Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/628

 G08 LIGHT Inter ference spec trum. Wave- lengths ,L,. homo- geneous rays. theory, that the ratio of the breadths of the bar and interstice has but little effect on the result, unless it be either very large or very small. Hence if A be expressed as a fraction of an inch, and n be the number of lines per inch in the grating, the angular deviations of the bright bands have the sines n, 2n, 3)i, &c. The mean wave-length of visible rays in air is about TTHTTn^h of an inch. Thus a grating with 5000 equi distant lines per inch will give with such light an angular deviation of about 6 for the first bright diffraction line. If we notice that the sine of the deviation is proportional to the wave-length, it will be obvious that when white light is used the result will be a series of spectra on each side of the central white image, their more refrangible ends being turned towards that image. When the grating is a very regular one, and the appearances are examined by means of a telescope adjusted for parallel rays, the spectra formed in this way show the Fraunhofer lines with as great perfection as do the best prisms. And they have one special advantage, which prisms do not possess. The relative angular separation of the various colours depends solsly on their wave-lengths, and thus the spectra formed by different gratings are practically similar to one another. There is, in fact, almost no irrationality in this kind of dispersion. In glass prisms and especially in those of flint glass, the more refrangible part of the spectrum is much dilated, while the less refrangible part is compressed. The counting of the number of lines per inch in a grating j 3 no t difficult, nor is the accurate measurement of the angle of deviation of any particular Fraunhofer line. Hence, by the help of the very simple formula given above, the wave-lengths of light corresponding to the various Fraunhofer lines have been determined with very great accuracy from the diffraction spectra of gratings. The following are, according to Angstrom, 1 a few of the chief values. A is expressed in ten-millionths of a millimetre. 2 A B C D (double) E F G H (double) Atmospheric Atmospheric Hydrogen Sodium Calcium and Iron Hydrogen Iron Calcium and Iron 7G04 6867 6562 5895 5889 5269 4861 4307 3968 3933 1 -3309 1-3317 1 -3336 1-3358 1 -3378 1-3413 1-3442 Comple mentary gratings. Shadow of circu lar disk. For the sake of a discussion to be entered on later, we have appended the refractive index from air into water for each of these rays, as given by Fraunhofer himself. 3 If now we suppose AB, CD, tfcc., to be transparent, while BC, &c., become opaque, it is obvious that the new grating will be the complement of the old one, and will give precisely the same appearances at points outside ths course of the direct beam. For when there is no grating there is practi cally no illumination at such points. This statement of course is equally true of any grating, whatever be the ratio of the breadths of the bars to those of the interstices. Another very curious result of the theory of interference, fully verified by experiment, is furnished by the fact that the central spot of the shadow of a small circular disk, cast by rays diverging from a distant point in its axis, is as brightly illuminated as if the disk had not been inter posed. The final example of interference which we can give here is noteworthy on account of a peculiarity which it 1 Spectre Solaire, 1863. - As there are nearly 25 millimetres in an inch, these numbers each multiplied by 4 give the wave-lengths approximately in thousand-mil- Honths of an inch. 3 Gilbert s Annalen, Ivi., 1817. presents. Let us consider the case of homogeneous light reflected by a thin plate or film of a transparent material. Let AB (fig. 33) be the direction of the incident ray, BdE the direction in which part of it is reflected to an eye E at a considerable distance : and let DE be the direction in which another part escapes after refraction into the plate at B and partial reflexion at the second surface of the plate at C. Then if Dd be drawn perpen dicular to BE, the re tardation of the wave in DE as compared with that in BE will be (2/x.BC - B&amp;lt;/)/A wave-lengths, where yu, is the refrac tive index into the plate. If a be the angle of refraction, and t the thickness of the plate, it is easily seen that Pa-flexk from and BC cos a = t, BD = 2BC sin a = 2t tan a. Hence 2/j.EC - Rd = fyt cos a. Hence whenever, for a given thickness of plate, a is such that 2/U&amp;lt; COS o is an integral multiple of A, the two rays should reinforce one another at E. The same will happen for a given angle of incidence when the thickness of the plate is i-ucli that 2ju&amp;lt; cos a is an integral multiple of A. When, on either account 2fj.t cos a is an odd integral multiple of A/2 ; the rays at E will weaken (perhaps destroy) one another. Hence, in homogeneous light, a thin plate, turned about, Colour: alternately reflects and does not reflect to an eye in a given | tlim position. And a fixed plate of non-uniform thickness 1 reflects light from some parts and not from others. When white light is used there will in general be colours seen which vary with the angle of incidence, and also with the thickness. If the plate is infinitely thin it would appear that there should be infinitely slight retardation only, and the plate should thus be bright in homogeneous light (and of course white in white light) at all incidences. In general this is not the case. Thus when a soap Black- bubble, or a vertical soap-film, is screened from currents of ness - air, and allowed to drain, the uppermost (i.e., the thinnest) part becomes perfectly black. It can, in fact, be seen only by the feeble light scattered by little drops of oil or particles of soap or dust on its surface. Here, again, Young s sagacity supplied the germ at least of the explanation. It is given in the following extract from his Theory of Light and Colours, the Bakerian Lecture for 1801 already referred to : &quot;PROPOSITION IV. men an imditJation arrives at a Surface Loss of which is the Limit of Mediums of different Densities, a partial half Reflexion takes place, proportionate in Force to the Difference of /he wave- Densitics. length. &quot; This may be illustrated, if not demonstrated, by the analogy ol elastic bodies of different sizes. If a smaller elastic body strikes against a larger one, it is well known that the smaller is reflected more or less powerfully, according to the difference of their magni tudes : thus, there is always a reflexion when the rays of light pass from a rarer to a denser stratum of ether, and frequently an echo when a sound strikes against a cloud. A greater body striking a smaller one propels it, without losing all its motion ; thus, the particles of a denser stratum of ether do not impart the whole of their motion to a rarer, but, in their effort to proceed, they are recalled by the attraction of the refracting substance with equal force ; and thus a reflexion is always secondarily produced, when the rays of light pass from a denser to a rarer stratum. But it is not absolutely necessary to suppose an attraction in the latter case, since the effort to proceed would be propagated backwards without