  We present calculations of the optical absorption and electro-absorption
spectra of graphene nanoribbons (GNRs) using a $\pi-$electron approach,
incorporating long-range Coulomb interactions within the Pariser-Parr-Pople
(PPP) model Hamiltonian. The approach is carefully bench marked by computing
quantities such as the band structure, electric-field driven half metallicity,
and linear optical absorption spectra of GNRs of various types, and the results
are in good agreement with those obtained using\emph{ab initio} calculations.
Our predictions on the linear absorption spectra for the transversely polarized
photons provide a means to characterize GNRs by optical probes. We also compute
the electro-absorption spectra of the zigzag GNRs, and argue that it can be
used to determine, whether or not, they have a magnetic ground state, thereby
allowing the edge magnetism to be probed through non-magnetic experiments.
