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Inside a Spherical Mirror

Dorfl

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Jun 19, 2005
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If an astronaut, equipped with a flashlight, was floating inside a sphere with a perfectly reflective surface, what would he see?

Is there any software which could render his view approximately, or can it be figured out just with pen and paper?
 
Sounds like everything would be reflected everywhere ... including the light from the flashlight.
 
As his body (and the flashlight) were the only things that absorbed the light, he would slowly heat up until he died. Assuming he didn't run out of oxygen first.

Visually, he would see the room get brighter almost instantly, and probably too bright to keep his eyes open. Whether it would be so bright he'd have to close his blast shield because his eyelids and, say, sun goggles weren't enough, who knows.
 
His best bet would be to move away from the exact center. In this way, some of the light would miss him and keep bouncing back and forth indefinitely.
 
Beerina said:
As his body (and the flashlight) were the only things that absorbed the light, he would slowly heat up until he died. Assuming he didn't run out of oxygen first.

Visually, he would see the room get brighter almost instantly, and probably too bright to keep his eyes open. Whether it would be so bright he'd have to close his blast shield because his eyelids and, say, sun goggles weren't enough, who knows.
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You don't think his body could absorb the light from his flashlight quickly enough to reach some sort of equilibrium? It's likely only a single bulb of light measured in a few watts. Of course, he could always turn it off at any time. I suspect things would go completely dark very quickly should he do that. Also, we don't know how big the sphere is ... could have a radius the size of the orbit of Mercury.
 
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Beerina said:
His best bet would be to move away from the exact center. In this way, some of the light would miss him and keep bouncing back and forth indefinitely.
Click to expand...
Depending on the size of the sphere relative to the size of the guy, he could also lie against the surface of the sphere and block some portion of it from reflecting the light.
 
I think there are a lot of variables that would effect what he saw. If the sphere is huge, the light would probably be so diffused that he might see a faint glow in some directions and probably blackness in others. If the sphere was pretty small (and we assume a regular flashlight, not a giant spotlight or anything) I think he would see kind of a blurry reflection of himself in some directions and a reflection of bright light (not any brighter than the bulb) in others. I think he would absorb enough of the light so that it wouldn't really be blinding, unless he lined up the flashlight so that it reflected right into his eye after only a couple reflections without being blocked by his body at all. Mirrors aren't perfectly reflective, so with each reflection some of the light would be lost (actually converted to heat).

Now if we consider a "point astronaut" :D then (I think) more of the energy coming from the flashlight would preserved as light instead of converting to heat in which case it might get to a blinding level ... if point astronauts have eyes :covereyes.

I don't think the thing would heat up enough to kill the astronaut. Eventually the sphere is going to reach an equilibrium where it's emitting the same amount of energy as is coming out of the flashlight, it's just a matter of how hot it get's before that equilibrium is reached. This is dependent on how much energy is coming out of the flashlight and how well the sphere can release heat. Fortunately for the astronaut, I don't think the flashlight would really be strong enough to kill him. However, if we make the sphere sufficiently insulated ... well, it would be curtains for the astronaut. Of course the astronaut would be creating his own heat as well. Hmm, there must be some point of insulation at which if the astronaut doesn't turn on his flashlight, he won't reach a temperature to kill him, but if he does use his flashlight, he'll overheat though I'm sure it's a very fine line.

Going back to the "point astronaut", when the inside of the sphere reached a point where there was enough light hitting the mirrored surface so that it's reflective inefficiency caused the sphere to lose enough heat to it's surroundings to reach equilibrium, it would no longer get any brighter inside. Adding an astronaut with physical size just gives the system another way to convert light to heat. And (I think), since there would be heat energy inside the sphere that could heat up the sphere shell, helping it to release heat, less light would have to strike it to be converted to heat to reach equilibrium.

So, the smaller the astronaut the brighter the inside of the thing would be.

