RADIATION IN AIR AND BALSAM 



55 



A dry objective was therefore supposed to be placed at a disad- 

 vantage when used upon balsam-mounted objects, its aperture being- 

 supposed to be ' cut down ' by the balsam, and the advantage of the 

 immersion objective was considered to rest on the fact that it 

 restored, in the case of the balsam-mounted object, the same condi- 

 tions as subsisted in the case of the dry-mounted object, allowing as 

 large (but no larger) an aperture to be obtained with the former 

 object as is obtained by the dry objective with the latter. 



The error here lies in the assumption of the identity of radiation 

 in air and balsam. If there were in fact any such identity, the 



170 IN 



AIR 



FIG. 38. 



conclusion above referred to would, of course, be correct, for if in 

 fig. 37 the air pencil of 170 was identical with the balsam pencil of 

 1 70 (shown by the dotted lines in fig. 38), there would necessarily 

 be a relative loss of light in the latter case in consequence of so 

 much of the pencil being reflected back at the cover-glass. 



When, however, the increase of radiation with the increase in 

 the refractive index of the medium is recognised, the mistake of the 

 preceding view is appreciated. The 170 in air of fig. 37 is not 

 equal to, but much less than, the 170 in balsam of fig. 38, and not- 

 withstanding that a great part of the latter does not reach the 



proportion of the squares of their radii, it follows that if we designate the radius by 

 n sin u (or p sin <f>), the area of the circle A will be to the area of the circle B as the 

 square of the radius of A is to the square of the radius of B, or as (n sin u)'* is to 

 (n' sin u') 2 . 



sin. 



Area, 



propo7^io7iaZ to 



FIG. A 2. The backs of two objectives of the same power but different apertures. 



The student will observe that the radius of B is twice that of the radius of A ; 

 consequently the area of B will be four times as great as that of A ; which means 

 that, since the numerical aperture of the objective B is twice as great as that of the 

 objective A, its illuminating power will be four times as great. 



