The index of refraction plays a role, but it is not the most important parameter. What matters most is the structure of the surface. Because there are many ways a surface might be structured, I hesitate to describe it as “roughness”. However, that’s the general idea. There are different parameterized descriptions of surface roughness, and most of them can be directly translated into scattering profiles.. In fact, going the other direction, scatterometry is a standard metrology technique for characterizing surface roughness. So what I’m trying to say is that scattering and roughness go hand-in-hand. Roughness, or similar surface structure, or similar micro inhomegeneity is the most important component of scattering.

if the surface has features that tend to be large compared to the wavelength of the light, then you can describe the scattering pretty accurately by assuming each little wavelength sized region is locally smooth. Each little region contributes its bit of Fresnel coefficient reflection and/or refraction. Angle of incidence equals angle of reflection, and Snell’s law applies. (which is how and why the index matters). Ray tracing applies. The net scattering is the sum of all the pieces (coherent sum if you are scattering a coherent light source) This simple construction doesn’t describe multiple scatterings. Particularly steep facets may reflect into another facet on the same surface, so sometimes a ray scatters twice or more. However that is often unimportant as in many cases the surface roughness doesn’t get that steep anywhere.

Note that it isn't just the refractive index of the scattering object that matters in these contexts, it is the *difference* between the refractive index of the background medium as compared to that of the scatterer. The bigger the difference in refractive index, the more reflection you get from interfaces.

Suppose the excitation/scattering is caused by a single plane wave and the scattering system is optically perfectly homogeneous, then inside that system only a single plane wave can exist. This is true independent from the type of description: continuum (refractive index) or discrete (Ewald/Oseen).

When the response obeys conditions of linear stimulated emission, the sources do the scattering. In the continuum description this is less clear, since they are usually eliminated in the early stages of description. In a discrete description the dipoles and their polarizabilities do the scattering. In general they do so in all directions. Only for the case that the dipoles have a perfectly crystalline geometry and occupy a half space, three plane waves suffice to describe the classical reflection/transmission story. That is

an exception. However, when these regularities do not apply and scattering

becomes visible, it becomes extremely difficult to find proper mathematical solutions and that is the real problem.