96 



MICROSCOPY 



n being tlie refractive index of the least refractive material between the 

 object and the objective lens. The greater the value of N. A., the better 

 the resolution. An objective lens with a working distance of 16 mm, 

 labeled 10 X by the manufacturer, has a numerical aperture of about 

 0.25. With other objectives the N. A. values range upward to a practical 

 limit of about 1.4. 



Ernst Abbe, probably the greatest of the German opticians, proposed 

 the value N. A. and developed the theory of resolving power of micro- 

 scopes. Perhaps at low magnification the image seen in the microscope 

 depends upon transmission and absorption of light by the object. The 

 examination and interpretation of very small units, however, probably 

 depends upon diffraction phenomena. Each small object is accompanied 

 by a series of interference bands which are responsible for the contrast 

 observed. If the interference bands of two objects overlap, the two objects 

 appear as one and cannot be resolved. Abbe reasoned that the limits 

 of resolution could be found by examining a diffraction grating. If the 

 lines of the grating are to be seen, the objective lens must include the 

 direct or axial ray plus at least the first diffracted ray (Fig. 8-9). The 

 angle (a) depends upon the wavelength (A.), upon the distance (ci) 

 between lines on the grating, and upon the refractive index of the me- 

 dium, or M sin a = \/d. However, n sin « = N. A. so that d = X/N. A. 

 This is the smallest value of d resolvable by an objective. If oblique 

 illumination is used, as from an Abbe condenser, this limit is reduced 

 to about half, ox d ■= A/2 N. A. This limit is unattainable for several 

 geometric reasons; the theoretical limit of resolution is usually given as 1.2 

 V2 N. A. If an object is illuminated with blue light (A. = 400 m/x) and 

 examined with a lens system (N. A. = 1.40), the limit of resolution is 



, 1.2X400 ^_ 

 ^= 2X1.40 =™^t' 



or about half the wavelength of the light used. 



Object^ 



;? X -^V ^ \n\ ^ 



Objective 



s=3 Cover glass 



V55 V 



? Slide 



Fig. 8-10. Oil immersion microscopy. 



