Microscopic Resolution. By Professor J. D. Everett, F.R.S. 27 



is e sin 7, giving a phase-difference -^— e sin 7. This is to be 

 added (with its proper sign) to the phase-difference v in (28), 



2 IT 



which is found, on examination, to have the value -^— sin a 

 (a denoting the numerical aperture). It is, therefore, simply 



2 7T 



necessary to assign to v in (28) the value -— — (sin a + sin 7), 



and (28) will be the general expression for the amplitude for any 

 obliquity of illumination (7 being zero when the illumination is 

 direct). This conclusion is in accordance with (45), which is the 

 final result deduced from (32). 



The value above assigned to v for direct illumination is 

 obtained in the following way. Let a denote the distance from 

 line to line in the geometric image of the grating. The magnifi- 

 cation a I e is, by the sine-law, equal to sin a j sin 6, the small 

 angle 9 being equal (in the notation of the paper) to ^ a 

 divided by /. As u stands for the abscissa of a line in the 



geometric image multiplied by — -, its increment v is 



*• / 



it a it a 2 f . 2 7r 



— a = — - e — -i- sm a = e sin a. 



\f \f a \ 



We assume (as usual) that the plane waves of illumination 

 intersect the plane of the grating in lines parallel to the grating 

 lines. The resolution will be most complete when sin a + sin 7 

 is greatest, that is, when the difference of optical path from line 

 to line is greatest. To this end, the grating (a small microscopic 

 object) should be on one side of the axis of the Microscope, and 

 the light should come from the other side ; sin a and sin 7 will 

 then have the same sign. 



