Influence of field potential on the speed of light

The paper discusses the affection of the scalar potential on the speed of light in the electromagnetic field, by means of the characteristics of octonion. In the octonion space, the radius vector is combined with the integral of field potentials to become one new radius vector. When the field potentials can not be neglected, the new radius vector will cause the prediction to departure slightly from the theoretical value of the speed of light. The results explain why the speed of light varies in diversiform optical waveguide. And there exist negative refractive indexes due to different scalar potentials in the gravitational field and electromagnetic field.