481 Dr. C. V. Drysdale on the 



Combining these equations we have immediately 



Fo + U'^ Fo-fFo + FoF^Y + fF^ + l)!^- 



V,'=F,+ 



(Fo + U^O^ + 1 Fo^' + l + VU'-x 



A + BU'-t 

 O+'DUCi' 

 AB 

 where =— 1. 



CI) 



To find the size of the image produced we have 



!-- _L I 



m m m 2 ' 



where m and m 2 are the successive magnifications at the 

 surfaces. 



But 1_ _V^ 1 _ V,' _ A + BU'-i Vx V + 1 



wio^U 7 -! m 2 ~tJ 1 '~0 + DU / _ 1 V,' 



and C + DU'_ 1 = V 1 ^' + 1 by the above. 

 Hence 1 _A + BU / _ 1 , 1 _ A + BU / _ 1 



This re-establishes the three Gauss relations in the con- 

 vergence form. It should be noted that the quantity A is the 

 reduced equivalent convergence of the lens. 



It will not be necessar}^ to show how the properties of 

 thick lenses may be deduced from these equations as methods 

 similar to those of Gauss can be followed. We may there- 

 fore pass on to the consideration of a complete system, but 

 before doing so reference may be made to the deviation or 

 Yon Seidel method. 



If we take our equation for a single surface 

 H^i~ At_iU_i = F 

 and multiply it by 7i , the lateral distance of intersection of a 

 pencil, we have 



jjli tan a l — fju_i tan cr 2 = F A . 



If we now denote the product of the tangent of an angle 

 by the refractive index of the medium, by the term " reduced 

 angle " and represent these reduced angles by accented 

 letters, we have 



<j{ — cr / _ 1 = F // . 



In the interspace between two refracting surfaces we have 

 clearly 



n 2 — ■ ^o = ~~ ^i tan <r*/ = — fix tan o- ', 



or P\ 



h 2 — Ao^c/i/. 



