Theories of Microscopical Vision. By A. E. Conrady. 621 



reach 1£ wave-lengths, and we easily deduce the following 

 rules : — 



When the width of slit is less than \ of the spacing, the spec- 

 trum is in phase with the direct light. 



f When the width exceeds ^, but is less than § of the spacing, 

 the spectrum is in opposite phase. 



When the width exceeds §, the spectrum is again in the same 

 phase as the direct light. 



The spectrum has maximum brightness for a width of slit of 

 respectively \, f-, and % of the spacing, and vanishes for a width 

 equal to -J and § of the spacing. 



It will be obvious how this may be carried up to spectra of 

 any order, and that the number of reversals of phase will con- 

 stantly increase. It will also be foreseen what an important bear- 

 ing these phase relations must have on the character of the image, 

 and how vital the knowledge of their existence and nature must 

 prove to a proper understanding of "diffraction" images. That 

 must be my excuse for going into the question at such length. 



The figures in the third column of the above table also show 

 that, with very narrow lines, the diffraction-spectra are almost of 

 the same brightness as the direct light, as there is little weakening 

 of the light by interferences. The broader the lines compared to 

 the dark intervals, the more does the direct light preponderate, 

 and a special application of this reasoning leads to the important 

 conclusion that with plane gratings the first spectrum is always 

 brighter than any other ; this follows because there must always 

 be more interference between the wavelets from different portions 

 of a slit which unite to form the higher spectra, than there can 

 be in the case of the first. 



We will now proceed to apply these principles to the Micro- 

 scope. 



As stated above, we assume for the present that our grating 

 is illuminated with parallel monochromatic light, such as would 

 be received from a distant luminous point, and, further, that the 

 Microscope is correctly focussed on the grating, i.e. that we are 

 looking at the image formed by- the diffracted light in the plane 

 of the geometrical image. The necessity of assuming this will 

 become apparent later. 



We will first take the case where oblique light is used, the 

 direct light entering through the outer zone of the objective on 

 one side, and a greater or lesser number of successive diffraction 

 spectra through other zones right across the objective. 



1. Let the aperture be sufficient to admit the direct wave and 

 the first diffracted one. We have seen that the latter is always 

 in the same phase as the direct one ; hence, by applying my first 

 theorem, i.e. that wavelets arrive at the conjugate point in the 

 same phase relation in which they left a point in the object, we 



