fuckyeahphysica:

The Illumination Problem

Ernst Straus asked this thought-provoking question:

Can a single point of light always illuminate a room that is lined with mirrors, entirely ? ( allowing for repeated reflections )

And the solutions are extremely fascinating from a mathematical and a physics perspective.

Roger Penrose’s Unilluminable Room

Roger Penrose solved the problem by using ellipses and cleverly placed mushrooms.

                     PC: cmglee

He showed that there exists a room that must always have dark regions if lit only by a single point source, irrespective of the position of the source.

                                           PC: Wolframalpha

Tokarsky and Castro  solution

Tokarky(1995) and Castro(1997) solved the problem in 2D for polygonal rooms.

They showed that for 26 and 24 sided polygons given below, if the red dot is the source, the X denotes a “dark spot” where the light does not illuminate.

                                                  PC: cmglee

Why is this cool ?

Well. whenever we think of rooms covered with mirrors, we are dwindled into thinking that all parts of the room are completely illuminated by a light source placed at any arbitrary position.

To most it might be a mundane question to ponder upon, but the profuse secrets that belies such a question is remarkable !

Have fun exploring the mysteries of the universe!

Source:

Tokarsky’s paper – Polygonal Rooms Not Illuminable from Every Point