It is always a fun exercise to play with your image in the mirror. Inspite of being right in front of you, it tricks you like nothing else. If you raise your right hand the image raises it’s left. But if you raise your hand up, the image also raises it up, not down. So what is exactly happening over here? After all the mirror is just a plane surface. How does it differentiate between the left-right and up-down directions?
Just say you hold a placard saying Loop in front of the mirror then it would show you the word pooL in it, of course with backwards letters but still right side up. At first, we may think that this horizontal flipping is because our eyes are placed horizontally, but believe me you get the same effect even if you see just through one of your eyes.
What is actually happening over here is that the mirror neither does the flipping in the x-direction nor in the y-direction. It is us who is doing the flipping. While you turn the placard towards the mirror you actually flip it by the vertical side.
Now try flipping by the top horizontal side. You will now get a vertical inversion in the mirror image instead of horizontal inversion as shown below.
So in front of a mirror if you point an arrow towards your right, the image points right. If you point it to your left, the image points left. If you point it upwards, the image points upwards. If you point it downwards, the image points downwards. But if you point it forwards away from you, the image points backwards towards you. So here is the flipping that the mirror really does. The mirror flips things along the z-direction (perpendicular to the mirror surface).
Thus, if you stand before the mirror then your image is equivalent to how you would look if you were flipped through your body in the z-direction which we accidently percieve as a horizontal flip. For example if you pull a right hand glove inside-out to reverse it then it becomes a left hand glove.
“ The mirror just shows to you what you presented to it just after a flip along the z-direction.”
For those of you who still didn’t get it from the text, here is a video of “Physics Girl” explaining the same.