Mirrors and Reflection: The Mysterious Maths

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    Mirrors Reflection
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Discussion Overview

The discussion revolves around the mathematical and conceptual understanding of how mirrors reflect images, particularly focusing on the perception of left and right versus front and back. Participants explore the implications of mirror reflection in terms of spatial orientation and handedness, seeking clarity on why certain aspects of an image appear reversed while others do not.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that mirrors do not switch left and right but rather reverse front and back, leading to the perception of handedness.
  • Another participant agrees that the notion of left and right being switched is incorrect and emphasizes that only front and back directions are reversed.
  • Several participants propose experiments involving drawing axes or letters on hands to illustrate their points about how mirrors reflect images and maintain spatial orientation.
  • One participant notes that turning the paper around changes the orientation of the axes, which may contribute to confusion about mirror reflection.

Areas of Agreement / Disagreement

Participants generally agree that mirrors reverse front and back rather than left and right, but there is ongoing debate about the implications of this reversal and how it is perceived in different contexts. No consensus is reached on the best way to conceptualize or demonstrate these ideas.

Contextual Notes

Some participants rely on specific definitions of axes and spatial orientation, which may not be universally accepted. The discussion includes various interpretations of how mirror reflection operates, highlighting the complexity of the topic.

lvlastermind
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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...
 
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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
 
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.
 
abeen said:
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.
 
abeen said:
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.
 
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