This formula can be better illustrated by an example. 

 Take an objective with an angle of aperture in air of 

 100 degrees, of which the numerical aperture is to be 

 determhied. The focal length of the objective is left 

 out of consideration as the formula depends entirely on 

 angle and index and it is evident that all objectives 

 having this same angle, in this case in air, will have 

 the same N. A. 



Considering the angle it, it wijl be readily seen that 

 this is one-half of 100 degrees, or 50 degrees. Now 

 referring to a table of natural sines or to a table of 

 logarithms it will be found that sine //, or the sine of 

 50 degrees is equal to 0.766, and as the intervening 

 medium is air, the value of index n is equal to i.o. 



Substituting the above values in the formula, we 

 have N.A.=(/z or i.o) x (sine u or o.766)=o.766. 



To make this computation we have always the value 

 of the index of refraction at hand, but the angular 

 aperture must be determined, and the method for 

 accomplishing this will be given in a succeeding 

 chapter. 



As a rule the designation as to power and numerical 

 aperture engraved on the mounting of an objective 

 from a responsible firm can be relied upon as being 

 quite close, the variations seldom being greater than is 

 incident to accurate human handiwork, and such 

 variations as do occur have little influence on the 



79 



