How many images will I see if I am surrounded by 4 mirrors? An image question got me today when I was reviewing image theory.
With 1 mirror -- I see 1 image out of phase of myself.
With 2 parallel mirrors, me being between them -- I see infinite images of myself.
With 2 mirrors at angle (let's say right angle) -- I see 2 out of phase images and 1 in phase image at the corner.
But what does the image distributions look like when I am surrounded by 4 mirrors making right angles? I know the number of images is going to be infinite but will there be images at the corner or so?
Since Bruce Lee died years ago, and I am quite far away from Walmart, does someone know how are images distributed if I am surrounded by 4 mirrors? (Those 4 makes right angle of each other, like a simple rectangular shape if look from above.)
 A: If the angles between the four mirrors are exact right angles then in theory you will see an infinite two-dimensional array of images. In practice, just as with two parallel mirrors, images that are further away get darker because a small amount of light intensity is lost at each reflection. So there is a limit to how many images you can actually see in practice.
In the two dimensional array there are four types of images. There are two types of reflected image, one type of image which is rotated through $180$ degrees (because it has been reflected an odd number of times in both mirror planes), and a fourth type of image that has been reflected an even number of times in both mirror planes and so is a non-reflected and non-rotated image. So if you look carefully you will find an image where you can see the back of your head.
A: gandalf61's answer is already complete, but since there were some discussions I wanted to give another answer with a picture. I will also talk about intensity losses because they actually help us understand what is happening, imho.
So, you know how you get a non-reflected image when you have a right angle between two mirrors (corner reflection). The following image is a generalization of this idea of an image at the corner.

In the center, you see the four mirror system (thick blue lines) with the visible object (yourself or Bruce Lee) in the middle. The mirror axes are continued and reproduced to give a grid of blue lines. Then, there is a lattice of mirror images. They lose intensity the more reflections are required to reach their position (cf. next image). You can see that mirror images with the same intensity form a diamond shape, $\diamond$, which I also want to explain with the next image.

In this one, you can see how the mirror image "two to the right, one up" comes about. If you connect the source and this particular mirror image (dotted arrows), the line will pass through 3 different mirror planes (blue lines) in the mirrored domain. But this domain is just a mathematical auxiliary, the real light ray (solid arrows) only moves within the square described by the four mirrors. You can then see that the mirror images arises because of a certain repeated reflection on the mirrors, given by the somewhat rhombic shape of the solid arrows.
This construction using infinitely repeated mirror planes is in essence due to the law of specular reflection, that means that incident and reflected angles are the same. By that, you can either look at a reflected ray of light in an unchanged world or at an unchanged ray of light in a reflected world. This can be done each time your light ray hits a mirror, and you can describe your light ray as a line passing through different reflected worlds.
With this, you can also understand why mirror images with the same intensity lie on a diamond shape, $\diamond$. If you connect them to the origin, you pass through exactly the same number of mirrors in the reflected world for each one of them. Note that passing exactly through a corner means passing two mirror planes at once.
Each of the diamonds boundaries has $4 n$ points, where $n$ is the number of mirrors you have to pass to reach the cluster (you can just consider it the separation on the $x$ axis). That means that if the first $N$ diamonds are visible, you have a total of
$$\sum_{n=1}^N 4n = 4 \frac{N(N+1)}{2} = 2 N(N+1)$$
mirror images. That number obviously goes to infinity as $N \to \infty$.
A: For four mirrors kept at right angles, there are 2 situations to be reviewed:

*

*The alternate mirrors are parallel.
This implies that infinite image will be images in both the pairs of parallel images.

*The adjacent mirrors are at right angles, so the number of images formed will be 3 in both the pairs of adjacent mirrors, which will themselves be then reflected and this would go on for ever.

While the total number of images will be infinite, the calculations say:
No. of images = infinite+infinite+3(infinite) = infinite.
