That's true, but also keep in mind that the visible light that is created by the excited particles will not be aligned in the same way, and should be uniformly dispersed from their point of origin.

In other words, just because the UV light went in one side, and came out the other, along a specific path, doesn't mean that the visible light emanating from the glow particles that got excited along the way is going to follow the same path. Each individual glow particle should send out light in all directions, regardless of what direction the light that excited it came from.

So, the visible light should be much more dispersed, because it will be emanating from many, many points inside the material itself, in every direction, instead of all coming from basically the same point, and in mostly the same direction.

Uhmmm... I hope this makes sense... I'm sorta tired today...