Brain Teasers
What Do You See?
You are standing in the middle of a cube-shaped room. Two of the walls that are adjacent to each other are completely covered with mirrors (one large mirror is covering each wall). You raise your right hand.
How many images of yourself will you see in the two mirrors, and which hand will each of the images appear to be raising?
You can turn your head as needed to view the full range of each mirror.
How many images of yourself will you see in the two mirrors, and which hand will each of the images appear to be raising?
You can turn your head as needed to view the full range of each mirror.
Answer
In the mirrors you will be able to see four images of yourself:- Looking directly into each mirror you will of course see your normally inverted mirror image. The person in each mirror will appear to be raising his left hand.
- Looking toward the corner between the two mirrors, you will see two more images of yourself, but these will be double-inverted because in each mirror you will see the reflection from the OTHER mirror. Because of this, the person in the mirrors will appear to be raising his right hand, just like you are.
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Comments
I don't understand what you mean by seeing two images in the corner. When I look in the bay window in our house (which sort of resembles two mirrors at right angles) I can see only one me. Where is the second image?
It's possible that two windows does not model this situation well enough. If you look directly at the corner between the mirrors, you will see one image immediately to the left of the corner and another one immediately to the right. Remember, you are seeing the refelction of a reflection each time, so maybe a window isn't good enough to make this double-reflection.
Surely you would see half of one image immediately to the left and half of one image immediately to the right. Are you counting these two half images as two seperate iamges? If I draw a bird's-eye view diagram with the corner, my left eye and my right eye, I still count only one image in the corner. I suppose I could try to find a room with two mirrors, or maybe visit a mirror shop. :-)
I got the idea for this teaser by sitting in a restaurant that had two large mirrors meeting flush at a corner. You have to be careful because if the two mirrors are not flush to each other (i.e. there is a piece of framework in the corner or something), then you will only be able to see a small part of the two images in the corner.
Oh, I see. Maybe the corner in the restaurant is not perfectly square, and this is what caused you to see 2 images in the corner instead of just one? Consider two walls meeting at a different angle (say 60 degrees) and then calculate how many images you could see. Now imagine the angle increasing up to 90 degrees and work out what will happen to the images... they will eventually overlap to make only one.
Maybe the editors will correct the answer for you if you ask them nicely, or can you correct it yourself?
I tried this in my bathrroom which has 2 mirrors set at about 120 degrees. It works fine depending on where you stand and what you are looking at. I held in my hand a can of shaving cream. In one mirror I could see the (full) image of a shaving can with the lettering inverted. In the second mirror I could see another (full) image of the can with normal lettering. Anyone who says that physics will dictate somethinmg else had better go back to the drawing board. I conducted the experiment and it works!
... however I'm not sure that it would be the same from the middle of the room. It does seem to vary with the viewing angle.
You'll see infinity of yourself....
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