Which virtual cells look the same as the basic cell?

1. Nov 14, 2013

PintoCorreia

1. The problem statement, all variables and given/known data

Above is the basic cell drawn with an object inside of it. You look in top view of the basic cell and the space around it filled with virtual cells.

You can see the top view of a basic cell (the square [that is marked blue] formed by the four real mirrors with a height of 10 cm, with the original physical object with a height of 5 cm inside ) and all the copies (mirror images and mirror images of mirror images) around it, which fill a plane.
Question 1: Which virtual cells look the same as the basic cell? Do You see a regularity/pattern?
Explain this mathematically.

2. Relevant equations
mirror reflections

3. The attempt at a solution
1. I don't understand that whether there is a name for those kind of patterns or not. And How many reflections I should draw. I guess it could be an infinite amount... So anyone a clue?

2. Nov 14, 2013

CWatters

Pretend each mirror in turn is the only mirror that exists. eg Just draw one reflection in each cell and see what you get.

3. Nov 14, 2013

PintoCorreia

well, how to image that it gets reflected like 4,5,6 times?

4. Nov 15, 2013

CWatters

I don't think the problem expects you to consider an infinite number of reflections. Just one in each mirror.

This is what I would expect. I've only shown two virtual cells...

Attached Files:

• Mirrors.jpg
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5. Nov 15, 2013

CWatters

PS: The multiple reflections (4,5,6 etc) would be located outside the virtual cells.