View from the center of a mirrored sphere

[godzillatemple]

I believe Larry Niven posed this question in one of his short-story collections years ago, but for the life of me I can't remember whether he had an answer or which book it is in.

Basically, let's say you have a large sphere (large enough for somebody to fit comfortably inside) that is mirrored on the inside. You bring it up into space and have somebody float in the center(obviously, the sphere would need to be constucted in two pieces and assembled around the observer).

The observer then turns on his flashlight. What will he see? Will he see a solid wash of light from all directions? A single light in whatever direction he looks? Something else? Would it matter if the light sourse was a flashlight that only shines in one direction or a point light source that shines in all directions at once?

Any thoughts?

Regards,

Barry

[malaka]

Along the same lines:

http://boards.straightdope.com/sdmb/showthread.php?threadid=62094&highlight=mirror+sphere+center

[Achernar]

If it's a flashlight, you'll only see it in one direction, because it's a directional beam. If it's a lantern, however, you will be able to see it in every direction that it shines.

That's to zeroth order. If you want to be more precise, you have to consider the question of where your eyes are in relation to the center of the sphere. To first order, you'll see whatever's on the opposite side. So if the center of the sphere is in your waist, you'll see your feet everywhere you look (except up, because there your view of your feet will be blocked by your head). If the center of the sphere is between your two eyes, then your right eye will see your left eye everywhere, and your left eye will see your right eye everywhere. This would be pretty freaky, I imagine.

[godzillatemple]

malaka: Thanks for the link. It looks like "Emperor Penguin" posed the same question in the middle of that thread, but nobody there was able to answer it.

Achemar: Thanks for the info. Any cites for that? What do you mean by "you will be able to see it in every direction that it shines"? Will you see multiple reflected images, a smear of light as all the images combine, or a single image at the center of your field of vision wherever you look?

Barry

[godzillatemple]

Oops! Make that Archernar and not Archemar...

[CalMeacham]

This question wasn't given by Larry Niven, but originally by Spider Robinson in one of his story collections. He said he never got a straight answer from anyone, so I thought about it a moment, and got the same answer as Achernar. If you're at the center of a sphere you're two focal lengths away, so you'll see you, basically. Of course, you'll be right in front of your eyes, so you'll be horribly out of focus. And if you're floating about your center of mass and looking straight ahead, odds are you'll be looking right at your feet.

I'm assuyming that your flashlight beam bounces around the walls efficiently enough to not be absorbed before it strikes those feet. Otherwise you'll see blackness.

[godzillatemple]

CalMeacham: Well, that would explain why I couldn't find it in any of my Larry Niven books! Now I'll have to start pawing through my Spider Robinson collection....

;)

Barry

[sailor]

Originally posted by godzillatemple
Oops! Make that Archernar and not Archemar... Better make that Achernar AKA Alpha Eridani (http://www.absoluteastronomy.com/stars/achernar.htm) The star Achernar (Scientific Name Alpha Eridani) is located at right ascension 1h 37.715m and declination -57° 14.200'.

Achernar is a relatively bright star with a magnitude of 0. It is of the spectral class B3Vpe.

[Cabbage]

As I recall, Edogawa Rampo (the Japanese answer to Edgar Allan Poe) wrote a story along these lines as well, The Hell of Mirrors.

[Achernar]

Ah, sailor always gives me the best introductions! :)

[dietrologia]

Actually, I thought it was Spider Robinson and his wife in the book Starmind, but I could be wrong.

[CalMeacham]

Actually, I thought it was Spider Robinson and his wife in the book Starmind, but I could be wrong.



He may have aised it in one of the three books the co-authored, but I know that I have it in my Spider Robinson omnibus anthology -- and I haven't managed to make it through even one of the collaborations.


Wha happens if you spread your legs, so that you don't see your feet? The you see the back of your head -- but really out-of-focus. Or else, if the light is insufficient, you see black.

[Sock Munkey]

I think it was in Callahan's Crosstime Saloon.
If the whole inside of the sphere is mirrored then shouldn't you see infinite reflections of reflections to the point of total image blurriness. Then it wold look like a blank featureless light in all directions with the color of that light being a blending of whatever colors you are wearing as the light wold be bonced off of you as well.

[Derleth]

No, you see a black screen with the words `segementation fault (core dumped)' after your raytracing program goes berzerk trying to render infinitely reflected rays of light.

"When I was a child, my parents always used to give me an Infinity Box for Christmas. It took me 364 days to get out, just in time for next Christmas ... "