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Why do mirrors flip left to right and not up to down?

Category: Physics
Published: January 5, 2013

Mirrors do not flip left to right. They flip front to back. Mirrors reflect light rays such that the angle of reflection equals the angle of incidence. For a three-dimensional object standing in front of the mirror, there is an image of the object created behind the mirror with the right side still on the right, the left side still on the left, the top side still on the top, the bottom side still on the bottom, but the front side is flipped to the back and the back side is flipped to the front. This can be easily seen by tracing the rays from significant points on the object and seeing where they end up in the mirror image. The drawing on the right shows the result, which confirms that mirrors only flip front to back.

ray tracing to create image in a mirror
Here we are looking down on a colored box on a white rug in front of a mirror. Tracing a few representative light rays from their reflection point on the mirror back to their image point reveals that a mirror preserves the position of the sides but exchanges front and back positions. If mirrors truly flipped left to right, then the green and blue parts of the box would be exchanged in the mirror image, which is clearly not the case. Public Domain Image, source: Christopher S. Baird.

But ambulances indeed seem to have the word "Ambulance" painted in a manner that is flipped from left to right so that drivers can read the word the correct way when looking in their rear-view mirror. Doesn't this show that mirrors flip left to right? No. Actually, the word "Ambulance" is not flipped left to right, or any way at all. It seems to be flipped left to right when you turn your head to look at the ambulance. But that is a result of you turning your head, and not of the mirror. If you hold up a word to a mirror so that you can see both the word and its image in the mirror at the same time, you will see that they both read the same direction and there is therefore no right-left flipping. This effect is captured in the image below. If you now hold the word behind you without turning the word, and then turn your head to look directly at the word, it now does appear flipped. This shows that it is the act of turning your head and not the mirror's reflection that makes the word "ambulance" seem backwards.

word flipped front to back in the mirror
Holding a word up to a mirror with no other obstructions reveals clearly that the mirror does not flip left to right, but instead flips front to back. Note that both the actual word and its mirror image can be read properly, as they both have the letter "R" on the left. Also note that on the real letter "E" you can read the word "FRONT" but on the mirror image letter "E", you read the word "BACK". This shows that the mirror image is flipped front to back. Public Domain Image, source: Christopher S. Baird.

Can you look at the word without turning your head? If so, the word would not appear backwards. In theory, yes. All you have to do is get behind the word and then you can look at the word and the mirror without turning your head. In practice, the word is often painted in a place such that if you get behind it, you can't see anything anymore. What if the word "Ambulance" was painted across the top of the transparent windshield such that it shows up correctly in someone's rear-view mirror. Now the driver of the ambulance is sitting behind the word. As he looks out his windshield, he can see the word without turning his head. As a result, he can read the word correctly. The word does not seem flipped left to right to him because he has not turned his head. This counter-intuitive notion arises from the fact that when we turn our head, we unconsciously rotate a word so that it reads correctly.

For instance, consider that you are standing in a long, narrow garage in between two vehicles. A car is parked on your left with its front grill facing you and a van is parked on your right, also with its front grill facing you. In order to have some fixed reference frame, let's call the wall right in front of you the main wall. Your job is to paint the word "POLICE" across the hood of each vehicle. You are supposed to paint the words so that someone looking directly at the front of each vehicle reads them correctly (with no mirrors involved). The main wall is the wall closest to the car's passenger side and closest to the van's driver's side.

You paint the word "POLICE" on the car's hood first. In order to make it read correctly, you put the letter "P" closest to the main wall, and the rest of the letters stretch away from the green wall. Now you paint the word "POLICE" on the van's hood. To make it read correctly, you now paint the letter "P" farthest from the main wall, and the rest of the letters stretch towards the main wall. Do you see what is happening? In relation to a fixed reference frame (the main wall), you painted the word in one direction on the car and in the opposite direction on the van in order to make them both read correctly. Why did you do this? Because when standing in between the two cars, in order to change your view from the car to the van, you have to turn your head. But turning your head would make words that are fixed relative to the wall end up flipped backwards relative to you. So you also flip the word that you are painting to make it come out right. Turning your head flips words, so manually flipping the word restores it back to its normal appearance. We do this all the time without realizing it. If you are looking in one direction and reading a book, then you turn your head and bring the book around to read it, you also turn the book. If you didn't turn the book, you would end up looking at its cover instead of the words inside.

In summary, turning your head flips images from left to right, but we don't usually notice because we unconsciously undo the effect by flipping the object as well. The unique thing about a mirror is that it allows us to flip our head and still look at an object, without flipping it left to right. We are so used to things flipping when we turn our head, and believing they haven't flipped, that when we turn our head and look at a mirror to see an object not flipped left to right, we see the opposite of what we're used to and assume the object has flipped. Our intuition is completely backwards. Ultimately, mirrors always flip front to back and not right to left, and any confusion about this fact arises from a misunderstanding of what happens when you turn your head.

Topics: flipping mirror, light, mirror, mirror image, optics, ray tracing