20 MICROSCOPE AND ACCESSORIES [CH. I 



§ 34. Significance of Aperture. — As to the real significance of 

 aperture in microscopic objectives, it is now an accepted doctrine that — 

 the corrections in spherical and chromatic aberration being the same — 

 (1) Objectives vary 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 aper- 

 ture of 0.50 would define or resolve only half as many lines to the 

 millimeter or inch as a similar objective of 1.00 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 man}' 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 2A.XN.A. That is 

 twice the number 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 ele- 

 ment 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- x 5) 

 it is believed that not more than ^ths of the numerical aperture .of an 

 objective is really available for microscopic stud}-, 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 2A. X Y\ ths N. A. =3/2/tN. 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 3/2 N. A. For 

 example suppose one uses ordinary daylight and assumes the average 

 wavelength is 146666 in., then there must be 46,666 per inch and 

 46,666X3/2 = 70,000 approximately. If the N. A. is 1, then the 

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

 proximate!}' 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-Dallinger, because in the latter the full aperture 

 is supposed to be employed and the light is of the greatest available 

 obliquity. 



