Localized surface plasmon resonance (LSPR) has been used to develop optical biosensors. Tuning the resonance wavelength to detect target biomolecules with a particular dipolar resonance is essential when designing LSPR biosensors. In this paper, the interaction of nanoparticles (NPs) with glass substrate (SiO(2)) for LSPR wavelength is investigated using the concept of the image-charge theory. Using the FDTD method, it is shown how the NP and substrate size change the plasmon wavelength. Next, this phenomenon is interpreted using the analytical electrostatic eigenvalue method.