194 



THE AMEEICAN MONTHLY 



[October, 



objective ai^e now brought, by refrac- 

 tion, to a smaller angular deviation, 

 the spectrum is taken up by the ob- 

 jective and the markings are resolved. 

 We can thus understand the action 

 and the advantages of immersion ob- 

 jectives. It has long been an axiom 

 with microscopists that resolution of 

 fine lines is dependent upon angular 

 aperture ; but in this case the immer- 

 sion medium has materially lessened 

 the angular aperture, yet the resolving 

 power of the lens is increased. Never- 

 theless, the angular aperture has been 

 shown, under the conditions pre- 

 viously mentioned, to determine the 

 resolving power. The apparent dis- 

 crepancy here is easily explained, 

 although it has caused interminable 

 confusion in the past. The explana- 

 tion in brief is this : Angular aper- 

 tures can only be compared under the 

 same conditions. Thus angular aper- 

 tures of objectives working di'y, or of 

 objectives working in the same im- 

 mersion fluid, can be compared among 

 themselves, but those of one class 

 cannot be compared with those of the 

 other class. Thus, a dry objective of 

 157° will resolve no more than one 

 having an immersion angle in water 

 of 94°, or in oil of 80°. 



It will be seen that such compari- 

 sons are apt to be very confusing, and 

 for this reason the term angular aper- 

 ture might better be entirely discarded. 

 A perfectly satisfactory method ot 

 designating the resolving power of an 

 objective has been adopted by micro- 

 scopists on the recommendation of 

 Prof. Abbe. It is by determining the 

 ' numerical aperture.' In highly re- 

 fractive media the undulations of light 

 become much shorter than in air, and 

 as the capabilities of the microscope 

 are dependent upon the wave-lengths, 

 it is obvious that dense media for 

 mounting add to the resolving power. 

 Moreover, the visibility of an object 

 is affected by the relation between the 

 refractive indices of the object and the 

 mounting medium. The more these 

 differ the more visible the object will 

 be. But time would not permit, even 



if it were desirable, a longer discus- 

 sion of the optical action of mounting 

 media of different refractive powers. 

 Suffice it to say that Prof. Abbe has 

 shown, both by experiment and cal- 

 culation, that the true aperture, dis- 

 tinguished w^hen desirable as the nu- 

 merical aperture of a microscope 

 objective, which is the capacity of the 

 objective to receive rays i'rom an 

 object to form an image, is the ratio 

 between the focal length and the 

 diameter of the back lens of an ob- 

 jective. This ratio will depend upon 

 the refractive index of the medium 01 

 immersion, and is expressed by the 

 product of the index of refraction 

 multiplied by the line of half the 

 angle of aperture for the particular 

 immersion medium employed. This 

 is expressed by the much-used for- 

 mula n sin. u. 



Since the resolving power of a mi- 

 croscope depends upon its numerical 

 aperture, and upon the wave-length 

 of light, it must be clear to any per- 

 son that when the mai^kings of an ob- 

 ject are so exceedingly minute that 

 they can no longer produce the diff- 

 raction spectra necessary to form a 

 correct image, they are beyond the 

 range of microscopic vision. It will 

 also be understood that since it is a 

 mfitter involving the wave-length of 

 light, the use of optically dense media 

 to reduce the amplitude of the vibra- 

 tions of light adds to the resolving 

 power of the microscope. Likewise, 

 finer details can be made out with 

 blue i-ays than with red, and struc- 

 tures finer than the eye can see may 

 be photographed. 



The limit of resolving power has 

 been calculated for different media 

 and apertures, ranging from 1.52, 

 which is theoretically the highest at- 

 tainable with an immersion medium 

 of refraction index 1.52, since it cor- 

 responds to 180° of angular aperture 

 in that medium, down to 0.50, and a 

 table giving the figures is regularly 

 published in the Am. Monthly Micr. 

 Journal. The range of resolving 

 power at present attained in practice 



