30 BELL SYSTEM TECHNICAL JOURNAL 



$ — potential at point in space, the electron source taken as zero 

 potential 



V — potential on the axis 



v' — derivative of v with respect to s 



V — is also used for the voltage of electrodes 

 d — focal distance in general 



T — focal time in general 



A - — the important coefficient for rays near the axis, a function of 



2 alone 

 u, w - — velocity functions corresponding to f and z 

 d\, di — conjugate focal distances measured from the two sides of a lens 

 fitfi — principal focal distances measured from the two sides of a lens 



As an approximation in thin lenses, the focal distances are measured 

 either from the mid-point of the lens, or from the point where \v"\ 

 is a maximum, provided that there is but one maximum in the lens. 



ai, (X2 — location of the principal planes with respect to the sides of 



a lens 

 Di, D2 — conjugate focal distances measured from the principal planes 

 7^1, F2 — principal focal distances measured from the principal planes 

 F — the focal term of a lens, not a focal distance 



Equations for Rays Near the Axis 



z = -yflv, 



^ - _ ^ r/r, 



^TvA' +A^ = ~ V 



TUt^ ^ ^ 2 



The important equations for a thin lens are : 



V2z'i xlvi _ 1 

 di di ~ F' 



h _ /2i'2 



jr "V2^' 

 --+-=1, 



di d\ 



\ _ r'i v" 



dz. 



