FIRST ORDINARY MEETING. 13 
Again, since parallel rays on incidence go to F",, and thence to F’, 
F’ is the image of F’, in L, Hence the line joining X, and F’; on 
the x axis gives EF’ 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 (a, w,.. .) 
which an object w, at R, produces may be determined as follows :— 
Let (A,4'1), (fy 7’2) --. be the principal focal lengths of Ly, 
D2! 
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), 
In like manner we have 
2 6’, 
Oy Oe Oe 
6; Ff» 
A 040% 
== wp tf == Wy —s ; &e. 
O09; FF 
Hence if w, = w,, Ry, R,, become the principal points of the sys- - 
tem, and 
Bod ng eaernt 
eo aoe.» 
19. The equation for the system of lenses being f +4= 1 
P 
referred to principal points, the corresponding equation, when the 
nodal points are origins, becomes f a Z = 1, in which /’, p are 
measured from N, and f, p’ from N’. | 
20. The lengths of object and image at various pairs of conjugate 
points may now be compared. 
Thus (Fig. 7), if w at P gives w’ at P’, we have 7 
wo + o! PR . PE 
or, BE 
aT 
+ Vide Croullebois, Lentilles épaisses, p. 32. 
