314 



COMPOUND AND ELECTRON MICROSCOPES 



Numerical aperture is the sine of half the angle of the cone of light 

 entering an objective, multiplied by the refractive index (ri) of the 

 medium between the object and the front lens of the objective, which 

 may be air, water, glycerine, or an oil. Thus 



N.A. = n sin a 



where a is the half angle of the cone of light entering the objective as 



seen in Fig. VIII-2. 



Thus, if air is the medium between the 

 object and the lens, the widest possible 

 angle of light that can enter a 16-mm ob- 

 jective of 0.25 N.A. is, as illustrated in 

 Fig. VIII-2, equal to 29°. 



N.A. = n sin a 



Lens 



Oil 



-^m 



N.A. 1.25 



Oil 



\ Pj-Q Object / 



Oil-immersion objective 



N.A. 0.25 



0.25 = 1.000 X sin a 

 a = 14° 30' 



Concave mirror" 

 N.A. 0.25 



16-mm objective 



Fig. VIII-2. N.A. = n sin o. 



If the medium between the object and 

 the lens is some liquid like water, cedar 

 oil, or Canada balsam, the focal length of 

 the lens is shortened. This type of objec- 

 tive is called an immersion objective. Thus, 

 for instance, a cedar-oil-immersion objec- 

 tive of N.A. 1.25 is used where object and 

 lens are immersed in cedar oil of index of 

 refraction 1.52. The widest possible cone 

 of light entering this lens is about 110°, since 



1.25 = 1.52 sin a 



a = 55° 20' 



A solid angle subtending 110° in air works out to a numerical aperture 

 of 0.82. Thus the insertion of oil increases its numerical aperture 

 from 0.82 to 1.25, which we shall see increases the resolving power of 

 the lens. 



Limit of Resolution 



By resolution we mean the measure of the smallest distance of ap- 

 proach of two luminous points so that they may be identified as two 

 entities. The geometric shadow cast by a very narrow slit, having sharp 

 parallel edges, when illuminated by a parallel beam of monochromatic 



