Penrose Unilluminable Room
Overview: A special room that was designed by Roger Penrose. A room with reflective walls where the shape of the room is such that no matter where a light source placed in the room there will always be at least one spot that the light does not touch.
Supplies: Penrose Unilluminable Room model, LED light source
Objectives: Move the LED light source around the room to see if it is truly completely unilluminable
Setup:
- Place the room model on the table
- Turn on the LED
How to run the demo:
- Move the light source around the model to show that it is truly unilluminable
What’s Happening?
Roger Penrose’s design consists of two elliptical walls on the top and bottom and a rectangular area with two umbrella cutouts. The only requirements for the design to work are that the top and bottom walls are described as an ellipse and that the focal points of the ellipse coincide with the corner points of the umbrellas.
How does it work? When you take into account the properties of an elliptical mirror (which we wont go into here), there are 3 things that happen with this room design. Refer to the diagram below.
- A light source placed inside
will only illuminate
, and
because it can never intersect the long axis of the ellipse between the focal points and enter the
area.
- A light source placed in
and
unilluminated because the light rays can only enter the lower half of the room between the two focal points of the lower ellipse. Thus, they can never intersect the long axis between the focal points and apexes and enter
- A light source placed in
Learn more: (external links)