Why do mirrors reflect back-to-front but not upside-down?

I looked at various different explanations for why mirrors seem to swap the right and left sides, but most of them made it more confusing, not less. The truth is, it's complicated. This Guardian Note & Queries article may be one of the the best resources, because it offers many different viewpoints from different people.

The short answer is that mirrors swap left and right because we tend to look at a vertical mirror on a wall. If we were to look at a horizontal mirror on the floor, then it swaps top and bottom instead. Think of looking at the reflection of mountain in a lake, for example.

The other thing at play here is our perception, and also our language. For example, if we think of absolute directions like north, south, east and west, when we point to the west, our reflection in a mirror also points to the west. But if we think in terms of relative directions like left and right, if we point to the left, our mirror reflection seems to be pointing to the right.

The operative word here, of course, is "seems", because from the mirror's point of view (think of yourself as an an ant on the surface of the mirror) you are still pointing to the left. But we tend to think of the image in the mirror as another person pointing. If we face a another person and they point, we tend to do a mental 180° rotation (as opposed to a reflection), imagining how it would be if we were in their situation. So, we talk about "my left, your right". But this in not what is happening in a mirror reflection. It is the same person, and it is still pointing the same way, be that left or right.

Another way of looking at it, which seems to make sense to some people but not so much to me, is that mirrors don't reverse images from left to right but rather from front to back. To give an example, if you point to one side your mirror image points to the same side (however you want to describe it). If, however, you point directly at the mirror, the mirror image seems to be pointing directly at you, i.e. the opposite direction. Hmm, OK.

So, clearly there is a complicated series of factors involved here, most of them cognitive and psychological rather than physical. Technically, in physical terms, photons (or rays of light, as you might think of them) from you hit the smooth surface of a mirror and reflect or bounce back rather than being absorbed or scattered. Those photons that bounce back from the mirror to the retina of your eye are what your brain interprets are being what you see (in this case a reflection of yourself). But then your brain tried to make sense if what it receives, which is the cognitive/psychological side of things as discussed above.

As always with the body and the brain, the truth is way more complicated than the appearance.