The optical properties of (8, 0) single walled carbon nanotubes alloyed with nitrogen (N) have been examined using relaxed carbon-carbon (C-C) bond length ab initio density functional theory (DFT) calculations in the long wavelength limit. The maximum value of the absorption coefficient is shown to depend strongly on the concentration of N in a non-linear way as well as on the direction of polarization. The reflectivity at normal incidence vanishes at some unique concentration of N. It is also observed that the peak of the loss function (in parallel polarization and unpolarized cases) shifts to a higher frequency indicating the enhanced metallic character. The observed variation of the plasma resonance frequencies with N concentration indicates the existence of a unique maximum for parallel polarization and a step function like behavior for the unpolarized situation with concentration.