Why does a mirror appear to invert the left-right directions, but not up-down?

Question

Mirrors invert front to back, not left to right.

The popular misconception of the inversion is caused by the fact that a person when looking at another person expects him/her to face her/him, so with the left-hand side to the right. When facing oneself (in the mirror) one sees an 'uninverted' person.

Answer 1

That's a good question.

The answer is that a mirror doesn't invert the left-right directions. The object you are looking at is a 3-d object. The mirror inverts the "front-back" direction. The direction that is closest to the mirror is swapped with the one that is furthest from the mirror. The up/down and left/right remain the same.

When you turn around the image of the object around in your head to compare it to the original object, you do so by rotating it around a vertical axis, so that the front/back axis is changed back again to the way it should be and the left/right is swapped instead. If you were to turn the image around in your head about a horizontal axis instead, the image would appear to be up/down reversed compared with the original object.

The reason we don't turn objects in this way is because left and right appear very similar, while up and down are considered to be very different from each other. Turning an object so that it is upside seems stupid, but it is a valid way of turning it and proves that the mirror doesn't invert left/right any more than it inverts up/down.

Answer 2

First of all, look at yourself in a mirror. Your head is still at the top, and your feet are still at the bottom of the mirror image. Most importantly, your left hand is still on the left, and your right hand is still on the right. So, immediately, we can dispel any notion that the mirror is choosing to do some sort of X-axis or Y-axis "flip" based on "knowing" what is left-and-right or up-and-down. What has actually happened is that the 3-dimensional image in the mirror (compared to the real-world model that it is a reflection of) has been flipped along its Z-axis (i.e. the "depth" dimension). This is fundamental; this is what (by definition) a mirror does. A mirror image is a 3-dimensional model that has undergone a Z-axis inversion. Z-axis inversions do not often occur in nature (reflections in water being the only example I can think of) and therefore our brains can't easily recognize what they are looking at.

Humans have a natural left-right symmetry. So do most living things. When we are standing face-to-face with another person, it is engrained in our brains to understand, without even thinking about it, that the other person is rotated 180º (on their Y-axis) with respect to ourselves. This is how the world works. Real objects get moved in all directions (X, Y and Z transpositions) and rotated in all directions (X, Y and Z axis rotations), all of which our brains are familiar and comfortable with. When we see an image of ourselves in a mirror it is almost impossible for our brains to not assume that if our mirrored persona "turns around" 180º then they would be just like ourselves. But they wouldn't be. They are a Z-axis inverted copy of ourselves, and if they could "turn around", they'd still be Z-axis-inverted, albeit now facing away from us.

Armed with understanding these facts, i.e. that (a) mirrors display a Z-axis inverted image, and (b) human brains are determined to interpret images as if they are real, we can now answer the questions we started with... mathematically.

A 3-dimensional model that undergoes a Z-axis inversion, is precisely the same (mathematically) as the same 3-dimensional model that undergoes a 180º Y-axis rotation followed by an X-axis inversion. Got it? This can be proven mathematically, but it is obvious by just thinking about it. In fact, a Z-axis inversion is precisely the same as an 180º rotation along any arbitrary perpendicular axis, followed by an inversion along the remaining third perpendicular axis.

Whenever we look in a mirror, our brains generally make the most sense of what we see (a Z-axis inverted image) by imagining that the object is rotated by 180º, along the Y-axis, with respect to our eyes. And that's correct, but we must also then see the corresponding X-axis flip. And we do, in such details as people's faces, and in writing being "reversed".

Answer 3

Actually the mirror does not invert anything at all. What is on the left you see on the left, and what is on the right you see on the right. You are trying to analyze an image from the point of view of the image, but that point does not make any sense, since images in the mirror do not actually exist. Mirror simply reflects the light from all directions and your eye assembles the image. If you leave the room with the mirror, there will be no images in that mirror left.

Answer 4

A mirror in reality does no longer invert left-correct OR proper-down. What it honestly inverts is the front-decrease back. that is in user-friendly words when we carry out a horizontal rotation in our minds, with the intention to align the guy we see with our own orientation, that start up to imagine correct and left were reversed.

Answer 5

Anyone who has played pool or billiards knows that when a ball bounces from a surface, the angle of rebound is equal to the angle of incidence. Likewise for light. This is the law of relection, and applies to all angles: The angle of reflection equals the angle of incidence. So when the rays meet the mirror, the rays spread out and bounces back in the mirror at same angle, but at the other side from which it enters. If light bounces to the right side of the mirror, it reflects back to the left.

Only a concave mirror can be used to produce an inverted image (up-side down, or scientifically called "real" image). It is only inverted if you hold the mirror past the focal point. The images you see will be virtual, which means that it'll looks like the images are floating off of the mirror and also and reduced (smaller).

Answer 6

Simply because left/right are relative directions and up/down are not. try using east/west instead of left/right and you will find the mirror does not invert east/west either! If I have a cup of coffee in my hand at east direction, in mirror, the image will still have the cup in east direction. But when I talk about left/right, I am applying MY relative directions to that of the IMAGE; and that's wrong, isn't it?

Answer 7

It doesn't, even though it seems it does. When you look in a mirror, light reflected from your face bounces off the mirror and back into your eye. It does this in a straight line, back and forth.
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It looks inverted because it is turned towards you. If you were at the mirror's perspective looking at yourself, you would look like your reflection. The mirror is pretty much a picture of where ever it is looking at. The right is still right and left still left. I'm sorrry I can't explain this more clearly.

Answer 8

There's no inversion. If you stand in front of a mirror, your right shoulder is directly across from your image's right shoulder. Same on the left. And the top of your head is directly across from your image's head. Same with your feet. Your mind expects it to be inverted so you perceive it as being flipped, but it's not.

Answer 9

??? it dosent ??? Lay on your side and look in the mirror. No difference up and down or side to side =)

if something is on the left side of you in reall life you must look to the left in the mirror too.

It is all you in your perception that it is not on the person in the mirrors left.

Answer 10

Let's not confuse things with a mirror.

You and I are standing facing each other. My head is at the top of my body just like yours. Your feet are on the ground just like mine. However, for us to shake right hands, my right hand must cross the centerline of our bodies to reach your right hand. If I reach straight across with my right hand, I get your left hand BECAUSE WE ARE FACING OPPOSITE DIRECTIONS in the VERTICAL plane only.
We are facing the SAME direction in the horizontal plane.

The same thing happens with both of your hands: Put your palms together. Since your hands are ALREADY inverted, the thumbs match up together without crossing over the vertical centerline. If you look at your right hand, the thumb is on the LEFT and looking at your left hand, the thumb is on the RIGHT.