A geometric optics method for calculating light propagation in gravitational fields

If one examines the general form of solutions to Einstein field equations, it can be seen that the space–time structure of light in a gravitational field and the definition of light speed in a medium can be expressed in the same form. On the basis of this, it is possible to consider a gravitational field to be a special kind of optical medium. By adopting this approach, this paper obtains an expression of the refractive index in a gravitational field. Equations pertaining to refraction and the delay of light propagation in gravitational fields are obtained by using a ray-tracing method derived from geometric optics. Taking the light traveling between Earth and Mercury as an example, which passes over the sun, the proposed method is used to calculate the refraction and delay of light propagated in the solar gravitational field. The calculated results are found to be in agreement with previous test results. The results are then compared to formulas based on general relativity and the validity of the geometric optics method is verified.