6 4 D O C U M E N T 4 3 L I G H T I N D I S P E R S I V E M E D I A wave pass through a dispersive medium, then within this medium the propagation velocity of the planes of equal phase is a function of location therefore, as they propagate within the dispersive medium, the equally phased planes experience a ro- tation that must manifest itself optically as light deflection. As Messrs. Ehrenfest and Laue doubted the conclusiveness of this consideration,[2] I examined the propagation of light in dispersive media more closely from the point of view of the undulatory theory and did, in fact, find that this consideration leads to an incorrect result. The reason lies—as Mr. Ehrenfest rightly judged[3] —in that by following the crest of a wave in dispersive media, places lying outside the group of waves under consideration come into reach although rotated, that plane of the wave crest does not physically exist anymore. Other new ones are formed elsewhere of different orientation in its stead. Our goal is to find an exact mathematical description of the process taking place within the dispersive medium from the point of view of the undulatory theory. In doing so we can restrict ourselves from the outset to considering two-dimensional processes, i.e., those whose field components are independent of the z- coordinate.[4] We assume that dispersive media act just like nondispersive ones with regard to purely perceptual processes. So if means a function satisfying the wave equation, e.g., the z-component of the electric field strength, (1) is then a solution for the wave equation for all r that are large compared to the wavelength , means the excitation at time t at a starting point (x, y), whose distance from a reference point ( ) equals r. A, , V, and signify real constants, where and V are linked by a relation due to the optical properties of the medium. Any additive connection of solutions of type (1) is yet another solution because of the linearity of the differential equations. We now imagine a continuous series of excitations that produce waves of type (1), continuously distributed over a given curve lying in the x-y-plane. The refer- ence points ( ) should be considered given as a function of arc length s mea- sured on the curve. At a sufficient distance from the curve, the integral over the curve (2) φ φ A r ------e j ω t r V --- – α + = [p. 19] 2πV ω ---------- λ = φ ξ η , ω α ω ξ η , φ A r ------ejH sd = H ω t r V --- – α + =