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XXYI. Graphical Methods for Lenses. 

 By R. S. Cole, M.A.* 



THE following graphical methods, which I have not seen 

 published, may be of interest. 

 They depend on the following geometrical construction : — 



Fig. 1. 



Let A B and CD be parallel straight lines terminated by 

 BD; let A D and B C intersect in E, and draw E F parallel 

 to A B or CD to meet B D in F ; then it can be proved 

 that 



EF~AB^CD* 



This furnishes a graphical method of compounding reciprocals. 

 Adopting the convention of signs which reckons lengths 

 positive when measured from the surfaces (or with thick 

 lenses from the nodal points) in a direction opposite to that 

 of the incident light, the usual lens formula is 



111 111 

 = 7, Or _==- + ~. 



V U J V U J 



If u and / are given and v is required, we must draw A B 

 and C D to scale to represent u and / respectively, and then 

 E F represents v ; and, on the other hand, if u and v are 

 given, draw A B and E F to represent them, and from these 

 complete the figure ; C D will then give the focal length. 

 Negative values of u, v, and /can be indicated by drawing 

 the lines corresponding below B D. 



The diagram exhibits the relative sizes of image and object, 



* Communicated by the Author. 



