Experiment of The Month
Just for fun, the picture shows a transparency placed in front of a mirror. It's held in place with masking tape and things lying around the lab.
The transparency presents its own question. The masking tape on the left side of the transparency gives a hint to the answer.
In fact, a mirror does not change left for right, any more than it changes up for down. The mirror gives back exactly what it is shown. "Gives back" is the important phrase. When it gives back, the mirror changes front for back.
Objects that are closer to the mirror (and farther from the observer holding the camera) have their images closer to the mirror (and therefore closer to the observer).
For the two bottles of hand lotion below, notice the direction of the pump nozzles. One nozzle points to the left, as does its image. (Changing front for back has no effect on the direction of that nozzle.) The other nozzle points towards the observer, but the image points away from the observer.
The front-for-back change is easier to see for text by looking at the enlarged figure below. On the white paper, the word "WHY" is farther from the observer than the word "IN." In the image, the word "WHY" is closer to the observer than the word "IN." We would say casually that the image is "upside down" from the original object. But it is clearer to say that the image has reversed front and back. Finally, the answer to the question is that for the transparency, front and back are identical.