On the Estimation of Aperture. By Prof. E. Ahhe. 401 



"was formerly utilized by the image-forming rays.t It must also 

 be a true reduction of aperture when, in any way whatever, the 

 emergent pencil is changed as «/ such a brass stop had been inserted, 

 provided the power of the system is unaltered. Consequently we 

 have loss of aperture when an air-angle of 180^ is substituted for 

 a balsam-angle of, say 100°. 



An imm>6rsion objective of balsam-angle exceeding twice the 

 critical angle has therefore a greater aperture than any dry lens 

 can ever have. 



V. — Different Angular Distribution of the Bays in different 



Media. 



The definition of aperture as relative opening, developed in the 

 foregoing discussion, is, it is seen, the only one which is justified 

 by the original sense of the term, and it is a point of special 

 importance that it should be understood that the definition is not 

 a matter of mere terminology, but that the very essence of the idea 

 of aperture is involved in the notion of opening, and that there is 

 no other reasonable base for grasping this essence. In whatever 

 way the idea of aperture may be defined, the actual significance 

 of that element in the Microscope can only be appreciated by taking 

 into account the image-forming pencil emergent from the objective, 

 and the change in its diameter consequent upon the admission of 

 difi'erent cones of light. This diameter afibrds a visible indication 

 of the number of rays (not mere quantity of light photometrically) 

 which are collected to a certain area of the image, and which con- 

 sequently must have been gathered-in by the lens from the conjugate 

 area of the object. If, in any case whatever, the diameter of the 

 emergent pencil is seen to be increased, whilst the amplification of 

 the image and the distance of its projection (or, more generally 

 speaking, the focal length) are unchanged, it is clear that the 

 system must have admitted more rays from every element of the 

 object, because it has collected more to every element of an equally 

 enlarged image. It would be an obvious physical absurdity to 

 declare that in any case a lens could emit more than it has taken 

 in. Consequently we get a true measure of what is admitted by a 

 system by estimating what it emits. 



Thus the essential idea of aperture (which means the greater or 

 less capacity of objectives for gathering-in rays from the objects) 

 necessarily leads to the estimation of apertures by the openings of 

 the systems. 



As long as we have the radiant in one and the same medium, 



t If it should be objected that ia wide- angled immersion glasses the marginal 

 zone does not transmit image-forming rays, every one may satisfy himself at once 

 by a simple practical trial that in a well-corrected objective all emergent rays 

 up to the edge of the clear opeijing are image-forming rays. 



