"Electron Trigonometry", a new tool for electron optical design

In electron-optical devices of circular symmetry whose axis potential is a quadratic function of distance, we have found that a very general law can be formulated which we call the "triangle theorem of electron optics." It deals with three individual phase angles which are defined, respectively, for image-space, object-space and lens-volume. The "triangle theorem" states that in any image-forming system as above, the sum of these three phase angles is 180 degrees for a converging electron lens, and zero for a diverging electron lens. The "triangle theorem" permits the immediate determination of size and position of an electron image including real as well as virtual images. It is not restricted to thin lenses but applies to long electron lenses as well.