  We compute the optical conductivity of graphene beyond the usual Dirac cone
approximation, giving results that are valid in the visible region of the
conductivity spectrum. The effect of next nearest neighbor hoping is also
discussed. Using the full expression for the optical conductivity, the
transmission and reflection coefficients are given. We find that even in the
optical regime the corrections to the Dirac cone approximation are surprisingly
small (a few percent). Our results help in the interpretation of the
experimental results reported by Nair {\it et al.} [Science {\bf 320}, 1308
(2008)].
