Ch. IX] FINDING THE NUMERICAL APERTURE 297 



§ 470. Significance of numerical aperture. — It is now universally 

 agreed that, the corrections in chromatic and spherical aberration 

 being the same, the power to define minute details depends directly 

 on the numerical aperture; the greater the numerical aperture the 

 greater the resolution (see also § 475-476). 



§ 471. Why a homogeneous immersion condenser is required. — ■ 

 If the definition of minute details requires adequate numerical aper- 

 ture it is evident that it is of fundamental importance that the sub- 

 stage condenser be able to supply the light at the adequate aperture. 

 Assuming that the substage condenser is properly constructed, the 

 question is, can it illuminate the object with the proper numerical 

 aperture? 



By referring to § 468, and to figures 158-160, it is evident that an 

 object mounted on a glass slide and separated from the condenser by a 

 stratum of air can get light from the condenser only up to the critical 

 angle, that is 41°, on each side of the normal, or a total of 82 , cor- 

 responding to a numerical aperture of 1. The objective may be cap- 

 able, however, of receiving and utilizing a numerical aperture of 1.40. 



If now the condenser also has a numerical aperture of 1.40 and it is 

 connected to the slide by means of homogeneous immersion liquid the 

 entire aperture will illuminate the object and can enter the homo- 

 geneous immersion objective. 



If the substage condenser is connected with the slide by means of 

 water, then, as shown in fig. 160, the object can be illuminated with 

 an angle of 6i° + 6i° or 122 , or a numerical aperture of n sin u; in 

 this case 1.33 X 0.875 = I - I ^37- If the greatest possible aperture is 

 required, as in dark-ground illumination (§ 125), and for some of the 

 most exacting work with photo-micrography and microscopic study, 

 the condenser should be connected with the slide by homogeneous 

 immersion liquid. 



§ 472. Determination of the aperture of objectives with an aper- 

 tometer. — Excellent directions for using the Abbe Apertometer may 

 be found in the Jour. Roy. Micr. Soc, 1878, p. 19, and 1880, p. 

 20; in Dippel, Czapski and Spitta, Chapter XIV. The following 

 directions are but slightly modified from Carpenter-Dallinger, pp. 

 394-396. The Abbe apertometer involves the same principle as that 



