496 GAUSS’S DIOPTRIC RESEARCHES. 
9. In a single lens 7, s being the radii of the first and second 
surfaces, ¢ its thickness, and » its index of refraction, the in- 
dices of the first and last media will each be unity, 
p—l t l—-E 
2Q= nee ad ant = =e 
whence 
et. | es 
r a [eos 8 
1 1 p—l ¢t 
k= =— | a=) 2 ee Se 
Hed at Eee 
SS i! a 
PE ile u(s—r—t) +? 
rt g—1 st 
ee iat w(s—r—t)t? 
Tt got 1. col, weenie 
aa. \r...',.. ae 
] 
(p—e) (f-9) (ee ee 
sf 8 pe Fay * 
(s— nr) + 
] 
m—n =a—-b — ad 7 ea a Om : 
i rege i [Yee ‘Tu ie 
Pom ilecad MG are 
w—l w—l i 
ee sincea—b=t 
w(s—r)—(e—1)t p’ 
py pe 2 
A cD) ee Ae 
pt peri +t pe’ 
or distance between focal centres = ot 
ri nearly. 
10. To determine the path of a ray after refraction through 
any number of lenses having a common axis. 
x s R 
N M L Q Ue 
Let L be the second focal centre and M, N the first and second 
focal centres respectively of two lenses having a common axis, 
RS the direction of a ray after refraction through the first lens 
in the plane SM L, QT its direction after refraction through — 
