524 Dr. F. W. Aston mid Mr. R. H. Fowler on 



The emergent ray starts from the point 



( I, I tan ol — ^-y-sec 2 a ) 



at the slope 



, ILel 



tan a ^- sec- a. 



v 2 



Fig. 3. 





> 



f 











' 6 





L 









_----<*!'" 



Z 









1 













X 









V* 









L 







Its equation can therefore be put in the form 



X^ 2 sec 2 a / ILel 



— I tan a. + 



^tan« - 2 -)(x-l), 



or 



Xel sec 2 a , ' 

 y — # tan a= g — ~ (^ _ 27' 



(10) 



which passes through the point (-JZ, $1 tan «)„ z. e. Z, for all 

 values of v. 



To find the conditions for more accurate focussing after 

 passing the magnetic field we may therefore think of the 

 rays incident on the magnetic field as diverging exactly 

 from a point distant V from its leading edge., where V is less 

 than the b of fig. 1 by d, or -JL, the radius of the field. We 

 shall assume, to simplify the discussion, that the leading- 

 edge is plane and at right angles to the median ray, which 

 is deflected through an angle 6 Q in the electric field. 



The path of a typical ray is shown in fig. 4, in which 

 A is the point of entry and B the point of emergence. 

 After reduction the exact equation of the emergent ray, 

 referred to axes Oxy, can be put in the form 



y cos ((f) — a) — x sin (<£ — a) + Br?(l — cos cf>) 



+ U tan a cos (<£ — a)=0, . (11) 

 where B is the constant Jj/(vcf>) and a and v are related by 