Also, there are many people on this forum that have much better understanding of physics than I do. So please, if anything I have said isn't accurate, don't have any reservations about letting me know.:)

edit: Missed the part about it being perfectly reflective. In which case, the mirror would not convert the light to heat. The point astronaut would result in the inside of the sphere becoming increasingly more bright until the flashlight stopped emitting light. The astronaut with physical size would be the sole converter of light to heat (assuming the inside of the sphere is a vacuum, which I think we're supposed to assume because it's in space) and his best bet would be to get as much of himself as possible pressed against the surface of the sphere so that conduction can occur. And turning off the flashlight might not be such a bad idea.
 
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Unlike a Bull said:
Now if we consider a "point astronaut" :D then (I think) more of the energy coming from the flashlight would preserved as light instead of converting to heat in which case it might get to a blinding level ... if point astronauts have eyes :covereyes.
Click to expand...

Now that I think about it, it isn't necessarily the case that both of the astronaut's eyes would have at all the same view, so maybe we should assume that he is point-shaped. But then again, if he lacked extension in space there would not be anything for him to see reflected inside the sphere. Maybe we should assume that he is one-eyed.
 
I'm sorry--What?
There is limited energy available in the flashlight. There is no way that the mirrored sphere itself can increase that. So the max temperature increase (from the flashlight) is that which would occur if the batteries discharged instantaneously.
Light brightness is proportional to the inverse of the distance traveled. Depending on the size of the sphere, the nth reflection is going to be too dim to see, and none of them are going to blind him any worse than the flashlight itself will if he looked directly into it (and the light that hits him is blocked/ diffused, and no longer as energetic.

He's in a hell of a lot more danger of overheating from his own metabolism
 
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rwguinn said:
I'm sorry--What?
There is limited energy available in the flashlight. There is no way that the mirrored sphere itself can increase that. So the max temperature increase (from the flashlight) is that which would occur if the batteries discharged instantaneously.

Light brightness is proportional to the inverse of the distance traveled. Depending on the size of the sphere, the nth reflection is going to be too dim to see, and none of them are going to blind him any worse than the flashlight itself will if he looked directly into it (and the light that hits him is blocked/ diffused, and no longer as energetic.
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I agree entirely with the first part, the second part makes a false assumption. The danger to the person inside the mirror is non-existent, no more so than if you took a flashlight and shined it on a spot on your arm until the batteries died. You wouldn't overheat, you wouldn't catch fire, nothing would happen of particular importance.

The brightness of light falls as the square of the distance traveled for a spherical emitter, however, in this case, assuming a perfect mirror, it would disperse, but the light would not escape, instead it would be continuously reflected back until it was absorbed. In short, it is not a spherical emitter.

If the person inside the sphere was coated with perfect mirror except for the eyes, then it would brighten until the eyes were absorbing the full strength of the flashlight, close to what you would experience by putting a flashlight right in front of your eyes and turning it on. At that point the flashlight would be releasing light into the room at the same rate that the eyes were absorbing it and you'd have an equilibrium of sorts.

If the person's eyes were perfect mirrors themselves (or point objects with zero surface area, or perfectly transparent, for that matter) then the person would be completely blind since it takes some absorption of light for vision to occur. That was what always bothered me about the invisible man...
 
If we assume that heating is not a problem, does anyone know what the astronaut's view would look like?

Intuitively, it feels to me like he would be seeing himself, smeared over the inside of the sphere. After all, a line drawn from his eye in any direction, reflecting off the walls, would intersect his body (or the flashlight) eventually. I might be wrong though, and it is not a very detailed picture anyway. Does anyone have a better idea?
 
jasonpatterson said:
I agree entirely with the first part, the second part makes a false assumption. The danger to the person inside the mirror is non-existent, no more so than if you took a flashlight and shined it on a spot on your arm until the batteries died. You wouldn't overheat, you wouldn't catch fire, nothing would happen of particular importance.

The brightness of light falls as the square of the distance traveled for a spherical emitter, however, in this case, assuming a perfect mirror, it would disperse, but the light would not escape, instead it would be continuously reflected back until it was absorbed. In short, it is not a spherical emitter.

