112 VISION WITH THE COMPOUND MICROSCOPE 



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

 every instance. In some forms of menisci, for example, they will fall 

 outside the lens altogether. 



With regard to the focus of the lens it follows the same rule ; 

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

 fromP'; similarly in lens 2, f" is measured to the right from ( t ). 

 a nd/'" to the left from Q'. 



Having determined the focal length of each lens, the distance 

 between the right-hand principal point of the first lens P' and tin- 

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

 manifestly is the distance of B from P' + the distance B C between 

 the lenses, Q being at the point C. Therefore, 



When these three data have been obtained that is, the focal 

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

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

 points E and E' of the combination. 



In selecting 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 

 622 inch to the left from Q'. 



<j> also is 1-28 to the left from E, and 0' 1-28 to the right from E'. 



These four points, E E' and r , 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 <j> and (j> f are the same. 



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

 proceed to find the conjugate of x. 



Let x equal the distance of the point x from the focal plane <j>. 

 and y the distance of its conjugate from <f> f . Then by formula (xiii) 



.I-// = f 2 , and as x = 1 inch, y = ] ' l84 = 1-6384. 



This numerically determines the position of the conjugate plane. 

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



and // = = 0, which means that y is coincident with $' '. 



The following is the graphic method of finding the conjugate of 

 V. From V, fig. 87, draw a line parallel to the axis to meet E', and 

 from the point where it meets E' draw a line through N, the point 

 where </>' cuts the axis, to W. 



From V draw another line through M, the point where cuts 

 the axis, to meet E, and from the point where it meets E draw a 

 line parallel to the axis, cutting the other line in W. W will be tin- 

 conjugate of V, which was required. 



