OBJECTIVES AND OCULARS 5 



scope), that can enter the objective arid 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 light-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. =«-sin a. 



If the above formula is accepted as true it is evident that if 

 the value of u is increased the numerical aperture will likewise 

 be increased. 



The light rays illuminating an object by transmission through 



