REVERSED AND NON-REVERSED SPECTRA. 



49 



if n' is the number of fringes between X and X'. Thus 



M'X-MX' 



(3) 



n = e- 



XX' 



or the number of fringes increases as e is greater. 



Equation (2) does not, as a rule, reproduce the phenomenon very well. 

 Since the grating space D of the two gratings is rarely quite the same, the 

 air-plate inclosed, in case of apparent coincidence of the sodium lines, is 

 slightly wedge-shaped, as in figure 32. Hence the two diffractions take place 

 at incidences o and a, respectively, and the corresponding angles of diffrac- 

 tion will be 6 and tf . If we consider the two corresponding rays / and I", 

 diffracted at the first and second face, respectively, and coinciding at c in the 

 latter, the points a, b, and a' (ba' normal to ac), are in the same phase, and 

 we may compute the phase-difference at the coincident points at c. Since 

 the distance be is 



cos a cos 9 



e = e- 



a) 



33 



1 34 



the path-difference is 



whence 

 (4) 



e cos a cos 

 cos (0 a) 



COS0) 



X cos (6 a) 



COS 0COS a (i COS 0) 



which changes into equation (2) when a = o and iz = i. Fortunately this 

 correction is, as a rule, small. In case of the Wallace gratings (D= 1.7 5 X lo" 4 

 cm.), for instance, if X= 58.93 Xicr 6 , then 0=19 40' or 8e= i.oiXicr 3 ; whereas 

 if a =5, then 8e =1.04 Xio~ 3 ; if a =10, then 8e =1.07 Xicr 3 , etc. 



If the incidence is at an angle i and the plates are parallel, figure 33, the 

 inquiry leads in the same way to an equation of more serious import. If the 

 gratings G and G' are at a distance e apart and the incident rays are I and /', 

 the points a, b, c are in the same phase. Hence the two rays leaving d and 

 diffracted along D correspond to a path-difference 



(5) 

 whence 



COS I 



i -cos (0-z)) 

 X cos t 



I COS (0 l) 



