152 A MANUAL OF BACTERIOLOGY 



collect, admit and transmit this scattered or diffracted 

 light, the better will be the definition and the greater the 

 resolution. The wider the angle of view embraced by 

 the lens, the angle of aperture as it is termed, the more 

 will this be the case. The medical reader will appreciate 

 what is meant by angle of aperture, if it be likened to the 

 field of vision of the eye a lens with a small angle of 

 aperture is comparable to an eye with a contracted field 

 of vision ; it does not take up widely-dispersed rays at the 

 margin of the field. Abbe found that the improvement 

 does not vary directly with the angle of aperture, but 

 varies as the sine of half this angle ; it also varies directly 

 with the refractive index of the medium between the 

 lens and the object. If u half the angle of aperture 

 and n = the refractive index of the medium, then numeri- 

 cal aperture, N.A. = n sine u. In practice, the numerical 

 aperture of a dry lens rarely exceeds 0-95, of a water- 

 immersion lens 1-15, and of an oil-immersion lens 1-4. 

 With the lower-power dry lenses, numerical aperture is 

 co-ordinated in manufacture with the magnifying power, 

 for Abbe showed that the number of lines to the inch which 

 a lens will resolve, or show visually, is equal to twice the 

 number of waves to the inch of the light employed multi- 

 plied by the N.A. Now a \ -in. dry objective with a high (10) 

 eye-piece gives a magnification of about 200 diameters, so 

 that lines separated by ^- in. would appear as if separated 

 by 2 J- in., and this interval is just appreciable by the 

 best normal eye. That is to say, up to 50,000 lines to the 

 inch, but not more, are resolvable under these conditions. 

 But the N.A. required for this is only about -53, and it is, 

 therefore, no use making it much more, so that for the 

 best ^-in. objectives a standard N.A. of about -65 has 

 been adopted. 



Three facts emerge from the foregoing : (1) the higher 

 the refractive index of the medium between lens and 



