OBJECTIVES AND OCULARS 
5 
scope), that can enter the objective and take part in the for¬ 
mation of an image ” (Carpenter-Gage). 
This angle is obviously that of the cone of light rays whose 
apex lies in the optic axis of the microscope at the point where 
the axis passes through the plane of the object and the diameter 
of whose base is equivalent to the opening of the front lens com¬ 
bination of the objective. 
Dry objectives may be compared with each other with refer¬ 
ence to their angular aperture. In general the angular aperture 
depends largely upon the diameter of the front combination of 
the objective, and usually in objectives of like magnifying power, 
the greater this diameter the larger will be the angular aperture 
and the wider and clearer will be the area or field covered. It is 
also generally true that the shorter the equivalent focus of the 
objective, the larger its angular aperture and that dry objectives 
of small working distance usually have large angular apertures. 
It is obvious that in dry objectives an easy comparison of the 
relative areas of field covered is afforded by a consideration of 
angular apertures. The true field of view of a compound micro¬ 
scope is, however, controlled by the ocular, as will be seen below. 
It would appear at first sight that the light-grasping power 
of an objective is indicated by its angular aperture. Such is not 
the case, for Abbe has proved that in comparing objectives as 
to their fight-grasping and transmitting power it is the sine of 
half the angle of aperture which should be taken into account and 
not the angular aperture; and further, that since objectives are 
not all dry, the index of refraction of the medium between the 
objective and the object must necessarily be considered. It is 
therefore now conceded that the light-grasping and transmitting 
power of an objective is equal to the refractive index of the 
medium in which the objective dips multiplied by the sine of 
half the angle of aperture. The product is what is known as 
the Numerical Aperture and is expressed N.A. = w-sin a. 
If the above formula is accepted as true it is evident that if 
the value of n is increased the numerical aperture will likewise 
be increased. 
The fight rays illuminating an object by transmission through 
