See here for the Finnish version: Miksi peilikuva vaihtaa vain oikean ja vasemman puolen keskenään
Presumably everyone reading this already knows that in a mirror image, the right and left side are on the opposite sides from the original. Indeed, this is sometimes confusing when you’re trying to do something with the help of a mirror. It’s pretty easy to see how the mirror image turns out like this. Consider, for example, your left shoulder, which becomes the right shoulder on the mirror you. It’s easy to envision how beams of light reflecting from the shoulder into the mirror move roughly straight ahead and reflect roughly straight back, putting the image of your left shoulder directly opposite to your left shoulder, whereas if you were standing in place of the mirror image, your right shoulder would be there.
But this leaves another question unanswered: Why left and right specifically? All directions in space are equal, so why is it that only a specific two switch places in the mirror? The up and down ends don’t switch — when a beam of light is reflected from your head to the mirror, it too reflects right back, just as was the case with your shoulder, but this time that just means that the head of the mirror image is at the same end as yours, not the opposite. And there’s one more equal axis in three-dimensional space, but surely your back and front sides are not switched in the mirror image either?
I started wondering about this in high school, but I think I have come up with the answer after that.
Not everyone will necessarily even see this problem, as the whole situation can be physically comprehended without paying it any attention. But it’s real, at least in the sense that there’s reason to ask the question of why it is that we say that the left and right sides are reversed, but there others are not. And that turns out to be the key to the answer.
The essential thing is to ask compared to what it is that the left and right sides are switched but the others are not. As already comes up above, they are switched in comparison to how they would be if you were standing in place of the mirror image yourself. Because our left and right sides are symmetrical, the image in the mirror automatically looks to us like someone standing facing us. After we get this impression, we need to make the adjustment that left and right have been reversed. It also applies to most other objects and creatures that at least their upper and lower ends are more distinct than their sides, and as beings living on the Earth subject to gravity, we tend to generally pay more attention to up and down as different than the sides (I guess).
But, even though it doesn’t feel so natural, image that someone is standing on their head in front of you, facing you, and compare this to the mirror image. Now their left and right are the same way around as the mirror image’s. But up and down are switched. And suppose someone was standing in place of the mirror image with their back turned on the viewer. Their left and right would also be the same way around as the image’s, but now back and front would be reversed.
So the answer is that the mirror does not reverse right and left specifically compared to how they’d be for you if you were in its place. Switching any two opposite directions describes it just as well. But because the image in the mirror looks like someone standing facing the viewer, you automatically compare it to how it would be if you moved into its place by turning to face the opposite way from now, which would switch just left and right to be the opposite way from the image’s. But it might just as well be compared to your having moved to its place without turning, switching back and front, or by turning upside down, switching up and down. So all directions in space are equal for the mirror image, and the difference only follows from what we compare it to.