Penrose Unilluminable Room
Penrose Unilluminable Room is a room with mirrored walls that can't be fully illuminated by a single point source of light
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
A room built with mirrored walls seems like it should be lit everywhere by a single lamp, since light keeps bouncing until it reaches every corner. The Penrose unilluminable room is a counterexample: a room shaped from curved, ellipse-like walls where some spots can never be reached by light from a chosen lamp position, no matter how many times the light reflects. Ellipses and their reflection property are not part of the standard DP syllabus, so this exploration relies on simulating reflection paths (angle of incidence equals angle of reflection) rather than a formula from the course, and on testing simple room shapes first to see why rectangular rooms are always fully lit.
Guiding Questions
- A room with mirrored walls can still have dark spots. How does light travel and reflect in 2D?
- Trace reflections in simple room shapes. Why does a rectangular room always get fully lit?
- The Penrose room uses curved (elliptical) walls. What property of the ellipse traps the light?
- Build or simulate the room and find the regions a single lamp can never light.