Exploring Mirrors and Reflection: Unanswered Questions in Image Reversal

[madness]

I have never understood how images are reflected in mirrors, even now that I am going into my fourth year of university I have some really basic (probably stupid) questions that I need to ask.
When an word is reflected in a mirror, why do the letters appear reversed but the word doesn't (the letters still appear in the same order)? Secondly, why do they appear reversed from side to side but not top to bottom?
I know these questions are probably stupid but I really can't work them out. Thanks.

 

[DaveC426913]

When an word is reflected in a mirror, why do the letters appear reversed but the word doesn't (the letters still appear in the same order)?

The letters and the word are reversed. Look again.

If you write ABC across your shirt and view it in the mirror, the letters read from right to left and the word reads from right to left.

Secondly, why do they appear reversed from side to side but not top to bottom?
I know these questions are probably stupid but I really can't work them out. Thanks.

A trickier one. This'll take some time to unravel. And BTW, this question has stumped many.

http://math.ucr.edu/home/baez/physics/General/mirrors.html

http://www.mathpages.com/home/kmath142.htm

 

[waht]

You can always draw a ray diagram.

 

[tiny-tim]

Hi madness!

Secondly, why do they appear reversed from side to side but not top to bottom?

If they were reversed from side to side and top to bottom, then they wouldn't be reversed at all, they'd only be rotated 180º.

Reflection can only be in one axis at a time (or three axes, or five, or …) … if it's in an even number of axes, it's the same way up, but rotated.

 

[DaveC426913]

Hi madness!


If they were reversed from side to side and top to bottom, then they wouldn't be reversed at all, they'd only be rotated 180º.

Reflection can only be in one axis at a time (or three axes, or five, or …) … if it's in an even number of axes, it's the same way up, but rotated.

OK, but that doesn't address the question: why always left-to-right and never top-to bottom.

I've read a lot of answers to this problem but I have yet to read one that is succinct.

 

[fedaykin]

Draw lines from the object to the mirror and back. That should help. If more is needed, think of looking at a sheet of paper with text on it, but from the opposite side.

 

[tiny-tim]

Succinctionalification!

OK, but that doesn't address the question: why always left-to-right and never top-to bottom.

I've read a lot of answers to this problem but I have yet to read one that is succinct.

Only vertical mirrors reverse writing left-to-right.

Horizontal mirrors retain left-to-right, but reverse top-to-bottom.

Succinctionalification! ​

 

[Andy Resnick]

OK, but that doesn't address the question: why always left-to-right and never top-to bottom.

I've read a lot of answers to this problem but I have yet to read one that is succinct.

Mirrors don't reverse left and right (or up and down), they reverse forward and back.

 

[HallsofIvy]

OK, but that doesn't address the question: why always left-to-right and never top-to bottom.

I've read a lot of answers to this problem but I have yet to read one that is succinct.

Okay, here's a succinct answer: Mirrors do NOT reverse left-to-right!

Seeing "reversed" images in a mirror in purely Psychological. If a person were standing in front of you, face to face, and raised his right hand, it would be directly opposite your left hand. But that is because the person had to "reverse", turn around, in order to face you. The same thing with words on a sheet of paper. If I were holding a sheet of paper, with words on it, in exactly the same way as I would to see the words in the mirror, I could not read it- the words would be facing away from me. In order to be able to read it, I would have to reverse the paper myself. The words and letters in a mirror look odd because they are NOT reversed. Looking at ourselves in a mirror, we look odd because the image is NOT reversed the way people we look at face to face are.

 

[jtbell]

Try this experiment: Write something on a sheet of paper. Stand in front of a mirror and hold the paper up in front of you so you can see the reflected image of what you wrote. It's mirror-reversed, right? But can you simultaneously see the original writing? No, because it's facing away from you.

Now, write something on a transparent sheet of glass or plastic. Stand in front of a mirror and hold the sheet up in front of you. Now you can see both the original writing (through the back side of the sheet) and the reflection in the mirror. How do they compare?

 

[madness]

To tiny tim - the mirror doesn't reflect the image along any single axis, and if you rotate the paper so that the words read vertically then the work becomes reversed from top to bottom instead of left and right. It is essentially the same as reading something written on acetate from the wrong side as jtbell said. I understand this but still find it confusing that the image seems to be reversed one way but not the other.
Thanks for the links DaveC, they were quite useful in understanding the reflection and also left/right handed bases.

 

[jtbell]

the mirror doesn't reflect the image along any single axis

Actually the mirror does reverse the image along one axis: the axis perpendicular to the mirror. Consider holding up a sheet of paper in front of you as in the experiment I described above. The front of the paper (the side with the writing on it) faces away from you, but the front of the image faces towards you. The back of the paper faces towards you, but the back of the image faces away from you.

And of course your own image is reversed front-to-back so that you're looking at the image of your face instead of the image of the back of your head.

 

[madness]

Yes I suppose it is reflected in that axis but this is more abstract, since the image is 2d and this axis is out of the image plane. This means something infront of the mirror appears behind the mirror, however the image is 2d so it is not literally behind the mirror. This is very different from a reflection in an axis on the plane of the mirror, where something on the left really would be on the right.

 

[madness]

And even given this explanation, it still seems confusing that is appears to be revered in a left to right sense. There is more than one way to turn a piece of paper so that it faces away from you - turn it one way and the writing looks backwards, the other and it looks upside down. The sense in which the image is reversed around the axis perpendicular to the mirror is the former and not the latter. The best explanation I have seen to the whole problem is in the links given by DaveC.