Obviously, if the only outgoing ray from the intersection point is the blue on in the diagram, we would have what is essentially an ideal opaque mirror. But since the green vector also goes through the material, I wonder if we may be able to control the opacity of the material perhaps by scaling or selectively removing the green vector. An alternative thought I had would be to make a probabilistic model where light would either reflect with probability p or go through the surface with probability 1-p, and have this probability change the "deeper" inside the (solid) material you are.
I find it interesting that the image to the left looks more like clear plastic than water to me. I think it's mostly because of the fact that most people associate water with a flat surface, not with a rounded, odd-shaped surface.
For ideal mirror surfaces we characterized them by the reflected ray direction with respect to our original ray; for ideal reflective/refractive material do we follow the same characterization? i.e. the refracted and reflective rays seem to be orthogonal in the image, is this part of the definition of the ideal case?
What's the distinction between BRDF and BSDF?