The incidence of light upon a transparent sphere of dimensions comparable with the wave-length

Source abstract

Abstract In a paper, now nearly thirty years old, I applied Maxwell’s equations of the electro-magnetic field to investigate the disturbance produced by an obstacle upon plane waves of light which travel through a medium otherwise uniform, giving particular attention to the case where the properties of the obstacle differ but little from those of its surroundings. The difference may consist in a variation of K — the specific inductive capacity, or of μ— the magnetic capacity, or of both; but it was shown that the last supposition leads to results inconsistent with observation, and that the evidence favours the view that μ is to be treated as invariable. Denoting electric displacements by f, g, h, the primary wave was taken to be h0 = einteikx, (23) so that the direction of propagation is alongx (negatively), and that of vibration parallel to z. ∆μ being omitted, the electric displacements (f1, g1, h1) in the scattered wave, so far as they depend upon the first power of ∆K, have at a great distance the values f1, g1, h1 = k2KP/4πr (αγ/r2, βγ/r2, – α2 + β2/r2), (35, 37, 38) in which P = ∭h0∆K-1e-ikrdx dy dz. (36)