112 VJsloN WITH THE COMPOUND MICROSCOPE 



their respective lenses, but it dues not follow that they will do so in 

 every in-tame. In some forms of menisci, for example, they will fall 

 outside 111" lens ;d together. 



\\"itli regard to the focus of the lens it follows the same rule ; 

 thus, /'in lens 1 is measured to the left from P, and/ 7 to the right 

 from P'; similarly in lens 2, /" is measured to the right from Q, 

 and/"' t. the left from Q'. 



Having determined the focal length of each lens, the distance 

 bet ween the right-hand principal point of the first lens P' and the 

 left-hand principal point of the second lensQ must next be found. It 

 manifestly i> the distance of 15 from P' + the distance B C between 

 the It-uses. () being at the point 0. Therefore, 



P' Q=-21 + -25 = -46 = c. 



\\"hen these thr lata have been obtained that is, the focal 



length of each lens, and the distance between them we are in ;i 

 position to apply the formulae (ix) and (x), p. 116, to find the principal 

 I mi) its K and E' of the combination. 



In .-.electing the value of the focus to be put into the equations 

 for both lenses, the last must be taken, that is, in lens 1 (iv) or 

 + 947, and in lens 2 (viii), or -1 '875. 



It will be noticed that the value of E being negative, it will be 

 measured '314 inch to the left from P. Similarly, E' is measured 

 <i22 inch to the left from Q'. 



<!> also is 1-28 to the left from E, and <p f 1 -28 to the right from E'. 



These four points, E E' and (j> <j>', are called the cardinal points 

 of the combination. 



Here it must be observed that in this work it has been necessary 

 for want of space to restrict the problem to dry lenses, that is, to 

 those cases where the ray emerges from the combination into air, the 

 same medium in which it was travelling on immergence. It is on 

 that account that the values of and $' are the same. 



Having now obtained the four cardinal points, we may at once 

 proceed to find the conjugate of .-. 



LetoM'ijual the distance of the point a: from the focal plane <f>, 

 and // the distance of its conjugate from tj/. Then by formula (xiii) 



= </; 2 , and as .- = I inch. .// = = ] -<i384. 



This numerically determines the position of the conjugate plane. 



If the rays incident on the combination are parallel, then x= oc. 



= (. which means that // is coincident with <//. 



following is the graphic t hod of finding t he conjugate of 



. lig. 87, draw .-. line parallel to the axis to meet E', and 



point vhereit -ts K/dra\\ a I ine t hron-'h X. the point 



\\ hen- / cuts 1 In- axis, to \Y. 



another line tlmm-h .M.the point where cuts 

 .ami from the point where il meets K draw a 



fche axis, cutting the other line in \V. \Y will be the 

 . \\ Inch was re'piired. 



