We have measured the ratio R of the vector ac-Stark effect (or light shift) in the 6S 1/2 and 5D 3/2 states of a single trapped barium ion to 0.2 % accuracy at two different off-resonant wavelengths. We earlier found R = ∆S/∆D = −11.494(13) at 514.531 nm where ∆S,D are the vector light shifts of the 6S 1/2 and 5D 3/2 m = ±1/2 splittings due to circularly polarized light, and now we report the value at 1111.68 nm, R = +0.4176(8). These observations together yield a value of the 5D||er||4F matrix element, previously unknown in the literature. Also, comparison of our results with an ab initio calculation of dynamic polarizability would yield a new test of atomic theory and improve the understanding of atomic structure needed to interpret a proposed atomic parity violation experiment.