What element, light spectrum etc. causes a mirror to reflect the image in front of it? And what causes it to reflect backwards?

This article should explain reflection and lateral inversion:

Light - Reflection

Actually mirrors don't reflect backwards. It may seem like it does, because you're used to looking at people facing you with their left on your right, so the fact that your image in the mirror has its right on your right makes it seem like the image is of a person facing you who has been reversed left and right. But actually what a mirror does is transform your image front-to-back. This front to back transformation is topologically equivalent to rotation about the vertical axis and then transposing left-for-right. But consider this: it's also equivalent to rotating about the horizontal axis (that is, standing on your head), and then swapping up-for-down. So next time someone says that mirrors reverse the image left-to-right you can tell them that it actually reverses it up-to-down. ;)