29 : 2/ Microscopy 



541 



As is seen in Figure 3, the limiting case of just the first-order diffraction 

 line and the central line occurs when b becomes so small that the angle 

 6 1 of the first-order diffraction line is given by 



tan 0j = 



2a_ 

 ~P 



(3) 



Grating 



Focal Plane 



+- ► Objective Lens 



Incident 

 Light 



Figure 3. Limiting case of only one order of diffraction other 

 than the central spot. 



where a is the lens radius. For most microscope objectives, — /> is just 

 slightly greater than/, and 6 1 is a small angle. Accordingly, the fore- 

 going condition of a first-order diffraction (and hence, an image) just 

 barely existing can be approximated by 



-jr = tan A, = sin v-, = T 

 J b 



or 



I ^ A 

 2a 2 sin d 1 



(4) 



Equation 4 gives the resolving power for a lens, provided the object is 

 illuminated by parallel light. The wavelength A is that of the medium 

 between the object and the lens. If this medium is different from air, 

 one may express A in terms of the wavelength A in air by the expression 



A = ^ 

 n 



Further, the product n sin 6 1 is often called the numerical aperture NA. 

 Thus, Equation 4 may be rewritten 



b = 



Xr 



2NA 



(5) 



The last equation was developed for a single lens. In the microscope, 



