Geometrical Optics in Absorbing Media

The problem of propagation of rays in a medium of variable absorption and refraction has acquired some practical importance in radiotelegraphy. The radio waves penetrate into the conducting and absorbing layer of the upper atmosphere(1) and describe there a certain path. The question was brought to my attention by Dr. B. Van der Pol of Eindhoven (Holland) who asked me to give a formula by which the shape of a ray in the conducting layer could be computed. The solution given in this paper is not restricted to electromagnetic rays, but applies, equally well, to waves and rays of other types. With respect to the radio waves, one of our results is that the rays, after going up, do not bend down again and do not ever come back to earth. The rays, observed by the receiving station, as coming from the conducting layers are not primary but secondary waves produced in it by reflection. The writer is preparing a second paper dealing with the problem of space reflection in an inhomogeneous absorbing medium.