On the Estimation of Aperture. By Prof. E. Able. 17 



A general criterion of identical and non-identical rays in different 

 media, which applies to every kind of radiation and leads to the 

 same conclusion, is obtained when we refer to the physical notion 

 of a ray. Physical optics defines " rays of light " as the orthogonal 

 trajectories through a system of waves. The principle of this defi- 

 nition implies, at the same time, that " homologous rays " in different 

 wave-systems are to be determined with regard to the rate of pro- 

 pagation in these systems ; and it is found that homologous rays 

 are closer together when the velocity of propagation is less, and 

 vice versa— in perfect analogy to the " lines of force " in a magnetic 

 or electric field when the electric or magnetic charge is increased. 

 The direct outcome from this is, that identical rays emanate 

 under smaller angles of obliquity in a medium of higher refraction, 

 and, in general, one and the same system of rays constitutes cones 

 of different angles in air, water, or balsam, in such a way, that the 

 " numerical " equivalents of these various cones (the product of the 

 SMie of the semi-angle by the refractive index) are always the sums. 



This theoretical inference bears directly on that kind of 

 radiation which is the most important one for the Microscope 

 — the radiation of objects by diffracted Hght. Every structural 

 object, whether the structure is regular or in any way irregular, 

 which transmits or reflects a narrow-angled incident beam of 

 light (or any number of such making together a wide-angled cone) 

 changes this beam (or each one of the several beams) into a wider 

 or narrower pencil, with varying intensity in different directions, by 

 virtue of diffraction. The interference of elementary waves emitted 

 from the transparent or semi-transparent elements of the structure 

 neutralizes the undulatory motion above the object in some direc- 

 tions, whilst in other directions the survival of the motion, or of a 

 fraction of it, develops rays of light of various intensities, which 

 emanate from the object in various directions as if it were self- 

 luminous. In the case of regular periodic structures, as lined 

 objects, diatoms, &c., the diffraction pencil originating from an in- 

 cident beam appears as a fan of isolated rays of decreasing intensity 

 around the direction of the incident beam transmitted through the 

 structure — the interference of the primary waves yielding in this 

 case a number of successive maxima of light with dark interspaces. 

 According to the well-established laws of the diffraction phenomenon, 

 the fan of diffracted beams from one and the same structure is 

 spread out under a wider angle when the wave-length of the 

 medium is increased or the refractive index is diminished, and is 

 more compressed together in the opposite case ; in such a way, 

 that the sine of the angle of obliquity of the same beams — for 

 instance, the first, or second . . . maximum — is changed in the 

 inverse ratio of the index. Owing to this, one and the same 

 solid cone at the object will embrace a larger number of diffraction 



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