4 BELL SYSTEM TECHNICAL JOURNAL 



the instantaneous focal distance.^ Defined in this manner, the focal 

 distance conforms with the optics of light ; it is positive when an 

 electron is moving toward a focal point ; and is negative when the 



Fig. 2 — Focal distance. 



electron is moving away from such a point. From the geometry of 

 the figure, it is seen that 



rz 



d = - 



(1) 



where r and i are the instantaneous components of electron velocity. 

 The focal distance of an electron varies continuously as the electron 

 moves along. The simplest variation occurs in field-free space, where 

 the electron travels in a straight line and the focal point remains 

 stationary; but even then the focal distance varies as the electron 

 moves; for the focal distance is measured from the moving electron 

 to the stationary focal point, as illustrated in Fig. 3. In an electron 



Fig. 3 — Focal distances, field-free space. 



lens, the focal point of an electron also shifts continuously as the 

 electron moves through the lens and the focal distance varies in a 

 complicated manner. 



The values of d at the two sides ^ of an electron lens, for any elec- 

 tron path, are called conjugate focal distances of the lens, and are 

 usually designated as di and d2. The theory of electron-optics is 

 largely concerned with the derivation of an equation relating these 

 conjugate focal distances. 



* The term is here used in a broad sense to include the distance to any intersection 

 point on the z-axis, even though the latter is not the point of convergence of an 

 electron beam. 



' The value of d as an electron enters the non-uniform field of the lens, and the 

 value of d as it leaves the non-uniform field. 



