358 SUMMARY OF CURRENT RESEARCHES RELATING TO 



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 ref. ind. x sine of the angular semi-aperture (n sin u) 

 yields the same value for both. 



Thus the unequal equivalent of equal angles is shown in this way 

 also, as well as by the purely dioj)trical method, and numerical aperture 

 (n sin u) is seen to be the true measure of the greater or smaller 

 capacity of an objective for collecting light — i. e. the true image- 

 forming light — from the object. 



2. Suppose one and the same (structured) 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. According to Fraunhofer's law, 

 the group of diffracted beams emitted from this object in hnlsam is 

 contracted in comparison to the group in air in the ratio of the re- 

 fractive index. But according to the law of refraction, this group, on 

 passing to air by the plane surface of the covering-glass, is spread 

 out — the sines of the angles being compared — in the ratio of the 

 same refractive index. Consequently the various diffraction pencils, 

 the first, second ... on every side, after their transmission into air, 

 have exactly the same obliquity which they have in the case of direct 

 emission in air from an imcovered object. 



If, now, any dry objective of, say, 133° air-angle is capable of 

 admitting a certain number of these pencils from the uncovered 

 object, it will admit exactly the same pencils from the balsam- 

 mounted object. The contracted cone in balsam of 75° angular 

 aperture embraces all rays which are emitted in air within a cone 

 of 133°. 



It is, therefore, shown in this mode also, as it was before dioptri- 

 cally, that there is no loss of aperture by mounting the objects in 

 balsam or other dense medium ; the aperture of an objective, whether 

 great or small, is never cut down thereby. No ray which could be 

 taken in from the uncovered object is lost by the balsam mounting. 



The full and undiminished aj)erture of 

 a dry objective always bears upon the 

 object with every method of mounting, 

 provided there is a plane surface of 

 emergence. 



3. A comparison of Figs. 108 and 

 109 will show that a cone of 82° within 

 the balsam medium embraces all the 

 diffracted rays which are emitted from the object in air or trans- 

 mitted from balsam to air. This, however, is not the totality of 

 rays which are emitted in the balsam. The formula of Fraunhofer 

 accounts for as many (/c) diffraction beams on each side of the direct 



beam as are reconcilable with the condition h — ; < 1, because the 



nb 



expression gives the sine of the angle of deflection. 



The number of the emitted beams is therefore greater in balsam 

 than in air in the same ratio as the refractive index. 



A structure of 8 (distance of the elements) = 4 x 0'55 // - 2*2 // 



