Abstract The main objective of this thesis work is to investigate the effect of size on the optical properties of silver nanoparticles based on dielectric function by applying size corrected Drude model. The effect of size on the dielectric function and refractive index of smaller size nanoparticles is higher, but its effect decreases with increasing the size of silver nanoparticles. As the size increase, the value of the dielectric function of silver nanoparticles closes to the bulk dielectric function. But, silver nanoparticles have large imaginary part and smaller real part than bulk silver. The real part of the dielectric function of silver nanoparticle mainly depends on frequency of the incident light but weakly depends of size. But, the imaginary weakly depends on wavelength, but mainly depends on size. The dielectric function of silver nanoparticles affect the optical density and extinction cross-section features such as full width at half maximum, peak position and the amplitude of the resonance. The resonance peak of the optical density of silver nanoparticle first increases size up to 30 nm, but it decreases above 30 nm. When size increases, the contribution of scattering for extinction increases. For smaller nanoparticles, resonance of extinction cross-section is due to absorption. For smaller nanoparticles ( 2R λ = 1:20), maximum extinction arises when the real part of the dielectric function equals the negative of twice the dielectric max function of the surrounding medium. At quasi-statics approximation the band width decreases with increases size. Key Words: dielectric function, Drude model, imaginary part, nanoparticles, plasmons, real part, size, spectra.