Page:The American Cyclopædia (1879) Volume XV.djvu/253

 SPECTRUM 241 FIG. 5. will be as the number of the order ; thus, the spectrum of the third order will be three times as long as that of the first order. It has also been found that the length of the spectrum of any order will be inversely as the distance separating the lines of the gra- ting producing the spectra ; thus, the spectrum of the second order produced by a grating of 5,000 lines in an inch will be half as long as that of the second order given by a grating having 10,- 000 lines in an inch. Let parallel rays of light from a distant point or from the slit of a collimating tele- scope fall perpendicu- larly on the plane of the grating G G, fig. 5. The plane of the wave front of the light will be parallel to the plane of the grating, and the vibrations of the ether at each point in the openings of the grating will have the same phase. But whenever light falls upon such mstructed apertures as those of the grating, points in these apertures, situated in the lane of the grating, become centres of ori- gin of vibrations, and the rays which have 3sed through the apertures diverge in planes right angles to the lines of the grating, le consideration of the mutual action of lese rays will lead at once to remarkable suits. All those rays which have traversed grating in the same direction as that in which they struck it will have the same phase )f vibration, and therefore when brought to- gether in the focus of a lens will form there a white image of the distant point or of the lit of the collimating telescope. But it is not with the parallel rays, which diverge lat- illy, say in the direction ae y bf, eg, dh, &c. these rays be brought to a focus by means a lens L, we shall observe at F not a . r hite image of the slit, but a colored one ; and is found that this color will depend on e inclination of the diffracted rays to R N, le perpendicular to the plane of the grating, ippose that the diffracted rays ae, If, eg, <., are so inclined to the plane of the grating lat a perpendicular, 51, let fall from the cen- re of one opening in the grating to the paral- ray a e emanating from the centre of the contiguous opening, cuts off on the ray ae a distance al, equal to the length of a wave of violet light of a definite tint. Also imagine other perpendiculars e2, dZ, &c., let fall in like manner upon the ray a e. Then if all of these rays a e, bf, eg, dh, &c., be brought to a focus at F, the vibrations of the ether at this point will all have the same phase, and hence will give at F a line which will be formed of violet light; and the intensity of this light will be equal to the sum of the intensities of all the rays a e, bf, c g, &c. The same reasoning will hold good for any other set of rays parallel to those just described, and all symmetrically placed in the openings. Hence all rays ema- nating from the openings and parallel to the rays a e. ~bf, c g, &c., and having wave lengths equal to al, will conspire in their vibratory actions when brought to a focus at F. But it is not so with other rays, which, although parallal to the rays ae, ~bf, &c., have not the same length of waves as al ; for they will not conspire when brought together at F, but will interfere, or in other words will be exactly opposed to each other in vibratory action, and hence will disappear as light when brought to the focus at F. For example, suppose we con- sider a series of rays of red light which pro- ceed parallel to ae, bf, &c., and come to focus at F. These rays are formed of waves which are about twice as long as those of violet light, or in other words as al ; hence red rays which have emanated from symmetrically placed points in two contiguous openings of the gra- ting and proceed in direction parallel to a e, will, on coming to the focus F, all differ by half of an undulation, and hence red light can- not exist at F with an inclination of diffracted ray equal to N c F, but can only exist at a point at such an angular distance from RN that the perpendiculars let fall from a, b, c, and d on to a e cut off on this latter line dis- tances respectively equal to double the lengths al, a2, a3, a4. Again, suppose that the wave lengths of two rays, emanating from symmet- rically placed points in two contiguous open- ings and proceeding parallel to a e, differ by only j-^ of the wave length of one of these rays, then these rays will also interfere when brought to focus at F ; because the phases of the rays emanating from points symmetrically placed in the 1st and 2d openings of the grating will differ by TTr V?r of an undulation ; those from the 1st and 501st openings will differ by Jfifa or half a wave length, and therefore will inter- fere. The same interference will take place be- tween the rays from the 2d opening and those from the 502d, and those from the 4th and the 504th openings, and so on. Hence rays of light having any other wave length than al will almost completely disappear as light by their interference, and the light collected at F will be that which is produced by ethereal vibra- tions of wave lengths equal to al. The same reasoning holds good for any bundle of paral- lel rays having diffracted angles different from NcF, and hence we have a pure spectrum formed at the focus F. It thus appears that there is a connection between the angle N c F of the diffracted rays, the length al, and the color observed at F. The color at F varies with the angle NcF, or, what is the same, with the length al. For the extreme red rays the angle E" c F is at its maximum/ and al is