114 VISION WITH THE COMPOUND MICROSCOPE 



tin- equations I'm- No. _! :mrl in those for both lenses. Further, / is 

 tin- same .-i-./'"../'"' as /". ami <t>' as (]>. Hence the problem is much 

 shorter tli.-in it looks. 



If the conjugate of a point on the nxis is only required, and if 

 tin- principal points and foci of each lens have been determined, it 

 will not be necessary to enter into the further calculation to find E. 

 K and 0, ijt/, tin- cardinal points of the combination, 



The method of procedure is as follows : If ,' is the given point. 

 its distance from/, tin- focus of lens No. 1, must first be measured. 

 Call this distance.,'. Then the distance of o its conjugate from the 

 other focus./'. supposing lens No. 2 to be removed, can be found by 

 formula 



o x = /-, o = - . 



X 



/'-' = -897, x = 1-6"); 



.'.o=' 897 = -543. 

 1-65 



'I'll is is the distance from,/' to o. 



As the distance from x to/ is positive, the distance between /' 

 and o is also positive ; so o is to the right off. 



lie fore proceeding it will be as well to examine other possible 

 cases which might occur. 



Suppose that x was at the point / then x would equal 0, and 

 o = x ; that is, o would lie at an infinite distance from /'. If, on 

 the other hand, the point x was to the right of / x would be nega- 

 tive, and o would be also negative, because f~ is always positive : 

 ft would then be measured off to the left of /', and the conjugate 

 would be virtual. This means that there will lie 110 real image, 

 because the rays will be divergent on the/' side of the lens, as if 

 they had come from some focus on the / side of the lens. But to 

 return. The point o having been found to be the conjugate of x, 

 due to the sole influence of No. 1 lens, we have next to measure the 

 distance between o and/ 7 ', and. by applying the same formula, find 

 the distance of its conjugate from /'", owing to the exclusive effect 

 of No. 2 lens now replaced. This distance of" may lie found thus; 



P'o=P'/ / +/'o=-947 + -543=1-49; 

 P' /"=!" B+BC+Q/"=-21+-25 + l-875=2-335; 

 I" /" -P'o=o/"=2-335 1-49 = -845. 



Calling this distance ( >, then, by formula // (_) = /" -, we shall find 



f" 2 3' 5 15 



the distance of // from/'"', which we shall call //. '/= = 



(.) "84:0 



-\'\ ti. which is posit ive ; therefore // lies 4" 1 1) inches from /"' to the 

 i ii^li' hand, //^therefore the conjugate of 03, due to the influence 

 ofl'oth lenses 1 and _!. Similarly, the conjugate of a.ny point on the 

 axis mav lie found through any number of len.se>. 



.Vo. 1 : l>dtn. Radius A. = -=; radius l! = 1 = r' : 



\ 



thicknes: , '^ : /'= ' : 1' = principal point mea- 



