From wave theory to ray optics

The aim of this article is to summarize the historical process which led to recovering the concept of a ray, typical of the pre-Maxwell theory of light, from wave theory. To this end, the contributions of Huygens (1690), Newton (1704), Young (1801), and Fresnel (1816), which can be considered the founders of the modern science of optics, are briefly described, giving evidence to some aspects that led to the formulation of the ondulatory theory of light. Then, it is seen how the concept of a ray was recovered from Kirchhoff´s diffraction theory, which can be interpreted as a rigorous formulation of Fresnel´s ideas. The key role of the Maggi-Rubinowicz (1888, 1924) representation of Kirchhoff´s diffraction integral, which can be interpreted as the mathematical expression of Young´s theory of diffraction, is discussed. Also, it is noted that the first theoretical derivation of diffracted rays, and of the cone of diffraction, was due to Adalbert Rubinowicz (1917). He was one of Sommerfeld´s assistants, in Munich, in analyzing the transmission of a high-frequency field through an aperture in an opaque screen. The ideas which are briefly summarized produced the basis for the statement of the geometrical theory of diffraction. This ray theory, which is the natural extension of geometrical optics (GO), was presented by J.B. Keller, in 1953.<>