  Despite the extraordinary attention that modified gravity theories have
attracted over the past decade, the geodesic deviation equation in this context
has not received proper formulation thus far. This equation provides an elegant
way to investigate the timelike, null and spacelike structure of spacetime
geometries. In this investigation we provide the full derivation of this
equation in situations where General Relativity has been extended in
Robertson-Walker background spacetimes. We find that for null geodesics the
contribution arising from the geometrical new terms is in general non-zero.
Finally we apply the results to a well known class of f(R) theories, compare
the results with General Relativity predictions and obtain the equivalent area
distance relation.
