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If an observer where too stand with a lamp in a room with mirroring walls, what would the observer view in the mirrors.

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Ideally one should be able to see infinitely many lamps due to multiple reflections from various walls, the floor and the ceiling, arranged into an optical illusion of a cubic lattice. However, each reflection appears to be more distant than the previous one, so eventually they become too small to discern. Moreover in reality mirrors are not perfect, some light is absorbed, some scattered, so after a finite number of reflections there is no light left to reflect further. As a result, only finite number (albeit possibly large) of reflections is visible.

See images under Wikipedia's infinity mirror article for what happens with just two parallel mirrors. For your case look at Kusama's Infinity Mirror Rooms:

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  • $\begingroup$ Can this be observed from outside the room. Whereby one of the walls are transparent on one side and reflective on the other. $\endgroup$ – John May 11 '17 at 20:29
  • $\begingroup$ @John Not exactly since the person inside can also look up, down, to the sides, while from the outside the view is only through one transparent wall. $\endgroup$ – Conifold May 12 '17 at 19:24
  • $\begingroup$ Moreover, the mirrors are not perfectly flat, so the "more distant" reflections become progressively more distorted. (I've been in a room like that---a temporary exhibit at some science museum, a long time ago. Today it would be called an "art installation.") $\endgroup$ – Solomon Slow May 12 '17 at 20:17
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    $\begingroup$ @John just stand outside and look through an edge-slot in the cube. (If the mirrors have slots where the edges join, then the interior 3D view will have a cubical lattice made of edge-slots.) My own sci-museum idea: tilt one vertical mirror, and the infinite floor becomes a finite sphere, then vary the tilt to select your asteroid diameter. Once you intuitively "feel" the Earth as being a very large ball, will the feeling ever fade? $\endgroup$ – wbeaty May 13 '17 at 6:43

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