Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/627

 LIGHT GOT bright band; and at P 3, where O 2 P 3 exceeds O^ by a wave-length and a half, another dark band ; and so on. Hence, as everything is symmetrical about the bright band through A, the screen will be illuminated by a series of bright and dark bands, gradually shading into one another. If the paper screen be moved parallel to itself to or from the prism, the locus of all the successive positions of any one band will (by the nature of the curve) obviously be an hyperbola whose foci are O 1 and (X. Thus the interval between any two bands will increase in a more rapid ratio than does the distance of the screen from the source of light. But the intensity of the bright bands diminishes rapidly as the screen moves farther off; so that, in order to measure their distance from A, it is better to substitute the eye (furnished with a convex lens) for the screen. If we thus measure the distance AP X between A and the nearest bright band, measure also AO, and calculate (from the known material and form of the prism, and the distance CO) the distance OjO.,, it is obvious that we can deduce from them the easui-c lengths of OJPg and 2 P 2 . Their difference is the length wave- -f (i wave of the homogeneous light experimented with, though this is not the method actually employed for the purpose (as it admits of little precision), it has been thus fully explained here because it shows in a very simple way the possibility of measuring a wave-length. The difference between O i P l and O. 2 P l becomes greater as APj is greater. Thus it is clear that the bands are more widely separated the longer the ivave-length of the homogeneous Effect of light employed. Hence when we use white light, and thus ,-liito have systems of bands of every visible wave-length super- r posed, the band A will be red at its edges, the next bright bands will be blue at their inner edges and red at their outer edges. But, after a few bands are passed, the bright bands due to one kind of light will gradually fill up the dark bands due to another ; so that, while we may count hundreds of successive bright and dark bars when homo geneous light is used, with white light the bars become gradually less and less defined as they are farther from A, and finally merge into an almost uniform white illumina tion of the screen. In this example, and in all others of a similar character which will be introduced into this elementary article, the solution is only approximate. The utmost resources of mathematics are in most cases required for the purpose of complete solution. We are now in a position to prove that light moves mal glower in glass than in air, by the process which was merely indicated while we were discussing the velocity of t light. For, if we could slightly lengthen the paths of the rays which come from 15 leaving those from 2 unaltered, lo ^ r. the system of bands would obviously be shifted in the ^ direction from A to P iu. the figure. This happens if a very thin film of glass be interposed in the path of the rays which appear to come from O r The best mode of making the experiment is to put a piece of very uniform plate glass, cut into two parts, between the prism and the screen, so that rays from O l pass through one part and those from O 2 through the other. So long as these pieces are parallel, no shifting takes place. But if one be slightly turned, so as to give the rays a longer path through it, the system of bands is at once displaced to the side at which it is situated. Also, we can now see how it is possible to discover whether light has its velocity affected by that of the medium in which it Ls travelling. We know that sound travels faster ivith the wind, and slower against it, than it does in still air. We may, therefore, suppose a disposi tion of the interference apparatus such that the two rays which interfere have each passed through a long tube full of water. A rapid current may be established, in either direction, in one or other of the tubes, or in opposite directions in the two, and the shifting of the interference- bands will at once indicate the nature of the effect. We cannot describe the details of the process. The result, however, is analogous to that of wind on sound, but of course very much smaller ; and it seems that the actual change of the velocity of light is less than the velocity of the current. See ETHER. Let us next consider the effect of a grating, a series of inter- fine parallel wires placed at small equal intervals, or a fcrence piece of glass or of speculum metal on which a series of 8 ratin - equidistant parallel lines have been ruled by a diamond point. We take only the case in which plane waves of homogeneous light are incident in a direction perpendicular to the plane of the grating, and when the bars and open ings of the grating are all equal in breadth. Consider the effect on an eye or screen at a considerable distance, in the direction BE (fig. 32). If there were no grating, practically no light would reach tluj eye from the aperture AD unless ABE wsre very nearly a right angle. This is, of course, the statement of Huygens already quoted. But Young s principle enables us to say why this is the case. Let us divide AD into a series of equal parts by lines perpendicular to BE, and distant from one another by half a wave-length of the homogeneous light employed. The portions coming to the eye from any two adjacent parts AB, BC will be practically of the same intensity, and will exactly neutralize one another s effects on the eye. For if we take points a and b similarly situated with regard to A and B respectively, the distances of a and b from the eye differ by half a wave-length, and rays from a neutralize those from b. This is true wherever a be taken between A and B. Hence, under the conditions assumed, no light reaches the eye. Now suppose the alternate parts AB, CD, &c., to be opaque. Similar reasoning will show that the remaining rays conspire to strengthen one another. Thus, when homogeneous light from a distant point falls perpendicu larly on a grating in which the breadth of the bars is equal to that of the interstices, it will be seen brightly in a direction inclined at an angle 9 (ABE) to the plane of the grating, the angle being such that AC cos = wave-length. Similar reasoning shows that the light is reinforced when ever is such that AC cos 6 is an integral multiple of the wave-length. The appearance presented when a long narrow slit is the luminous object, and the bars of the grating are placed parallel to it, is therefore (with homogeneous light) a central image with others equidistant from it on each side their angular distances from it being the values of the angle correspond ing to the sines A_ 2A. a &c a a a Here A. is the wave-length, and a is the sum of the breadths of a bar and an interstice. It is found in practice, and it is also deducible from the complete