24 MICROSCOPE AND ACCESSORIES [ CH. 1 



directly as their numerical aperture in their ability to define or make clearly 

 visible minute details (resolving power). For example an objective of 4 mm. 

 equivalent focus and a numerical aperture of 0.50 would define or resolve 

 only half as many lines to the millimeter or inch as a similar objective of i.oo 

 N.A. So also an objective of 2 mm. focus and 1.40 N.A. would resolve 

 only twice as many lines to the millimeter as a 4 mm. objective of 0.70 N.A. 

 Thus it is seen that defining power is not a result of magnification but of 

 aperture, otherwise the 2 mm. objective would resolve far more than twice as 

 many lines as the 4 mm. objective. 



Taking the results of the researches of Abbe as a guide to visibility with 

 the microscope, one has the general formula 2/1 X N.A. That is twice the num- 

 ber of wave lengths of the light used multiplied by the numerical aperture of 

 the objective. From this general statement it will be seen that the shorter the 

 wave lengths of the light, the more there will be in an inch or centimeter and 

 therefore the greater the number of lines visible in a given space. That is the 

 kind of light used is one element and the objective the other in determining 

 the number of lines visible under the microscope. 



Following Mr. E. M. Nelson (Jour. Roy. Micr. Soc. , 1893, p. 15, and 1906, 

 p. 521) it is believed that not more than % o f the numerical aperture of an 

 objective is really available for microscopic study, with a central, solid cone of 

 light. To determine the number of lines visible in a given space with a given 

 light the formula would become 2/lX^N.A.=3/2AN.A. To determine the 

 working-resolving power of any objective it is only necessary to know the 

 number of light waves in a given space, say an inch or a centimeter and to 

 multiply this number by 3/aN.A. For example suppose one uses ordinary 

 daylight and assumes the average wave length is 1/46666 in., then there must 

 be 46,666 per inch and 46,666x3/2=70,000 approximately. If the N.A. is i, 

 then the objective will resolve or make visible 70,000 lines to the inch, or 

 approximately 28,000 to the centimeter. If blue light were used the number 

 would be 32,000 per centimeter, or 80,000 per inch. It will be seen that the 

 number of lines here given is smaller than that in the table of Carpenter- 

 Dalliuger, because in the latter the full aperture is supposed to be employed 

 and the light is of the greatest available obliquity, while here only 34 of the 

 aperture is assumed to be available. 



(2) The illuminating power of an objective of a given focus is found to 

 vary directly as the square of the numerical aperture (N.A.) 2 . Thus if two 

 4 mm. objectives of N.A. 0.20 and N.A. 0.40 were compared as to their illumi- 

 nating power it would be found from the above that they would vary as 

 o.2o 2 :o.4o 2 =o.o4oo:o.i6oo or i -.4. That is the objective of 0.20 N.A. would 

 have but % the illuminating power of the one of 0.40 N.A. 



(3) The penetrating power, that is the power to see more than one plane, 



i 

 is found to vary as the reciprocal of the numerical aperture so that in 



N.A. 



an objective of a given focus the greater the aperture the less the penetrating 

 power. 



