APPLICATION OF THE DIFFRACTION THEOKY 



77 



axial pencil of incident rays. If this object is observed in air, the 

 radiation from every point of the object is, in consequence of the 

 diffraction effect, composed of an axial pencil S, fig. 66 (the direct 

 continuation of the incident rays), and a number of bent-off pencils, 

 S 1? S 2 , . surrounding S. 1 



If, now, instead of air, the object is immersed in a medium of 

 greater refractive index, n, it results from Fraunhofer's formula that 

 the sine of the angle of deflection of the first, second, . . . bent-off 



FIG. 67. 



brain is reduced in the exact proportion of , and the angle is re- 

 duced also that is, the whole fan of the diffracted rays is contracted 

 in comparison with its extension in air. Fig. 67 will represent the 

 case of the same object in oil. 



If now any dry objective (with a given angular semi-aperture u) 

 is capable of gathering-in from air the first, or the first and second, 

 diffraction beams on every side of the axial pencil, another objective 

 with a more dense front medium of the refractive index, n, will be 

 capable of admitting, from within the dense medium, exactly the same 

 beams (no more and no less), if its angular semi-aperture, v, is less 

 than u in the proportion : 



sin v : sin u = 1 : n, 



or 



n sin v = sin u, 



all other circumstances object and illumination remaining the 

 same. 



For example, a diatom for which the distance of the stria? is 0'6 /j, 

 will give the first bent-off beam of green light (/\ = -55/z) in air under 

 an angle of 66 '5. This will be just admitted by a dry objective of 

 133 angular aperture. In balsam (n = l'5) the same pencil will 

 be deflected by 37'5 only, and would be admitted, therefore, by an 

 objective of not more than 75 balsam-angle. Again, if the distance 

 of the lines should be greater, as 1'2/u, the second deflected beam 



1 In figs. 66, 67, and 68 S 4 and S 6 are supposed to be identical with the surfaces, 

 but are drawn at a slight inclination to them for the purpose of clearness in the dia- 

 grams. 



