316 COMPOUND AND ELECTRON MICROSCOPES 



lar separation of the first dark ring from its center is 



1.220X 



»- — 



in which d is identified as the distance of the foot of the intensity curve 

 (Fig. VIII-3) from the central maximum, and X is the wavelength of the 

 light forming the diffraction pattern. 



According to Rayleigh's criterion, the limit of resolution is reached 

 when two circular-aperture images are separated by the distance d as 

 given by the above relation. 



The resolution of two point sources of an object, that is obtainable 

 with the aid of a lens, depends on the angle of the cone of light which sub- 

 tends the lens and not on that which subtends the image, because the 

 lens has the properties of an aperture. The margin of the lens acts as 

 an edge of a circular aperture. If the lens forms a point image by means 

 of a wide-angle cone of light the diffraction disk is large. When two 

 adjoining diffraction disks are observed to be far apart, then according 

 to the Rayleigh criterion the resolution is large. 



The angular separation, 6, in the above formula is half the angle of the 

 cone of light forming the image and not of the light as it enters the object 

 lens. For a microscope, it is necessary to convert the above formula 

 into a form that expresses the distance of closest approach of the diffrac- 

 tion disks in terms of the aperture of the lens. 



A point source placed close to the objective of a microscope is ex- 

 amined. Such a source subtends an angle 2a in the object space, of index 

 of refraction n. The separation of two such points O and 0' in the 

 object plane will produce images I and 7 in the image plane that are 

 just resolvable. From simple geometrical considerations this separa- 

 tion S can be shown to be 



1.22X X 



S 



2n sin a 2 N.A. 



Abbe investigated this problem in detail and concluded that good 

 working results for the resolution were obtainable by assuming the factor 

 1.22 to be equal to unity. 



Resolving Power 

 The resolving power (R.P.) is defined as 



2 N.A. 



R.P. = cm 



-l 



