1. Why Your Mirror Image Seems to Raise the Opposite Hand
When you raise your right hand, the image in the mirror looks like it is raising its left hand. However, the image keeps its head at the top and feet at the bottom; the up-down direction is not reversed. If the mirror were a device that simply swaps left and right, why would the up-down direction remain the same? This question connects not only to physics but also to how people perceive images, a topic researchers have discussed for years [4]. We will think about this step by step, starting by checking what the mirror does optically.
2. How a Flat Mirror Reverses Only the Front-Back Direction
John Baez, a mathematician at the University of California, Riverside, explains that a flat mirror treats only one direction as special: the direction perpendicular to the mirror surface [1]. Only that direction—front and back—is reversed by the mirror. Physicist Masahiro Hotta also explains that a mirror is a device that reverses the "front-back" direction perpendicular to the mirror surface [2]. According to Hotta, the up-down direction, which is parallel to the mirror surface, does not change. The result of the front-back swap is what we perceive as a "left-right reversal."
Physicist Richard Feynman is said to have explained this using the example of pointing a finger at a mirror [3]. (I have not checked the original source; this comes from a summary in an article.) If you point your finger parallel to the mirror (for example, pointing east), the finger in the image points in the same direction. If you point your finger toward the mirror (for example, pointing north), the finger in the image points in the opposite direction (south). Only the axis perpendicular to the mirror is reversed. It may help to think of it this way: of the direction your hand points, the mirror reverses only the part that is perpendicular to the mirror.
3. Why Up-Down and Left-Right Are Rules People Add to the Mirror World
Baez suggests that the directions "up-down" and "left-right" are rules that people bring into the mirror world [1]. The mirror only reverses the direction perpendicular to its surface. According to Hotta, "left" and "right" are directions that are defined only after "up-down" and "front-back" are determined [2]. Therefore, in an image where only front and back are swapped, up remains up, but the appearance of left and right changes. It is easier to understand if you imagine that when looking at a mirror image, we unconsciously "walk around behind the image and stand facing the same direction as the image." When viewed this way, your right hand feels like it corresponds to the image's left hand.
4. Why Seeing Yourself and Reading Text Reverse for Different Reasons
According to the University of Tokyo's article, experiments by Professor Yotaro Takano showed that the mirror reversal of oneself (seeing one's own image as left-right reversed) and the mirror reversal of text are two separate phenomena caused by different reasons [4]. According to the university's article, 30 to 40 percent of people feel that "left and right are not reversed" when they face a mirror. However, for the readable text used in the experiment, everyone felt that left and right were reversed. Note that the 30 to 40 percent figure refers to the proportion of people who do *not* feel a reversal, not those who do.
It is also reported that people who know no Russian did not feel that Russian text was reversed [4]. It seems that the perception of text reversal is connected to whether or not you know the language being read.
5. Why Researchers Disagree About What Causes Mirror Reversal
In Takano's "multiple process theory," mirror reversal is considered a combination of three types of processes: a shift in viewpoint placement, a mismatch between mental representations of objects and their mirror images, and the optical transformation of the mirror. This was published in an academic journal in 1998, and a 2007 experiment by Takano and Tanaka is said to be consistent with it [5].
In contrast, other researchers propose that mirror reversal can be explained by the combination of the mirror's optical front-back reversal and how one defines the "left-right axis," without needing psychological processes [6]. Since both papers have only been checked via their abstracts, this is presented only as an introduction to these theories.
6. How You Can Test Mirror Reversal Yourself With a Mirror
You can try this today. Stand in front of a mirror and compare how your finger looks when you point it straight at the mirror versus when you extend it sideways. You can compare how the finger's direction appears. You can also observe how text looks by holding a paper with large letters up to a mirror. Comparing this to looking at the paper held up to light from the back can help you consider if the feeling of "reversal" is the same.
If you want to learn more, the source list includes an article from the University of Tokyo. It is available in Japanese, so you can read about the experiments and why researchers considered these "separate phenomena."
This only shows how the finger looks. It is a way to start thinking about the optical explanation, not a full test of it.