ZOOLOGY AND BOTANY, MICROSOOPr, ETC. 721 



Aperture Puzzle.— A problem which much troubled the older 

 generations in regard to aperture, was this : — 



" Aperture " meaning essentially the " opening " of the objective, 

 or its capacity for transmitting a greater or less amount of light, the 

 following seemed to be paradoxical. 



In fig. 173 a dry objective is used, and the object can receive light 

 from the whole hemisphere of 180^. If, for instance (as the matter 

 was put with the view of bringing it within reach of the meanest 

 capacity !), 180 candles were placed in a semicircle a h, light from 

 every one of the caudles would reach the object. 



Suppose now, that instead of a dry objective, whose aperture cannot 

 exceed 180° or 1*0 N.A., an immersion objective is used with an 

 aperture exceeding 1 • N.A., a hemispherical lens being employed 

 for the illuminator, as in fig. 174. 



It is suggested that in this case we have less light reaching the 

 object, for, continuing the example of the candles, only those between 



Fig. 173. 



a' and h' (or say 100 out of the 180) are efiective, none of those 

 between a and a', or between h and b' illuminating the object, and 

 they might as well not be lighted. 



The objective which has the smaller aperture, therefore, receives, 

 it is suggested, the light of eighty more candles than the objective 

 which has the larger aperture ! 



The explanation of the seeming paradox is simply that the efi'ect of 

 the spherical surface in the second case has been disregarded, as was 

 80 constantly the case in the old aperture discussions. 



The action of the hemisphere in fig. 174 may be illustrated by 

 fig. 175, which shows the course of the rays from a luminous surface 

 P to a definite surface element a b. 



Take the inner lines of the fig. as representing the pencil which, 

 in air and without the interposition of the hemisphere, would reach 

 the surface a b. If the hemisphere is interposed, the pencil, instead 

 of continuing in a straight line as before, is compressed (refracted), 

 and is now thrown on the smaller surface a (3. It is obvious tliat 

 the two surfaces a b (in air) and u ft (in glass) must each receivo 

 the same amouut of light, for the pencils which reach them aro 

 identical in their origin. If now wo take within the hemisphere a 

 surface a b, which is larger than a ft, the former (a b in glass), will 

 bo illuminated, as the fig. sliows, by a pencil wliicli, in its origin, is 

 larger than that illuminating the latter (a ft in glass) ; and as a /? in 

 glass is, as we have soon, idrnitical in illumination with a b in air, 

 a fe in glass will receive a larger pencil than a b in air, the excess 



