Optical properties of polymer capped gold nanoparticles of various sizes (diameter 3-6 nm) have been studied. We present a new scheme to extract size dependent variation of total dielectric function of gold nanoparticles from measured UV-Vis absorption data. The new scheme can also be used, in principle, for other related systems as well. We show how quantum effect, surface atomic co - ordination and polymer - nanoparticle interface morphology leads to a systematic variation in inter band part of the dielectric function of gold nanoparticles, obtained from the analysis using our new scheme. Careful analysis enables identification of the possible changes to the electronic band structure in such nanoparticles.