18 THEORY OF THE MICROSCOPE. 



opposite case the system is called divergent, because it acts as a 

 divergent lens and produces only virtual images of real objects. 



The distances of the object from the first, and of the image from 

 the second, principal plane may be called their conjugate focal 

 kngtlis in accordance with the terminology used in the case of 

 single refractions. Their values may be easily calculated from 

 what has been given above. The transposition of the equations 

 (14) and (15), in which f = E and (* = E*, gives 



. E 



k 



If these values are substituted in (13), where f, 77 and f*, 77* 

 represent the co-ordinates of the conjugate foci P and P *, they 

 become 



* = &. * ( E - f) 



=> ~,0 i 7, / V 



n + k(E - f ) 

 From the former of these equations we get 



or, if we denote (E %) by p, (f * j*) by JL>*, and the focal 

 lengths by /and/*, and if we also add the values of k from 

 (18), 



n * 



The analogy to the case of refraction at one surface is consequently 

 apparent. 



The magnifying power m, which expresses the ratio of the 

 ordinates rj* and rj, now assumes, in conformity with the expres- 

 sions in (19) and (20), the following additional forms: 



yi 1_ 1 / * + kp* 



1 + ~^ l ~ / ' 



