334 COMPOUND AND ELECTRON MICROSCOPES 



A thin electron lens may be defined as a region of non-uniform field 

 extending over so short a distance along its axis that an electron can 

 travel through it in an interval of time small compared to the focal 

 times. The focal time is the time elapsing while the electron travels 

 over a path length equal to the focal distance. Thus the optical con- 

 jugate focal distances may in a corresponding manner be called the 

 conjugate focal times of an electron lens. 



The velocity of the electron, at any point on the axis of an electrostatic 

 electron lens, is obtained from its kinetic energy \mv 2 = e V. This veloc- 

 ity is 



\2eV 



m 



so that an electron in traveling a distance d along the axis of the lens 

 arrives at a focal point in time t given by 





2eV 



d = */ t 



m 



The equation of a thin glass lens of index of refraction n immersed in 

 air is 



1 1 



\Ri RJ F 



di d \Ri R2J F 



where di and d are, respectively image and object distances, measured 

 from the optical center of this lens. If this lens is bounded on the object 

 side by a medium of index n , and on the image side by a medium of 

 index of refraction n-i, the lens equation reduces to 



ni n^ _ 1 

 di d F 



In the electrostatic electron lens, by analogy, y/V is used instead of 

 the optical index, 



VV i _^/jo = 1 



d t d F 



which describes the focal length of a thin electrostatic electron lens in 

 terms of the image distance d i; object distance d , and bounding electric 

 fields which accelerate the electron to the lens under a difference of 

 potential V and away from the lens under a difference of potential 



Vi. 



An apertured plate set at right angles to the lines of an electric field 

 practically fulfills the definition of a thin electrostatic electron lens. 



