Microscope Construction, Use, and Care 187 



some as two interwound threads. Tlie question to ask concerning an 

 objective is not "how small a thing can you see?" but "what is the 

 minimal separation between two objects that the lens can resolve?" 

 Ihe mathematical derivation of the formula for determining 

 resolving power can be found in textbooks of optics or physics. The 

 formula contains the following factors: 



// ^ the lowest index of refraction in the path of the rays, i.e., the 

 index of refraction of water, glass, air, cedar oil, balsam, etc. 

 u = half of the angle made by the effective cone of rays entering 

 the objective. This value can be obtained from a table in 

 Gage (1936) or from the manufacturers. 

 N.A. = numerical apertme, a number that is indicative of relative 

 resolving power. 

 The formula is 



N.A. = u -sin u 



The value of the numerical aperture is engraved on most modern 

 objectives and is given in the catalogues of the manufacturers. This 

 number is 0.25 in a lOx objective, for example, and increases through 

 progressively higher magnification, attaining the value 1.4 in an 

 expensive 90 X objective. 



Knowing the nimierical aperture, we can make a simple compu- 

 tation and arrive at a tangible value of resolving power. Assume that 

 we are using an objective of N.A. 1.0 and using light having a wave 

 length, in round numbers, of 0.0005 mm. The formula is 



I {= wave length) 0.0005 



= = 0.00025 mm. 



2 N.A. 2 



This means that if two bacteria or two chromomeres on a chromo- 

 some are separated by a space of 0.00025 mm., they can be seen as 

 two distinct bodies. As the numerical aperture increases, the resolving 

 power increases, the working distance and depth of focus decrease, 

 and the cost increases. 



The practicable upper limit of N.A. 0.95 is obtainable with dry 

 lenses, used with an air space between the objective and the cover 

 glass. In accordance with the foregoing formula, the N.A. can be 

 increased by increasing the value of n or of sin u or both. If the 

 angle of the ray that passes from the glass slide to air is greater than 

 41°, the light is totally reflected back into the glass. This phenomenon 

 limits the angle that determines ??. If a drop of cedar oil or synthetic 



