482 



tillyer: variation of equivalent focus 



axis in the planes A and B respectively, let d equal the separation 

 of these two planes and v the distance from A of the intersection 

 of this ray with the axial ray, then we have 



ad 



v = 



a-\-h 



which is the position of the focus as given by Hartmann. A var- 

 iation of V as A ?; from the limiting paraxial value is the spherical 

 aberration. 



7E 



T" 



Fig. 1 



Abbe has shown that, if we assume no spherical aberration, a 

 lens will be free from coma for points near the axis when the ''sine 

 condition" is fulfilled. If the object is at infinity this reduces to 



sin u 



where E is the equivalent focal length, h is the distance from the 

 axis of the entering ray and u is the angle this ray makes with 

 the axis after refraction. If E varies from the limiting zero value, 

 as A £' when h varies, the lens has a different equivalent focus 

 for each zone. It can be shown in a lens without artificial stops 

 and with spherical aberration, that the corresponding condition 

 for freedom from zonal variation of equivalent focus (coma near 

 the axis) is A £' — A z; = 0. 



