Are you asking about why we see ourselves the same? It is a very interesting questions, and mirrors and reflections are fascinating.
When you look in a mirror, you tend to think as your reflection as a person facing you, so left and right has switched (you move your left hand, the reflection moves its right hand). This is actually not what is happening at all, that is the brain misunderstanding what is going on. The brain compares the reflection to facing a person in real life, where their right hand is on your left, and vice versa. What actually is happening is that you have reversed front and back. To see this, stand infront of a mirror and point to the left, your reflection points the same direction as you are (for me it is towards my radiator). If you point up, your reflection points up. If you point towards the mirror, your reflection is pointing the opposite way, so the mirror is reflecting front and back.
Mirrors work by having a very smooth flat surface, which does not absorb light that falls on it (like a black tshirt, for example), but reflect almost all of it back. Because it is so smooth, the light that hits it stays in the same relative position to other light hitting it, and this makes it so that any image you see looks the same as it does in real life, except reflected.
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