114 VISION WITH THE COMPOUND MICROSCOPE 



the equations for No. 2 and in those for both lenses. Further, / is 

 the same as/",/" 7 as /", and < 7 as (/>. Hence the problem is much 

 shorter than it looks. 



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

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

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

 E' and </>, < 7 , the cardinal points of the combination, 



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

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

 Call this distances. Then the distance of o its conjugate from the 

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

 formula 



f'2 



o x = / 2 , o = -L-, 

 /2 = -897, ' x = 1-65; 



.. 



This 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 of/ 7 . 



Before 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 

 0=00 ; 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 ne.y;a- 

 tive, and o would be also negative, because / 2 is always positive ; 

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

 would be virtual. This means that there will be no real image'. 

 because the rays will be divergent on the/ 7 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/", and, by applying the same formula, find 

 the distance of its conjugate from / 7 ", owing to the exclusive effect 

 of No. 2 lens now replaced. This distance of" may be found thus : 



P 7 /"=P 7 B + B C + Q/"=-21 +'25 + 1-875=2-335 ; 

 p/ f p/ =o/"=2-335 1-49 = -845. 



Calling this distance O, then, by formula y 0=/" 2 , we shall find 



f" 2 3'515 



the distance of y from/ 7 ", which we shall call y. y= ='->.., 



O *o4o 



=4* 16, which is positive ; therefore y lies 4' 16 inches from/' 77 to the 

 right hand, y is therefore the conjugate of x, due to the influence 

 of both lenses 1 and 2. Similarly, the conjugate of any point on the 

 axis may be found through any number of lenses. 



Lens No. 1 : Data. Radius A = '- = / ; radius B = 1 = r' ; 

 foci,// 7 ; thickness = = d ; ^=1 P = principal point mea- 



