Just how long is the portal tunnel? By tunnel I mean the intermediary portion between portal ends through which you travel.
If it has no thickness and stuff that crosses the portal surface immediately appears on the other side then what happens if you push your hand against the edge (the oval glowing edge) of the portal? Think of pushing against the edge of a hole in a sheet of paper. I imagine that if it has a thickness and it's going to be small (really tiny) then you should get your hand cut in two.
Obviously, the full mechanic of portals is not implemented in the games - this is a question related to the "Portal" universe and not necessarily the portal games.