For gratings having an arbitrary symmetric profile, we prove that when the period becomes much finer than the wavelength the grating becomes equivalent to a graded uniaxial layer. We show for one polarization that this quasi-static equivalence holds when the ratio of wavelength to grating period exceeds 40. We also present a simple physical model which explains the anisotropic nature of the equivalent layer. We take the case of a finely-textured copper surface, and show that it can be a good selective absorber for polarized light, but that its performance in unpolarized light is much less satisfactory.