ELECTRON LENSES 



333 



surface, owing to the change in the index of refraction, so a beam of 

 electrons can be deviated from its path where it encounters a change in 

 the intensity of an electric field. 



In optics we know from SnelPs law that ni sin i\ = n 2 sin i 2 (Fig. 

 VIII-12a), where n\ and n 2 are the indices of refraction of the two media. 

 But Snell's law may also be written 



n 2 



sin i 2 

 sin t'i 



v 2 



(a) 

 Fig. VIII-12. 



where v\ and v 2 are the velocities of 

 light in air and glass respectively. 



What happens to an electron mov- 

 ing with velocity vi (Fig. VIII-126) 

 as it passes through a region in which 

 the potential alters suddenly from 

 Vi to V 2 1 If the electron arrives at the boundary, making an angle i\ 

 with the normal, it will be deviated and pass into the second medium 

 along the path v 2 making angle i 2 with the normal. The horizontal 

 components v Xx and v 2x of v x do not change in magnitude in passing into 

 the lower medium, so that 



Vi sin i\ = v 2 sin i 2 



If an electric field is used to accelerate the electron, its kinetic energy 

 is determined by 



or 



where a change in the potential at the boundary of the two adjoining 

 media is from V\ in the upper to V 2 in the lower medium. 



The " electric refractive index " is therefore analogous to the optical 

 refractive index in that the \/V replaces n. 



There is an important difference between the two deviation phe- 

 nomena, however. In the optical transition from air to glass the index 

 of refraction changes suddenly, and no further deviation takes place in 

 the second medium, whereas in the electron transition the refractive 

 index changes continuously along the path of the electron and as long 

 as it remains in the second medium. A uniform electric field set parallel 

 to the direction of the motion of the electron and a field-free space are 

 the only types of regions which produce no deviation in the path of the 

 electron. 



