necessary for Sensibly Perfect Definition. 355 



that the aberration of a plano-convex lens focusing parallel 

 rays of homogeneous light is unimportant, so long as the 

 fourth power of the angular semi-aperture does not exceed 

 the ratio of the wave-length to the focal distance [a 4 < (A//)L 

 a condition satisfied by a lens of 3 feet focus, provided that the 

 aperture be less than 2 inches. I propose at present to apply 

 similar principles to the question of focusing. 



The most convenient point of view is that explained* for 

 calculating the focal length of lenses. If the lens AB con- 

 verges parallel rays to a focus at F, the retardation of the 



central ray E F, due to the substitution of a thickness t of 

 glass for air, is (fi — l)t ; and this must be equal to the retar- 

 dation of the extreme rays passing the (sharp) edge of the 

 lens, i. e. AF-CF. Thus, if AC = y, FC=/, 



^^)t=v(r+f)-f^\j 



(1) 



approximately, which gives the focal length in terms of the 

 semi-aperture and the " thickness " of the lens. 

 If we suppose that fi varies, 



Bfi . t 





V, 



(2) 



giving the change of focus required to compensate the change 

 of fi. Let us, however, inquire what is the state of things 

 at the old focus. The secondary rays from {he extreme boun- 

 dary of the lens arrive with the same phase as before the 

 change of index; but the central ray undergoes a relative 

 retardation amounting to B/jl . t. This quantity tells us the 

 discrepancy of phase; and we know that if it is less than ^\, 

 the agreement of phase is still good enough to give nearly 

 perfect definition. Hence from (2) we see that a displace- 

 ment S/from the true focus will not impair definition, provided 



J y 2 



* Loc. cit. p. 480. 

 2C2 



(3) 



