Virtual boxes mirror reflection

[PintoCorreia]

Homework Statement

Finding lightpaths with 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 mirrorwalls 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.

Homework Equations

mirror images

The Attempt at a Solution

What do I need to do with those virtual squares? And why is the line drawn from A to B' through those other rooms?

 

[mfb]

The drawing looks quite complete to me...

And why is the line drawn from A to B' through those other rooms?

Mirrors do exactly what those virtual boxes represent: They show a "mirror world", like the box above your real box. That is not limited to a single mirror, you can fill the whole grid with those mirror images.
There are mirror arrangements where this is not helpful, but with a quadratic box it is nice.

 

[PintoCorreia]

I guess there suppose to be lines in other virtual boxes.

 

[mfb]

Then you can draw those lines. There is an infinite number of them, so I guess you have to restrict yourself to a few of them.

 

[CWatters]

And why is the line drawn from A to B' through those other rooms

This is a way of working out where the image appears to be to an observer..

If you stood at point A in the original cell and looked in the direction of the laser beam you would see point B but it would appear to you as if it was at point B'.