[math-fun] Inside a spherical mirror
What would it look like if one were inside a spherical mirror silvered on the inside? Suppose a you are suspended in mid-air inside the mirror, a bit off-center but with your eye in the same plane, holding a candle for light and looking in the direction of the center. What would you see? I don't know the answer. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele
My daughter is doing simple optics for a class, and she has explained some things to me. I think that the focus is half-way between the center of the sphere and the mirror. If one is outside of the focal length, the image is real and inverted, and, if one is inside the focal length, virtual (on the other side) and same-side-up, but magnified. If one were very close, it should look flat, I'd guess. If one is at the center, then the image is also at the center, inverted, of the same size. However, my knowledge of this is sketchy. Bill -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Dan Asimov Sent: Tuesday, November 18, 2008 9:55 AM To: math-fun Subject: [math-fun] Inside a spherical mirror What would it look like if one were inside a spherical mirror silvered on the inside? Suppose a you are suspended in mid-air inside the mirror, a bit off-center but with your eye in the same plane, holding a candle for light and looking in the direction of the center. What would you see? I don't know the answer. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Tue, 18 Nov 2008, Dan Asimov wrote:
What would it look like if one were inside a spherical mirror silvered on the inside?
I've always wondered about a related question: standing on the inside of an empty dyson sphere, with longitude lines drawn, standing on the south pole. The lines all diverge, but should also converge due to perspective (shouldn't they?).
On Tue, Nov 18, 2008 at 17:55, Dan Asimov <dasimov@earthlink.net> wrote:
What would it look like if one were inside a spherical mirror silvered on the inside?
One possible answer: http://www.flickr.com/photos/sbprzd/3043227134/ I've made another attempt, putting the camera closer to the sphere at the origin. Then comes another answer to Dan's question: if your head was in the center but your eye was not, you would see an inverted and deformed image of your head, and you would see all around even the back of your head (assuming that you are not an egg-head and that your head is spherical). If the head is not in the center, many strange images appear around the central reflection. Best, Seb
Beautiful collection! One of your pictures is a menger sponge sliced perpendicular to the diagonal of the cube; does an irrational slope give anything like a penrose tiling? On Wed, Nov 19, 2008 at 12:13 AM, Seb Perez-D <sbprzd+mathfun@gmail.com> wrote:
On Tue, Nov 18, 2008 at 17:55, Dan Asimov <dasimov@earthlink.net> wrote:
What would it look like if one were inside a spherical mirror silvered on the inside?
One possible answer: http://www.flickr.com/photos/sbprzd/3043227134/
I've made another attempt, putting the camera closer to the sphere at the origin. Then comes another answer to Dan's question: if your head was in the center but your eye was not, you would see an inverted and deformed image of your head, and you would see all around even the back of your head (assuming that you are not an egg-head and that your head is spherical).
If the head is not in the center, many strange images appear around the central reflection.
Best,
Seb
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On Wed, Nov 19, 2008 at 12:13 AM, Seb Perez-D <sbprzd+mathfun@gmail.com> wrote:
One possible answer: http://www.flickr.com/photos/sbprzd/3043227134/
On Wed, Nov 19, 2008 at 19:15, Mike Stay <metaweta@gmail.com> wrote:
Beautiful collection! One of your pictures is a menger sponge sliced perpendicular to the diagonal of the cube; does an irrational slope give anything like a penrose tiling?
The hexagonal slice: http://www.flickr.com/photos/sbprzd/1432723128/ I tried, but did not come out with anything - I remember to have read that such a slice has been found, but only with a dimension >= 5. Cheers, Seb
On Wed, Nov 19, 2008 at 09:13, Seb Perez-D <sbprzd+mathfun@gmail.com> wrote:
On Tue, Nov 18, 2008 at 17:55, Dan Asimov <dasimov@earthlink.net> wrote:
What would it look like if one were inside a spherical mirror silvered on the inside?
I've made another attempt, putting the camera closer to the sphere at the origin. Then comes another answer to Dan's question: if your head was in the center but your eye was not, you would see an inverted and deformed image of your head, and you would see all around even the back of your head (assuming that you are not an egg-head and that your head is spherical).
Just to follow up on this one, if your head was perfectly spherical, and in the center of the mirror, you would see an Azimuthal equidistant projection of your head, in one half sphere of the mirror (your head would block the other half). http://www.flickr.com/photos/sbprzd/3046151892/ Azimuthal equi-distant: http://mathworld.wolfram.com/AzimuthalEquidistantProjection.html Cheers, Seb
participants (5)
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Cordwell, William R -
Dan Asimov -
Jason -
Mike Stay -
Seb Perez-D