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, . Changes in dipolar resonances and scattering directionality conditions as a function of the core radius (R int) for a fixed shell size ( nm) have been analysed. An empirical formula to obtain the ratio by monitoring the influence of the magnetic dipolar resonance in 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 to m med. It has been demonstrated that multipolar contributions strongly influence . 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.