The influence of increasing the core size of Ag-Si core-shell nanoparticles has been investigated by using the values of the linear polarization degree at a right-angle scattering configuration, [Formula: see text]. Changes in dipolar resonances and scattering directionality conditions as a function of the core radius (R int) for a fixed shell size ([Formula: see text] nm) have been analysed. An empirical formula to obtain the ratio [Formula: see text] by monitoring the influence of the magnetic dipolar resonance in [Formula: see text] has been found. The effect of the refractive index of the surrounding medium, m med, in the zero backward and almost-zero forward scattering conditions has also been studied. We have weighed up the sensitivity of [Formula: see text] to m med. It has been demonstrated that multipolar contributions strongly influence [Formula: see text]. This influence can be used as a fast m med estimate. In all cases, the results show that the bigger the cores, the higher the sensitivity to m med.