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Mathematics Forum
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| Author | Message / Information |
| davo Quote | Reply | This message was updated on 6/19/2007 7:24:17 AM by davo | Transformation Geometry posted on: 6/15/2007 5:08:05 AM What minimum length of a vertical mirror on a wall do you need to see your full length? if your height is 180cms. thank you |
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cramwit
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Transformation Geometry
replied on: 8/29/2007 4:15:47 PM It depends on your distance from the mirror, & how perfect the mirror & your distance eyesight are. The smallest vertical mirror possible would be tiny & floating at eye level & at 1/2 of infinite distance. I think it is also more efficient to have the base of the mirror closer to you, because more of you is below eye level. If you lay a small mirror on the floor & cast your eyes down you get your full, if foreshortened, view of yourself. But since you stipulated that it should be perpendicular to the ground [vertical] & extend to/from the ground then i think with infinite distance & resolution it has to be just a whisper taller than eye level. It doesn't have to be your full height, but it must include your eye level, and just a bit for the top of your head. most of the bottom of the mirror will reflect the distance [miles] of floor between you & the mirror. I think it is easiest to think of a cone that starts from you eye point to the edges of the mirror, with equal angles of incidence [reflection] at the mirror that must include you in the widening base [scope of view]. At many angles of the mirror will miss you from that cone of inclusion altogether. if you are right up close to the vertical mirror it will have to be essentially your full height, to include the top of your head. (i think that is correct, if not let me know) |
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cramwit
Quote | Reply | This message was updated on 8/29/2007 4:18:59 PM by cramwit |
Transformation Geometry
replied on: 8/29/2007 4:16:53 PM oops, double post because of some server error msg, @@. *shrug* |
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ANewBeginning
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Transformation Geometry
replied on: 10/8/2007 1:47:18 PM Unfortunately, not only did cramwit double post, he double posted an incorrect answer! Imagine the ray of light from the top of your head to the mirror to your eyes. Since the ray makes equal angles when it reflects from the mirror (and assuming that the mirror is at least approximately the same distance from the top of your head and from your eyes, the two rays and the line connecting your eyes and top of head form an isosceles triangle. In particular, the perpendicular from the point where the ray strikes the mirror (where you will see the top of your head in the mirror) hits your body exactly half way between the top of your head and your eyes. Now look at the ray from your feet to the mirror to your eyes. Exactly the same argument shows that the point at which you see your feet in the mirror is where a perpendicular to your body will strike you body exactly half way between your feet and your eyes. In order to see your entire body in the mirror, the mirror must be at least 1/2 the length of your body, no matter how far the mirror is from you. If you are 180 cm tall, the mirror would have to be 90 cm tall. |
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cramwit
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Transformation Geometry
replied on: 10/11/2007 5:05:20 PM dang, i do believe you are correct ANewBeginning. |
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davo
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Transformation Geometry
replied on: 9/2/2008 6:29:52 AM Thank you ANewBeginning |
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