120 The Electron Microscope 



in bacteriology has amply repaid the efforts spent in developing 

 the ultraviolet miscroscope. It appears that the present hmit of 

 about 10 A conceals as important details of viruses as 2,000 A 

 did in bacteria. Moreover, the short depth of focus resulting 

 from increased aperture and improved resolution promises to 

 reveal far more detail than could be expected from a comparison 

 of the resolution limits. It will be, therefore, of interest to obtain 

 an estimate of these quantities. 



Figure 43 is a diagram of the fields in the lens combination 

 according to figure 41, together with an electron trajectory. 

 For simplicity let us consider the space charge density po at the 

 axis as constant along a length L. As the potential along the 

 axis, ^0, can be also considered as constant, the paraxial equation 

 (41) simplifies to 



^" = -^hE^ + -P« '• = f^ (46) 



Le is a real length if, as we have assumed, the space charge term 

 outweighs the magnetic term and the second lens acts as a di- 

 verging lens. The solution for the trajectory which leaves the 

 system parallel to the axis becomes 



(47) 



If Le is appreciably shorter than L, the space charge lens will 

 reduce the distance of the trajectory from the axis approximately 

 in the ratio 



2 exp 



(-fc) 



We can therefore reduce r ^m any desired ratio by making the 

 space charge lens longer. Lengthening it by Le means a reduc- 

 tion in the ratio - = 0.368. The focal length is reduced in the 



e 



same ratio. In practical units we can write equation (46) 



