Gaps between adjacent light rays from a light source

I can not seem to grasp light rays FILLING space like air and liquid in an enclosure. Two rays adjacent to each other coming from Sun, - do they not diverge as they go into space? If so is there not dark space gap between them, constantly increasing? How come when the sun is up in the sky, we do not perceive these dark spaces as night, as we travel around the sun while facing it, like an interference pattern? I hope my Q is clear.