  Close binary systems often show linear polarization varying over the binary
period, usually attributed to light scattered from electrons in circumstellar
clouds. One of the brightest close binary systems is Spica (Alpha Virginis)
consisting of two B type stars orbiting with a period of just over 4 days. Past
observations of Spica have shown low polarization with no evidence for
variability. Here we report new high-precision polarization observations of
Spica that show variation with an amplitude ~200 parts-per-million (ppm). Using
a new modelling approach we show that the phase-dependent polarization is
primarily due to reflected light from the primary off the secondary and vice
versa. The stars reflect only a few per-cent of the incident light, but the
reflected light is very highly polarized. The polarization results show that
the binary orbit is clockwise and the position angle of the line of nodes is
130.4 +/- 6.8 degrees in agreement with Intensity Interferometer results. We
suggest that reflected light polarization may be much more important in binary
systems than has previously been recognized and may be a way of detecting
previously unrecognized close binaries.
