How many dimensions are required minimum for an object to block light?
in 1d I doubt it's possible.
in 2d I think it could do it if only the light was limited to a dimension perpendicular to the 'thickness' dimension
in 3d I think it could do it no matter what dimension the object was looked at in.
Clarification: 3d -> A block of wood can "block light" (make a shadow) no matter how you shine light at it.
Edit: What about what are the minimum dimensions needed to block light assuming you are dealing with an $n$ dimensional space?