Almost every version of trapping lightrays with mirrors is either resolved---usually negatively---or open:
- "It is unknown whether one can construct a polygonal trap for a parallel beam of light": Serge Tabachnikov. Geometry and Billiards, p. 116.
- Can we trap light in a polygonal room?
- Trapped rays bouncing between two convex bodies
- Trapping light rays aperiodically: Mitchell, Zachary, Gregory Simon, and Xueying Zhao. "Trapping light rays aperiodically with mirrors." Involve, a Journal of Mathematics 5.1 (2012): 9-14.
- Light rays bouncing in twisted tubes
- Blocking light with mirrored convex objects
- Trapping Light Rays with Segment Mirrors
However, there are variations in the reflection laws that might change matters:
- Billiard dynamics with angle of reflection a fraction of angle of incidence
- Billiard dynamics under gravity
- Periodic billiard paths in hyperbolic triangles
My question is:
Q. Can one "construct a polygonal trap for a parallel beam of light" (to quote Tabachnikov) under a natural different model of reflection and/or paths under gravity?
I think for billiards under gravity the answer is likely Yes, but I have little intuition for reflections at a fraction of angle of incidence.
Trapping a ray between two disks.
Paths under gravity.
