Polarization optics of the Brewster's dark patch visible on water surfaces versus solar height and sky conditions: theory, computer modeling, photography, and painting.

When the sun is near the horizon, a circular band with approximately vertically polarized skylight is formed at 90° from the sun, and this skylight is only weakly reflected from the region of the water surface around the Brewster's angle (53° from the nadir). Thus, at low solar heights under a clear sky, an extended dark patch is visible on the water surface when one looks toward the north or south quarter perpendicular to the solar vertical. In this work, we study the radiance distribution of this so-called Brewster's dark patch (BDP) in still water as functions of the solar height and sky conditions. We calculate the pattern of reflectivity R of a water surface for a clear sky and obtain from this idealized situation the shape of the BDP. From three full-sky polarimetric pictures taken about a clear, a partly cloudy, and an overcast sky, we determine the R pattern and compose from that synthetic color pictures showing how the radiance distribution of skylight reflected at the water surface and the BDPs would look under these sky conditions. We also present photographs taken without a linearly polarizing filter about the BDP. Finally, we show a 19th century painting on which a river is seen with a dark region of the water surface, which can be interpreted as an artistic illustration of the BDP.