" The sine of one-half of the angle of aperture multi- 

 plied by the refractive index of the medium between the 

 front of the objective and the cover, is equal to the effec- 

 tive semi-diameter of the emergent pencil at the point of 

 its emergence from the posterior lens, divided by the equi- 

 valent focal length of the objective" This expression 

 Prof. Abbe calls the Numerical Aperture and its great 

 value lies in the fact that it serves to designate the 

 efficiency of an objective as to the quantity of light or 

 number of rays, essential for the formation of a perfect 

 image, that can be utilized by it. It has been proven 

 that the greater the value of the Numerical Aperture, 

 the more perfect is the delineation of fine structure in 

 minute objects and the greater is the degree of fineness 

 of detail that can be seen. Also, if objectives have the 

 same Numerical Aperture, no matter what their focal 

 lengths and the intervening media may be, they will 

 give equally good definition of fine structure. 



When designated on objective mountings or used 

 in tables, the term Numerical Aperture is abbreviated 

 to N. A. The formula for computing Numerical 

 Aperture is written, N.A.=/z sine u r where n is the 

 index of refraction of the medium between front lens 

 and cover glass, and it the half-angle of aperture. 

 Since the media are air, water, or oil, it is necessary to 

 know the refractive index of each, which is i.o for air. 

 1.33 for water, about 1.52 for oil, and for the regular 

 crown glass is, closely, the same as for the oil. 



78 



