We present a theoretical study on the effect of refractive index variations on static and dynamic light scattering in size-polydisperse suspensions of sterically and charge-stabilized colloidal particles with an internal optical structure (core-shell model) and size-dependent refractive indices. The equilibrium microstructure and the short-time dynamics of these optically, size-, and interaction-polydisperse systems are calculated using hypernetted chain and Percus-Yevick integral equation schemes. Our calculations show that, close to an index matching point, the scattered intensity I(k), the measurable structure factor S-M(k), and the measurable hydrodynamic function H-M(k) become very sensitive to the refractive index contrast with respect to the solvent. For this purpose, various definitions of index matching points are analyzed, and the strong relative enhancement of the incoherent part of the scattered intensity close to the matching points is discussed. For charge-stabilized systems we show that the anomalous behaviour of I(k) and H-M(k) in the matching regime of the solvent refractive index can be well described by a simple approximative scheme, which can be easily implemented. Consequences of our study for scattering experiments aimed to determine particle sizes or structural properties of colloidal dispersions are discussed,