274 ADAMS : RAYLEIGH-ZEISS INTERFEROMETER 



-> - f 



D being the geometrical (and also the optical) path difference 

 at 0'. The achromatic fringe will similarly be displaced N^ 

 fringes (again of wave-length X) to a point (say Q), where 



^ X 



Now if the refractive indices of solution, water, and glass are 

 represented by ni, n2 and n respectively and if we put v = ni — n^ 

 (with appropriate subscripts attached to v and n to denote the 

 wave-lengths to which they refer), then 



D = vl-p 



Consequently since v, n, and hence p are all functions of X we 

 may write 



D = /(X) 



We next determine D' in terms of /(X). Now the phase differ- 

 ence ^ at Q is 



= 27r(Z)'-Z))/X; 



Applying the necessary condition, d(t)/dX = 0, we find 



i)' = /(X)-X/'(X) 



where /'(X) -- df{X)/d\. Accordingly 



D' D 

 iVx-A^x=Y- ^ =-/(X) 



To evaluate /'(X) we write for the variation of refractive index 

 with wave length, according to the simple dispersion formula 



B 



n = A + 



also 



and 



