Mirrors and Reflection: The Mysterious Maths

[lvlastermind]

I wasn't sure where to post this and i apologize if its already been posted. I think there is an obvious answer for this but for some reason I cannot figure out a consistent answer. I am looking for a mathematical answer more than anything else. When you look in a mirror you image is switched and non-superimposable. i.e. your left hand is reflected as your right. How come a mirror does not switch in the plane of top to bottom? How come your feet aren't where your head is and vice versa?

thanks...

 

[Jimmy Snyder]

Answer:

A mirror does not reverse left and right. Things that are on your right in the real world are on your right in the mirror world. What a mirror changes is front to back. For instance, hold your arm out with your palm toward you and look in a mirror. In the real world, your palm is in front of the back of your hand. But in the mirror, the back of your hand is in front of the palm. In other words, the mirror reverses objects along a line perpendicular to the surface. Because a mirror changes front to back, it also changes something called handedness. That is, a left hand will look like a right hand. However, it will still be on your left.

eom

 

[abeen]

it is a wrong notion that left and right get switched.only the front and back directions are reversed. Just take a paper draw x,y and z axes , hold in front of the mirror and see it for yourself.

 

[Jimmy Snyder]

it is a wrong notion that left and right get switched.only the front and back directions are reversed. Just take a paper draw x,y and z axes , hold in front of the mirror and see it for yourself.

I didn't do as you asked, but I know what would happen if I did. The x axis, which points to the right because I draw these things in a conventional manner, also points to the right in the mirror. The y axis, which I would draw pointing up, continues to point up, and the z axis which I would draw pointing toward me (I used 3-d paper to draw on) points away from me in the mirror.

 

[Jimmy Snyder]

it is a wrong notion that left and right get switched.only the front and back directions are reversed. Just take a paper draw x,y and z axes , hold in front of the mirror and see it for yourself.

I didn't do as you asked, but I know what would happen if I did. The x axis, which points to the right because I draw these things in a conventional manner, also points to the right in the mirror. The y axis, which I would draw pointing up, continues to point up, and the z axis which I would draw pointing toward me (I used 3-d paper to draw on) points away from me in the mirror.

Edit: Actually, I did do the experiment. I drew the x-axis to the right as I normally do, but when I turned the paper around to present it to the mirror, it was now pointing to the left. This has nothing to do with the mirror, it happened when I turned the paper around. Is this the problem you are having?

Second edit. While standing before a mirror, hold an object in your right hand. Is it on the right hand side of the mirror, or the left hand side?

Third edit, best experiment of all. Draw the letter R on the back of your right hand and the letter L on the back of your left hand. Now hold the backs of your hands to the mirror. Your right hand will still be on the right and your left hand on the left. The letter R does not become an L, it becomes a backwards R.