We fabricate and measure graded-index “black silicon” surfaces and find the underlying scaling law governing reflectance. Wet etching (100) silicon in HAuCl4, HF, and H2O2 produces Au nanoparticles that catalyze formation of a network of -oriented nanopores. This network grades the near-surface optical constants and reduces reflectance to below 2% at wavelengths from 300 to 1000 nm. As the density-grade depth increases, reflectance decreases exponentially with a characteristic grade depth of about 1/8 the vacuum wavelength or half the wavelength in Si. Observation of Au nanoparticles at the ends of cylindrical nanopores confirms local catalytic action of moving Au nanoparticles.