  In the current article we discuss an illumination problem proposed by Urrutia
and Zaks. The focus is on configurations of finitely many two-sided mirrors in
the plane together with a source of light placed at an arbitrary point. In this
setting, we study the regions unilluminated by the source. In the case of
rational-$\pi$ angles between the mirrors, a planar configuration gives rise to
a surface with a translation structure and a number of planar infinities. We
show that on a surface of this type with at least two infinities, one can find
plenty of unilluminated regions isometric to unbounded planar sectors. In
addition, we establish that the non-bijectivity of a certain circle map implies
the existence of unbounded dark sectors for rational planar mirror
configurations illuminated by a light-source.
