce darkness. The undulations will plainly be in opposite phases when the lengths of paths differ by an odd number of half-wave lengths, but in the same phase when they differ by an even number. Hence, the length of the wave may be deduced from the measurement of the distances of A and B from each dark and light band, and it is found to differ with the colour of the light. It is also plain that, as we know the velocity of light, and also the length of the waves, we have only to divide the length that light passes over in one second, by the lengths of the waves, in order to find how many undulations must take place in one second. The following table gives the wave-lengths, and the number of undulations for each colour: Colour. Number of Waves in one inch. Number of Oscillations in one second. Red 40,960 514,000,000,000,000 Orange 43,560 557,000,000,000,000 Yellow 46,090 578,000,000,000,000 Green 49,600 621,000,000,000,000 Blue 53,470 670,000,000,000,000 Indigo 56,560 709,000,000,000,000 Violet 60,040 750,000,000,000,000 These are the results, then, of such experiments as that of Fresnel’s, and although such numbers as those given in the table above are apt to be considered as representing rather the exercise of scientific imagination than as real magnitudes actually measured, yet the reader need only go carefully over the account of the experiment, and over that of the measurement of the velocity of light, to become convinced that by these experiments something concerned in the phenomena of light has really been measured, and has the dimensions assigned to it, even if it be not actually the distance from crest to crest of ether waves—even, indeed, if the ether and its waves have no existence. But by picturing to ourselves light as produced by the swaying backwards and forwards of particles of ether, we are better able to think upon the subject, and we can represent to ourselves the whole of the phenomena by a few simple and comparatively familiar conceptions. As an example of the facility with which the ether theory lends itself to aiding our notions of the phenomena of light, take the explanation of polarization. Let us suppose that we are looking at a ray of light along its direction, and that we can see the particles of ether. We should, in such a case, see them vibrating in planes having every direction, and their paths, as so seen, would be represented by an indefinite number of the diameters of a circle. Now, suppose we make the ray first pass through a 412rhomb of Iceland spar: we should, if we could see the vibrating particles in the emergent ordinary and extraordinary rays, perceive them swaying backwards and forwards across the direction of the rays in two planes only, as represented by the lines, B D and A C, in the two circles, O o and E e, Fig. 214–-that is, half the particles would be vibrating in the direction B D, and the other half in the direction A C; and further, the two directions would be at right angles to each other—the vibrations forming the extraordinary ray being performed in a plane at right angles to that in which the vibrations producing the ordinary ray take place. If—these planes being in the position indicated in 1, Fig. 214–-we turn the crystal round through 90°, they would rotate with it, and would come severally into the position shown in 2, Fig. 214. Fig. 214. It was at one time objected to the theory which represents light as due to wave-like movements that, just as the vibrations which constitute sound spread in all directions, and go round intercepting bodies, enabling us, for example, to hear the sound of a bell even when a building intervenes, so if vibrations really produce light, these would extend within the shadows, and we ought to perceive light within the shadows, bending, as it were, round the edge of the shadow-casting body. This objection, which at one time presented a great difficulty for the wave theory, was triumphantly removed by the discovery that the luminous vibrations do extend into the shadow, and that this is in reality never completely dark. It is true that, although we can hear round a corner, we are in general unable to see round it; but it should be noticed that in the case of hearing, the sound is much weakened by intervening objects, and that there are what may be termed sound shadows. A ray of light produces sensible effects only in the direction of its propagation; but it can be shown that the successive portions of the waves advancing along it are centres of lateral disturbances producing new or secondary waves in all directions, which, however, interfere with and destroy each other. When an opaque screen intercepts a portion of the principal wave, it also stops a number of oblique or secondary waves, which would interfere more or less with the rest. Under ordinary circumstances, the remaining oblique or secondary rays are quite insensible in the presence of the direct light. But, with an apparatus which will cost but the two or three minutes’ time required to construct it, the reader may see for himself that light is able to pass round an obstacle, and he may witness directly phenomena of the same order as those presented in the experiment of Fresnel’s mirrors, which require costly apparatus for their production. He has only to take two fragments of common window-glass, and having 413made a piece of tinfoil adhere to one surface of each piece of glass, cut, with a sharp penknife, the finest possible slit in each piece of tinfoil, making the slit from ½ in. to 1 in. in length. If he will then hold one piece of glass about 2 ft. from his eye, so that it may be in the line between his eye and the sun (or other luminous body), and hold the other piece close to his eye with its slit parallel to that in the first piece, he will see the latter not simply as a line of light, but parallel to it a number of brilliantly-coloured rainbow-like bands will be seen on either side. If, instead of receiving the light from the sun, or from a candle-flame, the light given off by a spirit-lamp, with a piece of salt on its wick, be used, bright yellow stripes will be seen with dark spaces between them. Or, if the piece of glass next the sun be red-coloured, instead of plain glass, no rainbow-like bands will be visible, but a number of bright red stripes alternating with dark bands will be seen. The reader will