What would I see inside a sphere with mirrored walls?

[Semper Fi]

Ok, I thought about this and discussed it with a friend.

I think that from the point I am viewing myself in the mirror, suppose I am looking myself in the eye, the rest of my head would be proportional to the actual size of my head, and be flared along the side of the sphere.

Suppose I stood with my arms and legs extended outward, my fingertips would be reflected like a normal mirror and from there my arm would be flared and warped with the rest of the mirror, like my head. This would continue along the mirror until the reflection of my back and eventually my legs.

The mirrors on my right side would reflect my head like it did the front. Suppose my ear and the farthest point from the center of the sphere form a straight line, the very center of my ear (or the endpoint of this line) would be undistorted, and the rest of the right side of my head would flare throughout the mirror, proportionately.

Now this leads to my ultimate question: how many of me would there be? My first thought was there would be 360 of me, one for each degree. Also there may be 8 or 16 of me, or maybe 32, one for each general direction from which my body can be viewed.

I'll have to ask my chemistry teacher this one. Man this is gonna keep me up tonight...

 

[Semper Fi]

an object set in the dead center would heat up and possibly combust, as every photon that entered the room would eventually hit it.

Imagine if we could mass produce microscopic, interior reflective spheres and put a halogen element in the absolute center of it. We could have an alternate energy source, given that the halogen would indeed react with the masses of protons. The only problem I foresee, other than figuring a way to make the spheres, would be keeping the halogen from combusting before it is needed to, or perhaps there would be a way to put it in there when it is needed. Another problem would be getting a light source in there...there arent any halogens that emit light, is there?

 

[deaddude]

You would see an infine number of progressively distorted images of yourself.
This is assuming 100% reflection

 

[manu1959]

you wouldn't see a damn thing it would be dark

 

[Hobbit]

Imagine if we could mass produce microscopic, interior reflective spheres and put a halogen element in the absolute center of it. We could have an alternate energy source, given that the halogen would indeed react with the masses of protons. The only problem I foresee, other than figuring a way to make the spheres, would be keeping the halogen from combusting before it is needed to, or perhaps there would be a way to put it in there when it is needed. Another problem would be getting a light source in there...there arent any halogens that emit light, is there?

Incorrect. The energy needed to light up the inside of the sphere would be greater than the energy gained from the heating of the sphere, and since that energy is already in a usable form, why convert it at a loss? Law of conservation of energy.

 

[The ClayTaurus]

Incorrect. The energy needed to light up the inside of the sphere would be greater than the energy gained from the heating of the sphere, and since that energy is already in a usable form, why convert it at a loss? Law of conservation of energy.

Exactly. At best, you could maintain the energy source at a constant (with 100% reflection)

 

[Semper Fi]

Makes more sense now. Was just feeling ambitious that night.

 

[Mariner]

Unless you floated over very close to the glass, your primary reflection would be upside down and left-right reversed.

As for multiple reflections and distortion, it has to be incredibly complicated. You'd have to trace the rays, which would bounce many times before reaching your eyes.

One thing is certain--the only thing you could "see" would be images of yourself + the lighting source. So your whole field of vision would be filled with some kind of pattern of you + the light in the room. You wouldn't see any empty space around you. Immediately around your primary image there would be reflected images from the sphere behind you, the exact pattern of which would likely change a lot as you moved around. Some of them would be right-way-up and some not. The ones that bounced more would be dimmer, since the mirror would not reflect 100% of the light at each reflection. However, the light itself better not be very bright, because you would be seeing many images of it. You might need sunglasses. (Don't believe me? Take a regular light bulb, and arrange a few mirrors so the light is bounced to your eyes several times--it will be blinding, even though it's all coming from one light source.)

It would be fun to set up a computer model and do the ray tracing, perhaps for a simpler problem, e.g. a stick image within a circle.

Mariner.

 

[Mariner]

I searched the web, and found exactly the ray-tracing experiment that I suggested doing a few minutes ago, in interactive form.

The center blue dot is your head. The distant blue dot is the point you're looking at. If you put your head above center and look around, the ray tracing shows that you will see yourself upside down, until you look way high up, at which point you'll see various images of your feet and lower legs (depends how high your head is in the sphere).

On the other hand, if you put the head dot near the center of the sphere, and then look around, you start to get fanastic patterns of rebounding images, tending to infinite reflection as you look upwards.

Here's the website:

http://www.cut-the-knot.org/Curriculum/Geometry/MirrorSphere.shtml

See, liberals are good for something.

Mariner.

 

[Semper Fi]

See, liberals are good for something.

No they're not.

 

[Mariner]

trouble of thinking about your question, posting an answer, then finding you a great website and adding an explanation--and that's not good for something?

Aren't you aware that by historical standards everyone in America is a liberal? Our entire country is a liberal experiment, to see if the "little people" could govern themselves. The weekend is a pure liberal creation, brought to you courtesy of labor unions who fought to reduce the standard 12 hour a day, 6 day a week workweek favored by the 19th century and early 20th century capitalists. Don't you like liberal ideas like forbidding child labor, allowing women and minorities to hold property and vote, and making sure elderly people don't starve to death? Most "conservatives" do, but continue to put down liberals anyway.

If you're in a car accident, do you plan to ask your rescuers whether they're conservatives before you'll accept their help?

Mariner.

 

[The ClayTaurus]

trouble of thinking about your question, posting an answer, then finding you a great website and adding an explanation--and that's not good for something?

Aren't you aware that by historical standards everyone in America is a liberal? Our entire country is a liberal experiment, to see if the "little people" could govern themselves. The weekend is a pure liberal creation, brought to you courtesy of labor unions who fought to reduce the standard 12 hour a day, 6 day a week workweek favored by the 19th century and early 20th century capitalists. Don't you like liberal ideas like forbidding child labor, allowing women and minorities to hold property and vote, and making sure elderly people don't starve to death? Most "conservatives" do, but continue to put down liberals anyway.

If you're in a car accident, do you plan to ask your rescuers whether they're conservatives before you'll accept their help?

Mariner.

Deep breath, buddy. Take a deeeeeeeep breaaaaath...

 

[Mariner]

I think I've stopped hyperventilating--thanks,

Mariner.