Question: is there a fabric which allows you to see through it in one
direction, but not the other (rather like a one-way mirror, as used in
police stations to observe interviews from behind what appears to be a
mirror)? Doesn't have to be mirrored, but does have to allow vision in
one direction only.

This fabric also needs to be flexible, and have good strength
properties.  Some additional details (supplier, cost, weight) would be
appreciated.

For example, I would be able to hang this fabric sheet in the middle of a
room and be able to see through in one direction only.  The way that
you can see a torch shadow inside a tent at night is not enough.  I
accept that the light levels will probably have to be different on each side,
but I want to be able to see through clearly.

In the theater, there is a fabric called a Scrim that when lit from the front
is opaque to some degree but when standing behind, you can still see
through to some degree..  This will be better than the tent effect,
but the scrim by no means is transparent from behind, but you can see
through.

A previous google answer has listed numerous contacts for theatre
fabric suppliers,
http://www.answers.google.com/answers/threadview?id=355066

you can proably get a sample from one of the suppliers to see if it is
transparent enough from benhind for you.