TITLE: Symmetric black-hole curves
QUESTION [6 upvotes]: Is there a curve $C$ that connects $(0,1)$ to $(a,0)$ for some $a>0$, and, when reflected
to $C'$ in the $x$-axis, the shape $S=C \cup C'$ has the property that each horizontal
light ray entering $S$ from the left reflects off of $S$ (interpreted as a perfect mirror)
in such a way that it never emerges, i.e. it never again crosses $x=0$?
For example, a straight line $C$ fails to be such a curve:

REPLY [11 votes]: I will do it since Fedya has no time. 
An example of black hole for a strip of horizontal light rays can be constructed from two arcs of parabolas with common focus and vertical directrixes.

You can add horizontal mirrors and take a pair of them with reflections in $x$-axis and get the curve you want, say as it shown on the following picture.