60 



THE INTERFEROMETRY OF 



But these equations, though useful elsewhere, have very little immediate 

 value here, because the experimental variables, figure 41, are B', the distance 

 between two consecutive colored fringes and b" and b f the corresponding dis- 

 tance between the fringes in case of homogeneous light in each case X, X' ; and 

 the angle y', which indicates the inclination of the slit. Thus B'b'b" are 

 given by computation and y' is specified at pleasure. Obviously, if parallelo- 

 grams are to be obtained, figure 41, b' = b' f , appreciably. This is the case in 

 experiment. Hence if we evaluate the height in the triangle cgc' for each 

 angle it follows easily that 



, tan y' 



sin x =- 



If 



If B' = b', x' = go for all values of y'; i.e., the fringes remain vertical. 

 B' is equal to 26, x' = y', the fringes and slit are symmetrically equiangular 

 with the longitudinal axis of the spectrum. This is nearly the case in figure 

 41 and frequently occurs in experiment. If b' differs from b", the fringes would 

 not be straight. This also occurs, particularly when the thickness e of the 

 air-film is very small. 



26. Final treatment of reversed spectra. Hypothetical case. To obtain an 

 insight into the cause of the interferometer fringes as obtained with reversed 

 spectra and two gratings, it is convenient to represent both gratings, figure 

 43, GG and G"G', as transmitting, 

 and suppose both diffracted beams, 

 ID' and ID", subsequently com- 

 bined in view of the principal plane 

 PP of an objective or a lens. It is 

 clear that this simplified device can 

 apply only for homogeneous light. 

 In the case of white light, the opaque 

 mirrors M and N (of the interfer- 

 ometer, above) return a divergent 

 colored beam or spectrum, so that 

 only for a single color can the second 

 incidence be the same as the first. 

 Again, if the constants of the two 



43 



gratings are different, it is the func- 

 tion of these mirrors to change the 



&- 



71' 



incidence at the second grating correspondingly, so that for homogeneous 

 light the rays issue in parallel. Finally, no reference to the lateral displace- 

 ment OG" and OG' of rays need be made because, as more fully shown in 

 the next paragraph, this is eliminated by the theory of diffraction. 



The motion of the opaque mirrors M and N (above), on a micrometer, 

 merely shortens the air-paths GG' or GG" in its own direction, and conse- 

 quently the same fringe reappears for an effective displacement of half a wave- 

 length, as in all interferometers. 



