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The localized surface plasmon (LSP) enhancement in a gold nanoparticle is demonstrated in this paper. The enhancement of LSP is influenced by both size and the dielectric gain medium surrounding the nanoparticles. The nanoparticle is found to induce plasmonic enhancement of varying degrees depending on its size, and it is inferred that a gold nanoparticle of size 60 nm exhibits the maximum LSP for 532 nm excitation. Singularity due to cancellation of SP loss by an infinite gain medium and LSP enhancement are studied using a pump-probe Rayleigh scattering experiment. Gold nanoparticles of average size 60 nm exhibit the lowest threshold power to observe Rayleigh scattering. Furthermore, compared with the bare nanoparticles, a 12.5 fold enhancement of LSP is observed when the nanoparticle of average size 60 nm is kept in the gain medium.