The problem statement

Find the lightpath with a given starting and ending points via one or more mirrors.

In those kind of problems you try image someone pointing a laser with a very narrow beam at a certain direction to the mirror, so it will reach point B.

For example:

You are seeing a square mirror room (with mirrored walls a, b, c, d) where you point from point A via the mirrors c, b, d and a to point B. A sketch can be made easily made:


In order to find a more accurate solution, we flip the base cell with the points A and B a few times as shown in the image. After the mirroring is done, the line connecting A is drawn towards the mirror image B'.

Question: Construct the path in the original square. Complete the drawing.


My confusion

Why do I need to do with those virtual squares? I don't see an logical way to draw the reflections easily. And why is the line drawn from A to B' through all those other virtual rooms?


1 Answer 1


Your drawing is incorrect. The ray from A to surface c is not correctly reflected. The particular 4 faces c, b, d, a, are sequentially hit without involving any face(s) parallel to the plane of the page, so we are seeing the plane projection of any three-D paths.

The Ac, bd, aB lines must be parallel, just as the cb, da lines are parallel.

Optics is applied geometry. Freehand sketches don't work.


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