We have remotely mapped optical scattering and absorption in glacial ice at the South Pole for wavelengths between 313 and 560 nm and depths between 1100 and 2350 m. We used pulsed and continuous light sources embedded with the AMANDA neutrino telescope, an array of more than six hundred photomultiplier tubes buried deep in the ice. At depths greater than 1300 m, both the scattering coefficient and absorptivity follow vertical variations in concentration of dust impurities, which are seen in ice cores from other Antarctic sites and which track climatological changes. The scattering coefficient varies by a factor of seven, and absorptivity (for wavelengths less than ~450 nm) varies by a factor of three in the depth range between 1300 and 2300 m, where four dust peaks due to stadials in the late Pleistocene have been identified. In our absorption data, we also identify a broad peak due to the Last Glacial Maximum around 1300 m. In the scattering data, this peak is partially masked by scattering on residual air bubbles, whose contribution dominates the scattering coefficient in shallower ice but vanishes at ~1350 m where all bubbles have converted to nonscattering air hydrates. The wavelength dependence of scattering by dust is described by a power law with exponent -0.90 ± 0.03, independent of depth. The wavelength dependence of absorptivity in the studied wavelength range is described by the sum of two components: a power law due to absorption by dust, with exponent -1.08 ± 0.01 and a normalization proportional to dust concentration that varies with depth; and a rising exponential due to intrinsic ice absorption which dominates at wavelengths greater than ~500 nm.