APERTURE OF THE EFFECTIVE CONES OF LIGHT. 257 



the magnifying-glass is often provided with a stand enabling it to 

 be adjusted in the desired position relatively to the object; and 

 conversely, the higher powers of the simple Microscope are occasion- 

 ally held in the hand like the magnifying-glass, or attached to an 

 ordinary holder. The customary appellation is founded, therefore, 

 rather on the general form of the whole apparatus, than on its 

 optical construction. 



In theory it is immaterial whether the amplification is high or 

 low, the formation of a sharp image is in all cases combined with 

 the condition, that both kinds of aberration shall be as far as 

 possible eliminated for the given object-distance, which is, of 

 course, always somewhat less than the focal length. The manu- 

 facture of a good magnifying-glass or of a simple Microscope is 

 therefore accompanied by precisely the same difficulties as those 

 of an ordinary objective of about the same focal length. The fact 

 that in the former case virtual images instead of real ones come 

 into account, renders the task neither easier nor more difficult, 

 although it must be taken into consideration. Our discussion of 

 the combination of flint- and crown-glass lenses to form aplanatic 

 systems, may therefore be applied here also, and the testing of the 

 optical power and magnifying power may be effected as with the 

 compound Microscope. It remains for us, therefore, to indicate 

 specially those points which are essential to understand the path 

 of the rays under the given conditions, and which differ from 

 those we have previously considered. 



1. APERTURE OF THE EFFECTIVE CONES OF LIGHT. 



The aperture of the cones of rays incident from the object-points 

 is dependent, in a given system, upon the aperture of the pupil 

 of the observing eye and upon the size of the diaphragms. If a b 

 (Fig. 140) is the object, F the anterior, and F* the posterior focal 

 plane, E E* the pair of principal planes, and P the pupil ; then 

 the diameter of the pupil is for all finite distances of the virtual 

 image a' V evidently somewhat larger than the diameter of the 

 surfaces in which the optically effective cones of light cut the 

 principal planes. With a number of refracting surfaces each 

 incident cone of light consequently meets the first of them (JV) in 



s 



