Mirrors!

When you look at a mirror AB, a perfectly symmetric reflection of the entire room is created inside the mirror. This is equivalent to a virtual image of the room the mirror sits in, in the direction of the wall which holds the mirror, as in Fig. 1.

one mirror
Fig. 1: Virtual image of room because of mirror AB

What happens if we place mirrors on all four walls of a room? Each mirror creates a virtual image of the room, in the direction of the wall which holds the mirror.

Further, because the virtual images contain images of the real mirrors, an infinity of virtual rooms is created, going infinitely deep into virtual land.

EucliDraw allows a dynamic visualization of such a situation, down to any desirable level. Fig. 2 shows the situation for a room in the shape of a trapezium with mirrors on all four walls and the virtual images of the room going up to level 2.

four mirrors level 2
Fig. 2: Virtual images of room because of four mirrors on all walls, to level 2, with non-parallel walls

Fig. 3 is the same situation down to level 3, with the walls being parallel.

Four Mirrors Level 3 Parallel
Fig. 3: Virtual images of room because of four mirrors on all walls, to level 3, with parallel walls

If the walls are non-parallel, the situation becomes quite complex and is very interesting, as in Fig 4:

Four Mirrors Level 3 Non-Parallel
Fig. 4: Virtual images of room because of four mirrors on all walls, to level 3, with non-parallel walls

Notes/References

  1. Download a EucliDraw dynamic geometry document which shows the resultant reflections to level 3, here. Click and move any point on the document, to witness the reflections. For this you'd need to download the free EucliDraw viewer to open this document.

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