If I think about the wave nature of light, then a material's refractive index is sort of the "density" of the medium. Light travels more slowly through materials with higher refractive index. As you know, this is actually due to the absorption and retransmission of photons from atom to atom, somewhat analogous to your marbles illustration of sound. Both models support wave-like behavior in aggregate.

Thus, when light moves from a "faster" medium to a "slower" one, refractions and reflections result that are similar in character to acoustic reflections.

That's how I think of it anyway.