FIRST ORDINARY MEETING. 13 



Again, since parallel rays on incidence go to ¥\, and thence to F', 

 F' is the image of ¥\ in Lg. Hence the line joining Xj and F'l on 

 the X axis gives F' on the y axis. 



In the construction, of course, any pairs of conjugate points may 

 be employed instead of the principal points. 



18. In the system of § 16 the lengths of the images (w^, u>^ . . .) 

 which an object w^ at Rq prodixces may be determined as follows : — 



l^et {fi,f\), {A,f'^ ... be the principal focal lengths of Lj, 

 Lj, . . . 



Then, since (§ 20) in a thick lens the ratio of the lengths of object 

 and image is that of their respective distances from the nodal points, 

 we have (Fig. 10), 



io^ _ N'lRi _ FiX _/i _ ^1 



m, ~ n; Ro ~ f;ro ~ ^, ~/V 



In like manner we have 



Hence if w^ = w„, Rq, R„ become the principal points of the sys- 

 tem, and 



^0^1 • • • =/l/2 • • • 

 ^'l^'2 • • • —f'l/'i • ■ ■ 



19. The equation for the system of lenses being - -\ , =^1? 



referred to principal points, the corresponding equation, when the 



nodal points are origins, becomes 1 ; = 1, in which f, p are 



p 2^ 

 measured from N, and f, p' from W. 



20. The lengths of object and image at various pairs of conjugate 

 points may now be compared. 



Thus (Fig. 7), if oi at P gives w' at P', we have f 

 <y + w' _ PR _ PF 

 ~a/ RF^RF"^ ■ 



t Vide Croullebois, Lentilles epaisses, p. 32. 



