  Within the framework of independent particle approximation, the optical
activity tensor of solids is formulated as from different contributions: the
magnetic dipole, electric quadrupole, and band dispersion terms. The first two
terms have similar counterparts in the theory of finite systems, while the last
term is unique for crystals. The magnetic dipole and electric quadrupole
transition moments are calculated with a sum-over-states formulation. We apply
the formulation to calculate and analyze the optical rotation of elemental
tellurium and the circular dichroism of $(6,4)$ carbon nanotube. Decomposed
optical activity into different contributions are discussed. The calculated
spectra agree well with experiments. As a showcase of achiral crystals, we
calculate the optical activity of wurtzite GaN.
