7 8 VISION WITH THE COMPOUND MICROSCOPE 



would be emitted in air under an angle of 66'5, but in balsam the 

 third would attain the same obliquity. Whilst now the dry objective 

 of 133 air-angle cannot admit more than the two first diffraction 

 beams on each side of the axis, the immersion of 133 balsam-angle 

 is capable of admitting from balsam three on each side under exactly 

 the same illumination. 1 



It follows, therefore, that a balsam-angle of 75 denotes the same 

 aperture as the larger air-angle of 133, and a balsam-angle of 133 

 a much greater aperture than an air-angle of the same number of 

 degrees, and in general two apertures of different objectives must be 

 equal if the sines of" the semi-angles are in the inverse ratio of the 

 refractive index of the medium to which they relate or, which is the 

 same thing, if the product of the refractive index multiplied by sine 

 of the angular semi-aperture (n sin u) yields the same value for both, 

 i.e. if they are of the same numerical aperture. 



2. Suppose the same object to be observed by a dry objective 

 of a given air-angle, at first in air uncovered, and then in balsam 

 protected by a cover-glass. The first case would be represented by 



A i it 



FIG. 68. 



fig. 66, and the second by fig. 68. As we have seen, the group of 

 diffracted beams from the object in balsam is contracted in com- 

 parison to that in air in the ratio of the refractive index. But 



1 The following are the actual angles represented in the diagrams, viz. : 



(Striae = 2'2 /*, wave-length A = '55 /JL, medium air n = l.) 



51 = 14 30' 



5 2 = 30 0' 

 83=48 36' 

 S 4 = 90 0'. 



Strise = 2'2 /A, wave-length A = '55 ju, medium balsam n 1*5.) 



51 = 9 36' 



5 2 = 1928 



5 3 = 300' 



5 4 = 41 48' 



5 5 = 56 26' 

 8,5 = 90 0'. 



