JOURNAL 



OF THE 



ROYAL MICROSCOPICAL SOCIETY. 



DECEMBER 1889. 



TEANSACTIONS OF THE SOCIETY. 



XI. — On the Effect of lUumination hy means of 

 Wide-angled Cones of Light. 



By Prof. E. Abbe, Hon. F.R.M.S. 



{Bead dth October, 1889.) 



Tee diffraction theory leads to the following conclusions in regard to 

 the mode of illumination in question. 



(1) A wide-angled illuminating cone must be considered as com- 

 posed of a multitude of (infinitely) narrow pencils, which have very 

 different directions of incidence upon the object — from perpendicular 

 incidence (the axial pencil) to a certain degree of obliquity, with all 

 intermediate directions in gradual change. 



(2) Provided the structure under observation admits of a per- 

 ceptible diffraction-effect, every single (i. e. infinitely narrow) beam 

 of incident light is " split-up " in its transmission through the 

 stiucture, into the "diffraction-pencil" (or "fan") which is peculiar to 

 the structure ; and gives rise to a certain diffraction-spectrum at the 

 back of the objective. 



According as this elementary diffraction-fan of every incident ray 

 has more or less angular extension, and according as the incident ray, 

 to which it belongs, is more or less oblique — both these points con- 

 sidered with regard to the aperture of the objective— a smaller or 

 greater part of such an elementary diffraction-spectrum is admitted to 

 the ol>jective, and utilized for the formation of the image. 



(3) In the case of a suflSciently wide-angled illuminating cone 

 (at all events, when the incident light fills the whole aperture) the 

 multitude of elementary diffraction-pencils, corresponding to the 

 multitude of elementary incident rays, mingle together at the back of 

 the preparation — and the diffraction-spectra at the back of the 

 objective — overlapping one another to such an extent, that nothing 

 else but white light, filling out the whole aperture, can be observed. 



Nevertheless these various elementary diffraction-pencils, mingled 

 together within the objective, produce images of the object quite 

 separately ; every single elementary pencil gives rise to its own 



1889. 3 E 



