Curvature Method of Teaching Optics. 47i> 



and dipolar quantities has its origin in the distinction between 

 simple and double frequency vectors. 



Combinations of Tiro Thin Lenses. — These may be men- 

 tioned here before considering thick lenses, as they do not 

 imply a knowledge of refraction at a single surface. Con- 

 sidering two thin lenses of convergences F and F 2 separated by 

 an interval rf l3 parallel light falling on the first emerges from 



it with a convergence F n which becomes -^-tt^ ? or = — JL - 



l/F -d l-F d Y 



on reaching the second. To this is added the convergence 



of the second lens, giving us the emergent convergence as 



_F __ , F _ F +F 2 -F F 2 ^ 



l-F (/i 2 l-F di ' 



This maybe termed the "back - " or "emergent" convergence 

 if desired, corresponding to the " back focus," and the other 



•n -i .1 1 F + F.,-F F 2 ^ 

 emergent convergence will evidentlv be — - — „ ~ -.^ 



6 ' 1 — F 2 ^ 



Equivalent Convergence. — Introducing the equivalent lens 



as that giving the same size of image as the combination, 



, tan a -^ tan a . 



we nave x — -^ or r = — , where « is the angular mag- 



_T X 



nitude of the object and x the magnitude of the image. For 

 the first lens we have x Q = „ , and the magnification by 

 the second lens is 



\. l-F^Fo+F^F.bVi F () + F 2 -F F 2( /," 



Hence 



tan a. F _ tan a, 



m F +F 2 -F F 3 rf 3 " F + F 2 -F,F^' 





and F = — * = F n + F 2 - FoF-rf,. 



,/• 



Nodal <>r Principal Points, — The Nodal ]>oints being 

 defined as those points through which light passes undeviated, 

 we have, since the deviation at any zone of a lens = FA, 



F,A, + FA' = 0. 



or Y u d Q +Y 2 d, + (see fig. 6), 



but d — <!., = d the distance between the lenses. 



