ANGULAR APERTURE. [ 45 ] ANGULAR APERTURE. 



the object, and transmitting them to the 

 image. 



In the microscopic object-glass, the an- 

 gular aperture is determined by the ratio 

 between its focal length and the diameter 

 of the emergent pencil at the plane of its 

 emergence from the back lens of the com- 

 bination. 



This ratio is expressed for all media and 

 all cases by n sine u ; n being the refractive 

 index of the medium, and u the semi-angle 

 of aperture. The values of n sine u, for any 

 particular cases, are the numerical apertures 

 of the object-glasses, so that in dry object- 

 glasses n = l; in water-immersion, n T33; 

 and in homogeneous immersion object- 

 glasses, w=r52. 



F. Crisp gives a Table of the relation of 

 the ordinary expression of the angular 

 aperture to the numerical (Jn. Mic. Soc. 

 1881, i. p. 325). Thus : 



180 aperture = 1 num. apert. ; 

 98 = 0-76; 60=0-50 &c. The 

 corresponding immersion-apertures are also 

 given in this Table. 



As an object-glass of large aperture ad- 

 mits a greater number of oblique rays than 

 one of less aperture, the central rays being 

 in nowise interfered with, so the total num- 

 ber of rays admitted is greater, and objects 

 will thereby be more brilliantly illuminated. 

 This is one of the advantages gained by the 

 use of an object-glass of large aperture ; and 

 the explanation applies especially to its use 

 in the examination of opaque objects, in re- 

 gard to which it can be readily understood 

 that a greater number of the rays reflected 

 from all parts of an object being admitted, 

 will render it more luminous and distinct. 

 In this case the same effect would be pro- 

 duced by condensing an additional amount 

 of light upon the object. 



There is, however, another far more im- 

 portant use of large angular aperture in an 

 object-glass. It was first found by Goring 

 that the longitudinal and transverse lines 

 upon the scales of Lepidopterous and other 

 insects could be seen under certain object- 

 glasses, but not under others ; and that the 

 power of displaying these, or the penetrating 

 power of the object-glass, as it was called, 

 depended upon the magnitude of the an- 

 gular aperture. The same has since been 

 found the case with the markings upon the 

 valves of the Diatomacea3, thus : 



1. If the valve of a Pleurosigma angulatum 

 be examined under an object-glass of 1-4 

 or 1-8 of an inch focus, and an angular 



aperture of 60 or 70, as illuminated by 

 the ordinary light of the mirror, nothing 

 more is seen than the more or less coloured 

 valve with a distinct outline, the central 

 line and the nodules; and no change is 

 produced in the appearances, however in- 

 tensely the object may be illuminated. But 

 if an object-glass of larger angular aperture 

 be used, a number of fine dark parallel lines 

 are seen traversing the valve. Hence the 

 object-glass of larger aperture possesses a 

 particular power of rendering indications of 

 structure evident, which is not possessed by 

 the one of less aperture. 



2. If, in the same experiment, the mirror 

 be brought towards one side of the stage, 

 and the light be then thrown upon the ob- 

 ject, the lines will become more distinct if 

 previously visible, and frequently visible 

 when not so before. 



3. Placing a stop in the condensing lenses 

 of the achromatic condenser or object-glass 

 will increase the distinctness with which the 

 markings are seen, if already visible, and will 

 frequently render them visible when not so 

 before. 



These experiments show, that using an 

 object-glass of large aperture in the exami- 

 nation of an object, bringing the mirror to 

 one side, and placing a central stop in the 

 object-glass or the condenser, or in both, 

 produce the same effects, viz. that of render- 

 ing the markings upon an object visible 

 when not so previously, or of rendering 

 them more distinct if previously visible. 

 And it is evident that the alterations of the 

 conditions under which the object is exa- 

 mined in the above experiments, involve 

 simply the viewing of the object when illu- 

 minated entirely or more completely by ob- 

 lique light. For an object-glass of large 

 aperture admits more oblique rays than one 

 of less aperture, the central rays being in 

 nowise interfered with ; inclining the mir- 

 ror to one side, causes all the rays which 

 are reflected from it to become oblique ; 

 and the use of central stops excludes all 

 the central rays, so that only the oblique 

 rays are admitted. Hence the visibility or 

 greater distinctness of the markings upon 

 an object depends upon its illumination by 

 oblique light. 



Experiment also shows that the degree of 

 obliquity of the light requisite varies with 

 the delicacy or fineness of the markings, 

 being greater as these are more delicate ; so 

 that the most delicate markings require the 

 most oblique light which can possibly be 



