In this work we analyze the internal reflection (Fresnel reflection) from Au nanoparticles on the end face of optical fibers. We demonstrate that changes in the refractive index of the surrounding medium can be detected by shifts in the reflection spectra associated with changes in the Localized Surface Plasmon Resonance of the Au-Nanoparticles. The spectral response is simulated using a model based on the interference in multilayer structures and can be described by transfer-matrix method.