REVERSED AND NON-REVERSED SPECTRA. 



59 



inclined as before, an alternation of bright and dark elements will appear in 

 the image of the slit ed, corresponding to X'. If we suppose that for white 

 light and the fine vertical slit the position of the fringe (X') was at c', we may 

 again regard c' as an axis of rotation. To find the fringes such as//", it is then 

 only necessary to connect corresponding black elements on ab and ed. Their 

 inclination is thus opposite to ab and ed, or they have rotated in a direction 

 opposite to that of the slit. If, for instance, the slit image ab or ed is gradu- 

 ally moved back to the vertical, the points g and h will move with great 

 rapidity and in both directions toward infinity and the fringes // and /'/' 

 become vertical lines through c and c' , respectively. 



It is interesting to inquire into the frequency of fringes, n, when the angle 

 of diffraction, 6, is changed. From the original equation e = n\/(i-cos 0), 

 since d\/dd = D cos 6, the rate of change 



dn e i e 



av D i+cos0 D+1/D 2 -X 2 



where e is the distance apart of films and D the grating space. Since cos 6 

 varies but slowly with 6 and is additionally augmented by i, dn/dd is nearly 

 constant and about equal to e/2D. 



41 



42 



Ih, 



The fringes and slit images are thus given by the two sides of the parallelo- 

 gram cgc'h for the two colors X and X'. The diagonal cc' represents dd; the 

 diagonal gh has no signification. On the other hand, the normal distances 

 apart, D' and D", of//" and/'/' and ab and ed are both important. 



If D' and D" are the normal distances apart of the fringes and the slit 

 images, respectively, B and B', the two diagonals of the rectangle cgc'h, modi- 

 fied for convenience in figure 42 , 



D' =D"(cos <p-}-\/B f2 /D" 2 i sin <p) 



which may be obtained from the two small triangles below c'. If B = D", 

 D' = D" cos (f>; and if <p = o, D' = D" = dd, remembering that c and c' lie on two 

 consecutive colored fringes obtained with white light and a fine slit. If the 

 slit images and fringes are symmetrical, each is at an internal angle, po-<p/2, 

 to the longitudinal axis of the spectrum. 