If the person inside the sphere was coated with perfect mirror except for the eyes, then it would brighten until the eyes were absorbing the full strength of the flashlight, close to what you would experience by putting a flashlight right in front of your eyes and turning it on. At that point the flashlight would be releasing light into the room at the same rate that the eyes were absorbing it and you'd have an equilibrium of sorts.

If the person's eyes were perfect mirrors themselves (or point objects with zero surface area, or perfectly transparent, for that matter) then the person would be completely blind since it takes some absorption of light for vision to occur. That was what always bothered me about the invisible man...
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I think we said the same thing.
 
Beerina said:
As his body (and the flashlight) were the only things that absorbed the light, he would slowly heat up until he died. Assuming he didn't run out of oxygen first.

Visually, he would see the room get brighter almost instantly, and probably too bright to keep his eyes open. Whether it would be so bright he'd have to close his blast shield because his eyelids and, say, sun goggles weren't enough, who knows.
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NO!

The flashlight has an "ON" and an "OFF" switch. Everyone knows that "OFF" switches DARK ON. Thus the flashlight operates both as a light emitter, and a lightsucker.

"OFF" mode is very efficient, allowing the flashlight to be used as a propulsion device by the astronaut in the sphere by simply pointing where he wants to go, clicking the switch, and vacuuming up photons, which creates the powerful pull forces required for intersteller travel inside a spherical mirrored device.

What is done with the vacuumed up photons? They are resold on the black market - regions of the universe high in dark matter.
 
mhaze said:
What is done with the vacuumed up photons? They are resold on the black market - regions of the universe high in dark matter.
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I bought some of those photons once. They're not nearly as good as fresh photons. You should always buy your photons from a reputable source.

By the way, I've squandered some of my precious day off doing some math on this.

If we assume the flashlight uses two size D batteries and they each contain 75,000 joules of energy ( http://www.allaboutbatteries.com/Energy-tables.html we'll assume alkaline batteries although I'm sure NASA uses some crazy alien-technology, area 51 type battery. Probably Lithium-ion.) that would be some 150,000 joules together.

http://www.engineeringtoolbox.com/human-body-specific-heat-d_393.html says the average human body has a specific heat of 3470 J/kgC. So if we ignore his gear and flashlight, and assume he is 70 kilograms ... his temperature will go up by about .6 degrees C. Not enough to kill him. We need bigger batteries.
 
Dorfl said:
If we assume that heating is not a problem, does anyone know what the astronaut's view would look like?

Intuitively, it feels to me like he would be seeing himself, smeared over the inside of the sphere. After all, a line drawn from his eye in any direction, reflecting off the walls, would intersect his body (or the flashlight) eventually. I might be wrong though, and it is not a very detailed picture anyway. Does anyone have a better idea?
Click to expand...

As I understand it, he wouldn't be seeing anything but a glare from any direction - the flashlight is the only emitter of light, whereas his body etc. only reflect - this would be swamped by the continuous emission from the flashlight.

(Just tried to model that in a Bryce scene, with a light source and a stone texture cube inside a perfectly reflective sphere. Sure enough, once you enable total internal reflection to a high degree (obviously infinite is not available, but a couple hundred iterations can be done in acceptable time), it's all shapeless glare. I wouldn't treat that as any great evidence obviously, although Bryce's laws of optics are pretty good.)
 
He would receive no more energy than he would if he shone the light directly on himself. The sphere only reflects energy, it does not amplify it.

Seeing as the mirror is convex though, it would reflect back as a tiny point of light (which he would see in any direction he looked). Depending on the focal length of the sphere's convex side, though, he might be focusing the flashlight to a tiny point that could give him small local burns.

Note also that we only need to be concerned with the first reflection of the light. After it is reflected and the distance between the source and the observation point becomes so great that the light is greatly diffused and will just provide a dim glow.

Don't look at the first reflection directly though, although if my scenario is correct, the only way that could focus directly on the eyes is if he was holding the flashlight between his eyes.

Anyway, that's my take.
 
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