Given a point $A$ inside a non-convex polygon $P$, is it always possible to place a finite set of mirrors (not necessarily along the boundary of $P$, any position inside $P$ is allowed) given by straight segments such that every point of $P$ is visible from $A$? (Light-rays propagate along straight lines, are reflected in the usual way on both sides of mirrors and are absorbed by the boundary of $P$.)

Is there a position of mirrors which is "universal" in the sense that any pair of points inside $P$ are within view of each other?

These questions have of course obvious higher-dimensional generalizations.