The Refractive Index in Electron Optics and the Principles of Dynamics

We are indebted to Drs. ABSTRACT. In view of mis-statements made in the literature, the origin of the refractive index in electron optics is discussed in some detail, and the uniqueness of an expression previously given IS demonstrated. On this basis, some general properties of electron optics are investigated. Whereas the refractive index is unique in terms of the magnetio vector potential A, this itself is arbitrary to some extent. It is shown that A must, for purposes of electron optics, be chosen so as to satisfy Stokes' theorem and that, if it does, no observable effects result from the arbitrariness of A. An expression for the optical path difference is given in terms of the magnetic flux enclosed. The results are applied to a number of questions, viz. the differential equations for tra-jectories, the focusing properties of an axially symmetric field and the interference pattern produced by two converging bundles of rays which enclose a magnetic flux. A relation between ray direction and wave normal is obtained. in light optics the refractive index of a medium is in the first instance an experimental datum, and its accurate value is the basis of W any detailed discussion of the performance of optical instruments, all geometrical electron optics is entirely contained in Lorentz's equation for the forces acting on a moving charge. As a result, all equations for trajectories can be derived directly from that equation by specifying the electricand magnetic fields. Thus the rBle of the refractive index in electron optics is far less obvious than that of its counterpart for light, and in fact different authors have proposed essentially different values of the refractive index for the same field without arousing much