Indirect lightning/ light source reflection

I’m trying to render the following scene as show with my simplified scheme. The goal is to capture the exact form of the reflected light that falls on the plane. Basically everything in my scene should be completely dark and only the shape of the reflected light on the plane should be as bright as possible with sharp border between light and dark.
I’ve tried to play with the indirect lightning options in the blender renderer and also with the external yafaray renderer, but I wasn’t able to achieve the desired target.
I’d be grateful for any help pointing me in the right direction on how to achieve this task.