REVERSED AND NON-REVERSED SPECTRA. 



37 



which may be further simplified to 



N COS<T-{- n 



-de) cos (a/2) 

 From this the path on the other side will be 



>_i_ 'i i 



" 



cos 



COS (0 2 +d0) COS (<7/2) 



The path-difference, AP, thus becomes, nearly, 



i \ _N_cos_ff-j-n 2 sin 2 

 cos (62 d 6)) cos (07 2) cos 2 2 



r cos 0-+w 



COS (0-/2)\COS 



This is perhaps the simplest form attainable. If, apart from diffraction, 

 this should result in interference, the angular breadth of an interference 



fringe would be (AP = X) 



X cos 2 2 cos (0^/2) 



2 sin 2 N cos ff-{-n 



and if D is the grating space and sin = X/Z)', 



(D' 2 -X 2 ) cos (cr/ 2 ) 



zD'(N cos 



25 



22 



dA JM 



/u, 4-' Y' 



6- a./ z > % 



&~ ~~nE 



<M 



JL 



or 



23 



In case of a single grating 



cr/2 = 2 =0 N = 



cos 2 2 sin 



24 



COS (7= 2 COS 2 61 



AP = 



cos cos 2 



a result which may be reduced more easily from figure 24. Hence, the 

 angular distance apart of the fringes would be (AP = X) 



X D cos 



de= 



tan 



4 JV 



if D is the grating space. To find the part of the spectrum (d\) occupied 

 by a fringe in the case postulated, since sin = X/D, 



de d\ _D_ 



cos 6~ D cos 2 0~ 4A/ T 



