12 



BELL SYSTEM TECHNICAL JOURNAL 



In this type of lens, the non-uniform field at the aperture covers a 

 distance along the axis about equal to its diameter. ^^ If the diameter 

 is small compared to vjv', there is little change in potential throughout 



Fig. 6 — An apertured plate. 



the lens and the •V2y may be considered as a constant in the integration 

 32) for the inverse focal term. With this approximation, 



F 



4Tv J 



(39) 



when V is the potential of the plate and Vi and Vz' are the electric 

 intensities of the two uniform fields. The lens equation 35 is then 



■\2v -xlv 

 di di 2 



l\ V2' - Vl' 



21 42i 



which may be written in the simpler form 



V2' — Vl 



dz 



d, 



4v 



(40) 



(41) 



In this type of lens, the electrical refractive index -slv is the same on 

 both sides of the lens and the two principal focal distances are equal, 

 just as they are for a thin optical lens when it is bounded by air on 

 both sides. ^^ 



13 "Two Problems in Potential Theory," T. C. Fry, Bell Telephone System Mono- 

 graph B-671. 



i"* A complete electron-optical system usually involves a combination of lenses. 

 The calculations for a combination are illustrated by the example in Appendix 1. 



