48 



Messrs. C. and M. Barus on the Interference of 



It is therefore definitely wedge-shaped. In fact when the 

 auxiliary mirror M is used, the fringes may be put anywhere, 

 either in front of or behind the principal focal plane, by 

 suitably inclining the mirror. 



3. Equations. 

 If we suppose the film of the grating gg to be sandwiched 

 in between plates of glass each of thickness e, it will be seen 



Fj>. 1. 



cM 



that triplicate rays pass in the direction t\ (0/>e), or of 

 t 2 (0 2 '<?')> which will necessarily produce interference either 

 partial or total. With respect to t u the only light received 

 comes either from D 1 by direct diffraction at gg, or from 

 RIJ U by reflexion from the lower face ff and thereafter by 

 diffraction at gg ; or from DB^ by diffraction at gg and 

 reflexion at ff. Similarly, the light along t 2 comes in like 

 manner either from D 2 , or DR 2 , or RD 2 . With regard to 

 the angles of incidence and refraction or of diffraction within 

 the glass or outside of it, we have the equations for the first 

 and second order of spectra (D being the grating space). 



sin %x = /jl sin r u (1) 



sin 6V= /^ sin l9 ■ . (2) 



sin 2 = jju sin 2 , (3) 



sinr- sin<9 2 = A/Z>/* or =2\/Dfi, ... (4) 



$»in 0i- sin r=\/D/j, or =2\/Dfi, ... (5) 



smi-sm0 2 ' = \/D 1 , etc., (40 



sin e{— sin i == X/A, etc., ■ . (5') 



