Abstract
The analogy between optics and mechanics provides a unified way to describe particle motion in mechanics and light propagation in geometrical optics, and recent publications have demonstrated that this analogy can also be applied to general relativity, specifically when dealing with static metrics. In this paper, we use the material medium approach to obtain the refractive index associated with the gravitational field of a compact object having a quadrupole moment. Within this approach, we explore well-known effects of general relativity such as redshift and radar echo delay, deriving mathematical expressions for these phenomena taking into account the influence of the quadrupole moment.