Refractive attenuation formulas for an unstable critical ray in a circularly symmetric medium


  • Belinda J. Lipa,

  • Thomas A. Croft


Through application of the basic equation of geometrical optics, the eikonal equation, we have derived an expression for the refractive defocusing of a critical ray in a medium which has circular symmetry. The equation of the ray itself is simply a circle, since by definition its radius of curvature is exactly the same as its distance from the center of symmetry. This mathematical development has a practical significance in that it permits for the first time the calculation of the strength of a signal which travels in the atmosphere of a planet at a fixed critical height. Our specific interest in this matter was due to the probable existence of such a critical ray about 33 km high in the atmosphere of Venus; at this altitude the pressure and temperature are reasonably Earth-like and, as a result, some advanced space exploration studies have considered telecommunication by means of the critical ray (J. E. Blamont, personal communication, 1974). Through the application of the result given here, the strength of such a propagation mode can be determined. The result also has potential applications in geocentric studies and in other media which possess either spherical or cylindrical symmetry.