1882.] 



MICROSCOPICAL JOURNAL. 



95 



however, can hardly be claimed as 

 an alga. 



o 



Numerical Aperture. — We have 

 reason to believe that a plain state- 

 ment of what numerical aperture is, 

 will be acceptable to some of our 

 readers. 



In the first place, a few words 

 about angular aperture. Suppose we 

 have a dry objective with an an- 

 gular aperture of 157°. Testing the 

 resolving power of this lens, we find 

 that it will resolve about 95,000 lines 

 to the inch, and no more. 



Take now a water-immersion ob- 

 jective that will just resolve the same 

 lines, and a homogeneous-immersion 

 that will do the same, and measure 

 the angular aperture of these in the 

 respective immersion fluids. In this 

 way we find the angular apertures of 

 the immersion lenses corresponding 

 to the angular aperture of the dry 

 lens ; in other words, we find the an- 

 gular apertures in air, water and oil, 

 which correspond to a certain resol- 

 ving power. These three correspond- 

 ing apertures are about 157° in air, 

 95° in water and 80° in oil. 



According to the old notion of an- 

 gular aperture, the larger the angle 

 the greater the resolving power. But, 

 in this case, the actual effect is the 

 very opposite, for, as we introduce 

 immersion media the angle grows 

 less, but the resolving power remains 

 the same. Evidently, therefore, the 

 old notion was wrong in some way. 

 Increase of aperture in a given me- 

 dium, as air, water, glycerin or oil, 

 does give greater resolving power, 

 and thus far the notion is well 

 founded. But since, in passing from 

 air to water, from water to glycerin, 

 and from glycerin to oil, the angle 

 of aperture grows less, while the re- 

 solving power remains the same, it is 

 clear that resolving power does not 

 depend alone upon the angle of aper- 

 ture. Some other element must be 

 considered, and it naturally appears 

 that this is dependant upon the im- 

 mersion-fluid, — there is some relation 



between the angular aperture, the 

 immersion-fluid, and the resolving 

 power. It has been found that the 

 index of refraction * of the immer- 

 sion-fluid is the element to be con- 

 sidered. 



Before explaining numerical aper- 

 ture, let us inquire what practical 

 value it has. It was stated above 

 that 157° air-angle was equivalent to 

 95° water-angle. A manufacturer of 

 objectives makes a water-immersion 

 lens and perhaps marks it as 157° 

 dry-angle. Such a mark is proper 

 enough, since the lens resolves the 

 same as a dry objective of that angle. 

 Nevertheless, it has no dry angle, 

 and therefore it should be marked 

 95° water-angle. Well, suppose it is 

 marked 95° what does this mark 

 signify ? Suppose we wish to com- 

 pare that objective with others, some 

 dry, some glycerin-immersions, some 

 oil-immersions, how can we tell how 

 these lenses should compare in re- 

 solving power ? We would be obliged 

 to take the apertui»es marked by the 

 makers for the different media, and, 

 by troublesome calculations, reduce 

 them all to corresponding apertures 

 in any one of the four media. Not 

 until we do that can we tell whether 

 a dry objective of 160", a water-im- 

 mersion of no", a glycerin-immer- 

 sion of 90*^, or a homogeneous-im- 

 mersion of 70°, in their respective 

 media, should resolve the finest lines, 

 if all are equally well made. 



Numerical aperture, however, tells 

 at once the resolving power of a lens, 

 no matter whether a dry-lens or an 

 immersion in any fluid whatever. 

 Numerical aperture, therefore, con- 

 siders not only the angular aperture, 

 but the effect of the refractive index 

 of the immersion-fluid upon the an- 

 gular aperture. It expresses the nu- 

 merical relation between these two. 

 It is determined by measuring the 

 angular aperture and the refractive 



* The index of refraction of any medium 

 is the numerical relation of the sines of the 

 angles of incidence and refraction. 



