10 



The Microscope 

 D 2.54 N.A. 



The figure for N.A. that is engraved on the barrel of an objective is 

 therefore an indication of the maximum resolution of which the lens is 

 capable. It is not, and this cannot be reiterated too often, a measure of 

 the resolution that the lens will automatically produce. It is only a 

 measure of what the objective can be made to yield in the hands of a 

 skilled microscopist provided with all the necessary auxiliary equipment. 



i = t 56 



Figs. 9, 10, and 11. Diagrams to show relation between angular aperture and reso- 

 lution. Fig. 9 shows the concave mirror of a freshman-type microscope (Fig. 18) 

 casting a narrow cone of light into the objective. This cone has a total angle of 64° 

 so that the numerical aperture is 0.6. Fig. 10 shows a substage condenser used to 

 increase the angular cone to 96°. Since the system is working in air (i = 1) the nu- 

 merical aperture is 0.8. Fig. 11 shows both the substage condenser and the objective 

 oiled to the slide. The angle of the cone is 116° and i, for the oil, = 1.56. The N.A. is 

 thus 1.3. The relation between N.A. and resolution is explained in the text. 



Figures 9 to 11 will make this clear. Figure 9 shows the setup with an 

 ordinary elementary class microscope. The objective is focused from 

 above through a coverslip on an object on a slide. Some distance under 

 the slide is a concave mirror reflecting a cone of light into the objective. 

 The maximum angle of this cone is dependent on the size and distance of 

 the mirror and on nothing else. In the example shown, drawn to scale for 

 a standard microscope, this angle is 64°. Since the lens is working in air 

 (i = 1), it follows that the maximum numerical aperture of the system is 



N.A. = i sin 6 = 1 X sin 32° = 0.6 



It does not matter in the slightest what N.A. figure is engraved on the 

 barrel of the lens. The maximum possible N.A. of the system is 0.6, and 



