Physical Interpretation
The physical meaning of the eikonal equation is related to the formula
where is the electric field intensity and is the electric potential. There is a similar equation for velocity potential in fluid flow and temperature in heat transfer. The physical meaning of this equation in the electromagnetic example is that any charge occurring in the region is pushed outward at a right angle from lines of constant potential and this charge travels along lines of constant force given by the field of the E vector. Corresponding variables occur in thermodynamics and fluid flow. Ray optics and electromagnetics are related by the fact that the eikonal equation gives a second electromagnetic formula of the same form as the potential equation above where the line of constant potential has been replaced by a line of constant phase and the force lines have been replaced by normal vectors coming out of the constant phase line at right angles. The magnitude of these normal vectors is given by the square root of the relative permittivity. The line of constant phase can be considered the edge of one of the advancing light waves. The normal vectors are the rays the light is traveling down in ray optics.
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