Mr. E. S. Cole on Graphical Methods for Lenses. 21? 



for they are in the ratio v :u or E F : A B ; the image being 

 direct or inverted according as E F and A B are or are not 

 on the same side of B D. 



The construction can also be used for finding the focal 

 length of the lens equivalent to any number of lenses in con- 

 tact, for this is done by adding the reciprocals of the focal 

 lengths. 



An extension can be made to the case of two lenses sepa- 

 rated by a definite interval a, to find the focal length of the 

 equivalent thick lens and the position of its nodal points. 



Fig. 2. 



Let AB and C D be parallel and let them represent fi and 

 f 2 ; produce them to E and F so that 



AE = CF = a. 



Join A D, B F intersecting in H, and BC, ED inter- 

 secting in K. 



Draw H L and K M parallel to meet B D in L and M, 

 and let H L cut B in X and K M cut AD in Y. Then 

 it can be proved that 



a+fi+A 



KY= a (\ „ , XL=YM- 



Hence — H X and K Y represent the distances of the 

 nodal points from the two component lenses, and X L or Y M 



represents the focal length of the equivalent thick lens. 



* 



Devonport. 



Phil. Mag. S. 5. Vol. 41. No. 250. March 1896. Q 



