CH. /.] MICROSCOPE AND ACCESSORIES. 17 



According to some other authors the angle of aperture is the angle 

 between the extreme rays from the focal point which can be transmit- 

 ted through the entire objective. This would give a somewhat greater 

 angle than by the first method as the focal point of the objective is 

 nearer to it than the axial point of the object (Figs. 10, 11). 



In general, the angle increases with the size of the lenses forming the 

 objective and the shortness of the equivalent focal distance (§ 13). If 

 nil objectives were dry or all water or all homogeneous immersion a com- 

 parison of the angular aperture would give one a good idea of the rela- 



Fig. 26. Diagram illustrating the angular aperture of a 

 microscopic objective. Only the front lens of the objective is 

 shown. 



Axis, the principal optic axis of the objective. 



B A, B C the most divergent rays that can enter the objective, 

 they -mark the angular aperture. A B D or C B D half the 

 angular aperture. This is designated by u in making Nu- 

 merical Aperture computations. See the table, \ 30. 



tive number of image forming rays transmitted by different objectives ; 

 but as some are dry, others water and still others homogeneous immer- 

 sion, one can see at a glance that, other things being equal, the dry ob- 

 jective (Fig. 27) receives less light than the water immersion, and the 

 water immersion (Fig. 28) less than the homogeneous immersion (Fig. 

 29). In order to render comparison accurate between different kinds of 

 objectives, Professor Abbe takes into consideration the rays actually 

 passing from the back combination of the objective to form the real im- 

 age ; he thus takes into account the medium in front of the objective as 

 well as the angular aperture. The term " Numerical Aperture," (JV. 

 A.) was introduced by Abbe to indicate the capacity of an optical in- 

 strument " for receiving ra}-s from the object and transmitting them to 

 the image, and the aperture of a microscopic objective is therefore de- 

 termined by the ratio between its focal length and the diameter of the 

 emergent pencil at the point of its emergence, that is the utilized diam- 

 eter of a single-lens objective or of the back lens of a compound objec- 

 tive." 



§ 29. Numerical Aperture (abbreviated N. A.) is then the ratio 

 of the diameter of the emergent pencil to the focal length of the lens, 

 or as usually expressed, the factors being more readily obtainable, it is 

 the index of refraction of the medium in front of the objective (z. e., air 

 for dry, and water or homogeneous fluid for immersion objectives) mul- 

 tiplied by the sine of half the angle of aperture. The usual formula 

 2 



