The anisotropic optical response of Si(111)-(4x1)/(8x2)-In in the midinfrared, where ab initio studies predict significant changes in the band structure between competing models of this important quasi-1D system, has been measured using infrared spectroscopic ellipsometry (IRSE) and reflection anisotropy spectroscopy (RAS). Both IRSE and RAS of the (8x2) phase show that the anisotropic Drude tail of the (4x1) phase is replaced by two peaks at 0.50 and 0.72 eV, which appear in ab initio optical response calculations for the hexagon model of the (8x2) structure, but not the trimer model.