Chap. XXIX.] OP TIC A L CONS TA NTS. 379 



called the anterior focal length, and the distance F'P' 

 the posterior focal length. 



The nodal points are N and N', and are such that 

 an incident ray, which passes through N, the first nodal 

 point, will correspond to an emergent ray, which will 

 pass through N', the second nodal point, and both rays 

 will be parallel to one another. In a simple lens the 

 only point through which a ray may pass and issue 

 parallel to its original direction is the optical centre, 

 and straight lines other than the principal axis, pass- 

 ing through the optical centre of a lens, are secondary 

 axes. In a system of media, then, lines which pass 

 through both nodal points may be counted as secondary 

 axes. N and N' thus represent the optical centres for 

 the surfaces to which p and p' belong. 



The optical constants being known, the path of 

 rays through the different media may be traced, and 

 the image of an object constructed. 



Thus in the figure let AB represent an object from 

 which rays pass through the system of media. From 

 A draw a line parallel to the axis. It cuts the first 

 principal plane in c, and the second principal plane 

 in c', equally distant from the axis. From c' it passes 

 through the point F', since incident rays parallel to the 

 axis emerge so as to converge to the posterior focal 

 point. ISText draw a line to the first nodal point, it 

 must pass through the second nodal point N', and 

 emerge parallel to its incident direction, that is, in the 

 line N'A'. It cuts the line through F' in A'. Draw a 

 third line from A, and let it pass through the anterior 

 focal point F. After cutting w in H and vV in the 

 corresponding point K f , it issues from the media 

 parallel to the axis, and thus cuts the other two 

 lines in A'. All these lines meet in A', and therefore 

 A' is the image of A. By the same construction the 

 image of B would be found in B'. Thus A'B' is the 

 image of AB. 



