Principles of Microscopy 9 



resolution. The spread is measured in terms of the widest angle from 

 which the lens can bring rays to a focus and form an image. Resolution 

 is measured as the number of lines or dots per inch that can be separated. 

 "Angular aperture" is thus a potent factor in resolution. 



The effectiveness of angular aperture is, however, limited in practice 

 by the wavelength of the light used. Again it is necessary to ignore theo- 

 retical arguments as to the structure of light rays in favor of a practical 

 analogy. Suppose that light is propagated as a series of waves of varying 

 wavelengths. Now mentally transpose these waves to the surface of the 

 ocean. A liner will leave a perceptible wake— or, in optical terms, shadow 

 —as it passes through even the largest waves. A child's toy boat will leave 

 a wake of only the tiniest of ripples. Light rippling past an object on 

 its way through a microscope to our eyes follows just the same rules. 

 No object smaller than the waves of light can create a disturbance in 

 the waves that is perceptible to the eye. It follows that the shorter the 

 wavelength of light, the greater the possible resolution. 



It must be reemphasized at this point that resolution, from the practical 

 point of view, is a measure of crispness or clarity. People often fail to 

 see how the number of lines or dots per inch that can be separated, or 

 resolved, is a measure of the sharpness with which larger objects can be 

 seen. Actually everything is seen against a background of something 

 else. Sharpness and clarity are just measures of how well the object is 

 separated from, or resolved against, the background. 



Wavelength, resolution, and angular aperture have very simple rela- 

 tionships. In the first place it must be obvious that the angle of the cone 

 of light that can enter any lens is dependent on the refractive index 

 of the medium in which the lens is working. This dependence, or "nu- 

 merical aperature," is expressed by the relation 



N.A. = i sin 



where 8 is one-halt the angle of the entering cone of light and i is the 

 refractive index of the medium surrounding the lens. Since i for air is 1, 

 and since sin 6 cannot be greater than 1, it follows that no lens working in 

 air can have a theoretical N.A. greater than 1. 



The relation between N.A. and resolution is just as simple for 



where X is the wavelength of the light and R is the number of lines that 

 can be separated. R or A can be given either in inches or millimeters. 

 Some books prefer to express resolution in lines per inch and wavelength 

 in millimeters, in which case the relation becomes 



