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Problem 31: Trapping Light Rays with Segment Mirrors
 Statement
 Is it possible to trap all the light from one point source
by a finite collection of twosided disjoint segment mirrors?
A light ray is trapped if it includes no point strictly
exterior to the convex hull of the mirrors.
The source point is disjoint from the mirrors.
Although several versions of the problem are possible, it
seems to make the most sense to treat the mirrors as open
segments (i.e., not including their
endpoints), but demand that they are disjoint as closed segments.
 Origin
 O'Rourke and Petrovici [OP01].
The question seems natural enough to have been raised earlier, but no other
source is known.
 Status/Conjectures
 Conjecture 9 from that paper:
``No collection of segment mirrors can trap all the light from one
source.''
 Partial and Related Results
 In [OP01] several other conjectures are formed that
imply a resolution to the posed problem.
The strongestthat no collection of mirrors as above can support
even a single nonperiodic ray, i.e.,
one that reflects forever (so is trapped)
but never rejoins its earlier pathwas disproved by
Ben Stephens in 2002, who designed
a contruction of 8 mirrors that traps a ray reflecting
nonperiodically.
A similar construction was discovered and described in [MSZ09],
which also established that any finite number of rays can be trapped
nonperiodically.
Milovich [Mil04] proved that if the angles between the lines
containing the mirrors are rational multiples of π,
then all but a countable number of light rays escape.
In his book on billiards, Tabachnikov says,
``It is unknown whether one can construct a polygonal trap
for a parallel beam of light'' [Tab05, p. 116].
This is in contrast to known nonpolygonal traps for such beams.
 Related Open Problems
 Pach's ``enchanted forest'' of circular mirrors.
 Appearances
 Presented at the Open Problem session of the
13th Canad. Conf. Comput. Geom.,
Waterloo, Ontario, Aug. 2001. Also, Oberwolfach, Jan. 2009.
 Categories
 visibility
 Entry Revision History
 J. O'Rourke, 28 Aug. 2001; 24 Feb. 2003; 5 Oct. 2005; 7 Sep. 2009.
 Mil04

David Milovich.
Trapping light with mirrors.
MIT Undergrad. J. Math., 6:153180, 2004.
 MSZ09

Zachary Mitchell, Gregory Simon, and Xueying Zhao.
Trapping light rays aperiodically with mirrors.
Unpublished manuscript, August 2009.
 OP01

Joseph O'Rourke and Octavia Petrovici.
Narrowing light rays with mirrors.
In Proc. 13th Canad. Conf. Comput. Geom., pages 137140, 2001.
 Tab05

Serge Tabachnikov.
Geometry and Billiards, volume 30 of Mathematics Advanced
Study Semesters.
American Mathematical Society, 2005.
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The Open Problems Project  September 19, 2017