How much larger will your classroom seem to appear if the entire two adjacent walls of your classroom consist of plane mirrors?

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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As you probably know, an image reflected from a plane mirror is located behind the mirror at the same distance from the mirror as the object. Also, the straight line connecting an object and its reflection is perpendicular to the mirror.

This and the path or the ray from the object (`O` ) to the watcher (`W` ) are shown at the right part of the uploaded picture. Note equal angles and equal lengths marked.

So each mirror wall gives us one imaginary room adjacent to the real. But two mirrors can work together: some rays will reflect from one mirror, then from the another. This gives us the third imaginary room adjacent to the two imaginary rooms mentioned before.

Please look at the left part of the uploaded picture for the proof. `O_1` is the reflection of `O` at the first mirror, `O_1` resides in the first imaginary room. `O_2` is the reflection of `O` at the second mirror, it resides in the second imaginary room.

`O_3` is the result of a double reflection. The path of the twice reflected ray from `O` to `W` is shown and equal angles and lengths are marked.

It is possible to say that `O_3` is the reflection of `O_1` from the virtual mirror, obtained by the reflection of the second mirror from the first mirror (or vice versa, `O_3` is the reflection of `O_2` from the virtual mirror, obtained by the reflection of the first mirror from the second mirror).

So the answer is: our classroom will seem to appear twice larger by each dimension. And it will 4 times greater by the area.

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