174 



J. RHEINBERG ON THE ABBE EXPERIMENTS. 



constructed that Ave can experiment with comparatively coarse 

 objects, and in which the back focal plane of the objective is 

 readily accessible. The object on the stage is a coarse grating 

 of about 100 lines per inch, in which the width of the black lines 

 and of the spaces are just equal. A grating in which the bars and 

 spaces are equal happens, as we shall see, to be the best for 

 our purpose. All you have to do is, whilst looking at the grating, 

 to move the diaphragm in the back focal plane by about yg- in. 

 to the right and left alternately, and in the one position the lines 

 of the grating will be seen correctly, in the other they will be 

 seen doubled. 



The explanation is this : The visible spectra which a grating 

 with bars and spaces of equal width forms in the upper focal 

 plane of the objective are spaced so that the distance between the 

 central (or dioptric) beam and the first spectrum on either side 

 is just half as great as between the first spectrum and the second 

 visible spectrum [Fig. 1 (3)]. This curious arrangement follows 



2. 



Fig. 2. 



from the theory of diffraction applied to gratings, upon which I 

 need not enter here, but only invite you to note that the spacing 

 of the spectra is dependent upon the nature of the object, and 

 has, of course, no connection whatever with the diaphragm in 

 the back focal plane, the sole function of which, in this experi- 

 ment, is to stop certain spectra from reaching the eye piece. 

 What we do, therefore, is first to use the diaphragm so that it 

 permits the central beam and the first spectrum on both sides to 

 pass through [Fig. 2 (1)]. Under these conditions, the object is 

 seen to have the correct number of lines. 



Then we shift it to the second position, in which it will allow 

 only the first and second visible spectrum to pass [Fig. 2 (2)] ; 

 and as the spectra are now twice as far apart as in the former 

 case, the lines in the image are seen doubled, as explained in the 

 descriptions of Abbe's experiments in the text-books. 



I think- ii will be admitted that this conclusively shows that 

 the effect is due to the object, and not to the diaphragm. 



. Q-uekett Microscopical Club, Ser. 2, Vol. IX., No. 56, April 1905. 



