The Abbe Diffraction Theory. By J. W. Gordon. 375 



the experiments described by Dr. Zimmermann. Those experiments 

 are hard to follow for two reasons : — 



(1) They are performed with a great deficiency of light ; and 



(2) They are displayed by an object of insufficiently large dimen- 

 sions. 



But when we realise that the Abbe phenomena depend not upon 

 diffraction produced by the diffraction plate, but upon diffraction 

 produced by the Abbe diaphragm, we see at once that both these 

 defects can be cured. To take the first. The deficient lighting is 

 due partly to the small aggregate amount of light passed by the 

 diaphragm, but even more to the diaphanous quality of the fine 

 silver film in which the ruling is traced. It can be improved by 

 substituting a more opaque background for the Zeiss film. 



The difficulty of the small scale of the Abbe phenomena as 

 exhibited by Zeiss' apparatus may be overcome by another simple 

 expedient. The dispersive power of a diffraction grating is inversely 

 proportional to the distance from centre to centre of its constituent 

 Hues. Now the Abbe diaphragm (fig. 79) has a distance of t £q in. 

 from centre to centre, and its dispersive power is barely sufficient to 

 double the coarse ruling of the diffraction plate under the magnifying 

 power of the a a Zeiss objective. If now we reduce the separation of 

 lines in the diaphragm, we shall in corresponding measure increase its 

 dispersive power. Thus, with a diaphragm passing the same quantity 

 of light as that shown in fig. 79, but having six apertures in the 

 place of three, we shall obtain dispersive power enough to double a 

 ruling on the stage so coarse that its lines will stand g^ in. apart. 

 If in place of the six openings in the diaphragm we introduce sixty, 

 the dispersive power will be equal to doubling lines that stand yoo in. 

 apart. These are very convenient dimensions to work with, and will 

 be assumed as data in the description of the following experiments. 



Third Experiment. — The diaphragm being arranged in the Zeiss 

 carrier, a mercury globule is placed upon the stage, and so illumi- 

 nated that it forms a minute 



image of a distant lamp flame Fig. 81. 



serving in the well known 

 way as a point of light. The 

 point, viewed now through the 

 above described diaphragm, con- 

 structed as a grating with sixty 

 spaces, shows a set of diffrac- 

 tion spectra as in fig. 81, where 

 the five-image pattern results 

 from bright, and the three-image 



pattern from moderate illumination. The number of visible diffraction 



images depends, of course, upon the brightness of the point. When 



the naked flame is reflected in this way the point is very bright, nad 



a system of five, seven or even m^re images may easily be visible. 



