480 Lord Rayleigh's Investigations in Optics. 



In the secondary focal plane there is no diminution of effec- 

 tive aperture due to obliquity. Instead of (4) we have 



£r=2tcoscf>, (6) 



or 



/•_ y 1 . (7) 



j2 Atcos<j> 



In this case the favourable effect of obliquity shows itself 

 directly in the increased value of/ 2 . 



We will now consider the effect of errors in a refracting 



Fig. 10. 



surface. The error of retardation due to an elevation BD is 

 /*QS-QQ' = QQ'{/*cos(0-0')--l} 



_ jw, cos (/> cos <j>' + /jl sin (f> sin tf> f — 1 



"~ COS0 



-r,.^ tjb cos (b go s rf/— (1 — sin 2 6) - riT . / ', 



= BD ck^ =BD0*COBf-COS^), 



since 



//,sin c// = sin$. 



As a function of obliquity ytt cos <£/ — cos <£ is least (yu.— 1) 

 when the obliquity is zero; it is greatest ^/(/x 2 — 1) when the 

 obliquity is 90°. Thus the retardation for a given error of 

 elevation increases somewhat with the obliquity, being in the 

 case of glass about twice as great at a grazing as at a perpen- 

 dicular incidence. 



Before concluding this section, it may be worth while to 

 point out how the principles of the wave theory may be ap- 

 plied directly to calculate the focal length of lenses. The 

 relative retardations of the rays DAF and ECF (fig. 11) 

 are evidently A F — C F and (/jl — l)t, if t denote the thickness 

 of the lens at the centre. Thus, if A C=y, F C=/, 



o«-i)«= >/(r+f)-f=i y j .... (8) 



