There is a solid glass sphere that is 1 mile in diameter. It is completely covered in dirt and rock, except for one small room that is built adjacent to the sphere. One of the four walls of this room is the surface of the sphere. What would the sphere look like to someone standing in this room holding a pitch torch?

I understand the answer might depend on what type of glass the sphere is made of. Please feel free to assume whatever type of glass makes answering this question easiest. The sphere can even be diamond, or any other "clear" mineral, if using glass is a problem.

EDIT1: Assume a very fine polished surface.

EDIT2: It seems I have to clarify. When I ask "what would the the sphere look like", I want to know what a person looking at the surface of the sphere would see. Unless 1 mile wide blocks of glass cause blindness, "nothing" is not an answer. I want to know, very literally, what looking into this sphere would be like. If the glass is completely dark, please elaborate: is it dark like a gloomy room behind a glass panel, or is the surface of the glass completely black as if made of obsidian? Would bringing the source of light closer to the surface of the glass have any effect?

  • Comments are not for extended discussion; this conversation has been moved to chat. – James Aug 14 at 21:38
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    Try it in a raytracing renderer like povray! – user25907 Aug 15 at 3:05
  • @BaileyS For an entire 0.5 mile radius? Send that out; don't run it on your personal computer. – can-ned_food Aug 15 at 6:27
  • @can-ned_food I am not sure if you are joking? – user25907 Aug 15 at 17:55
  • Let's say that you went with 72 pixels of texture map per inch. If you worked with that scale, mapping the texture of the cave outside the sphere, then you certainly wouldn't want to tie up your personal computer for all that. That's what I meant, @BaileyS – can-ned_food Aug 16 at 0:22
up vote 48 down vote accepted

If the glass is unflawed, the opening will look like a flat, nearly-black mirror.

When you look at glass, you see a combination of the light reflecting off the surface and the light coming through it. (Think windows at night.) This is the key to Pepper's Ghost.

In this case, there will be no light coming through the surface, since even glass isn't transparent enough for any meaningful amount of torchlight to travel a mile through it, reflect off the opposite edge, and travel all the way back.

So all you'll see is the light reflecting off the edge of the sphere, or possibly reflecting off flaws and imperfections inside the sphere (but I'm assuming "solid" rules that out). Given how big a mile-diameter sphere is, it'll appear utterly flat.

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    Thank you! I'm glad I asked this question: your answer is not what I expected would be the case. – Pink Sweetener Aug 14 at 2:09
  • I disagree. Looking up Optical Fibre on Wikipedia yields an upper bound of 0.2dB/km for pure silica. This would give ONLY 0.8dB for a round trip from the far end (assuming a 2km diameter ball, order of magnitude calc). This would give only a 10% transmission loss. However you will still suffer from inverse square losses. The optical distance of the far end is approximately 0.66 miles ish... – Aron Aug 14 at 10:34
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    @Aron: An optical fiber is a waveguide; the light propagates in a different way. For something comparable to the situation described in the question you should look at the transmittance of photographic lenses. – AlexP Aug 14 at 11:06
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    Best answer so far. It wouldn't appear completely dark in there, the glass will appear to have a greenish tinge (…) as the transmitted spectrum of light is highest around the middle of the visible spectrum, and light will occasionally be backscattered from the glass molecules. You can see this a little if you line up two second surface mirrors to be nearly parallel, or look at a large block of glass. – Mauser Aug 14 at 20:39
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    @Mauser That's an excellent addition! You're welcome to make your own answer or edit mine, or I can add it in. I'd think it would still look like a faintly greenish mirror, but you know more about those effects than I do. – Draconis Aug 14 at 20:50

Also worth touching on refractive and transparent colour - which can vary wildly depending upon specific trace elements in the glass... and which can also significantly impact reflectivity and refractive index - as can heat: some glass compositions, when unevenly heated, create surface coatings not unlike thin film, which then hugely impact refractive index - think soap bubbles and their amazing coloured waves...

So it's really hard to prognosticate effectively with this little data.

I can say (I'm an architectural renderer, so I do in fact spend a fair amount of time thinking about and researching reflectance and refractance properties of specific glass types) that given you stipulate the sphere's entirety being covered in dirt and rock with the sole exception of ONE single opening adjacent to the glass sphere, there will be no other incident light, no other refracted light, and so you would most likely only have surface light interactions - how scratched the surface is, what finish texture (glossy, semi-gloss, semi-matte, matte; cracklure, rippled, frosted, etched) the surface has and to what depth that finish is applied will have profound implications on the appearance.

You might for example (if there's a scratched and almost frosted surface with some depth to it - say 1/2") get some significant sub-surface scatter (SSS) effects... or if the surface is matte but the matte portion is quite a thin layer, get none at all.

It would most likely look a lot like thick sea ice at the poles when exposed - incredibly dark, with a slight green-tinted SSS, but almost featureless unless light is at a very glancing angle.

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    Thank you for your answer. After a little googling, I'm not sure what "sub-surface scatter" or "thick sea ice at the poles" looks like. Throw a bone to a layman? – Pink Sweetener Aug 14 at 11:42
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    sub surface scatter is the effect you see when low-angle or back-angle incident light is transmitted inside a material, and then re-exits, giving a softening "glow": think candle wax, human ears or noses... it's an effect which renderers have spent a long time trying to master for more photorealistic results - and in translucent materials such as frosted glass, if the layer is thick enough, this effect can be noticeable. Dark thick ice:… – GerardFalla Aug 14 at 15:31
  • So instead of a mirror, you suggest it might look more like a dark, milky material that fades into opaqueness? – Pink Sweetener Aug 14 at 15:43
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    well no - I'm saying the basic materiality would be incredibly dark and opaque, but... where there is surface damage, you might see a cracked, almost frosted glass appearance, and in that sense, it might look one hell of a lot like those ice lake images I posted. The real issue controlling appearance here is not just the surface damage / quality, but also where and how much incident light the observer has: one single point source (flaming torch) with no ambient is going to be pretty matte and dull: if there are surrounding sources behind your observer too, you might well see SSS. – GerardFalla Aug 14 at 15:53
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    Got it, thanks! Matte and dull is just fine. I don't need it to look pretty, just plausible. – Pink Sweetener Aug 14 at 15:56

Not really much of anything.

Assuming that the sphere is completely flawless, you won't see anything inside of it. A torch probably doesn't put out enough light to illuminate the far side of the sphere, so there simply won't be anything to see (except your reflection, of course). If there were something to see, it would be slightly distorted by the shape of the glass but, as RonJohn's answer points out, the curvature is so slight as to be negligible.

Now, in all likelihood a huge glass sphere isn't going to be completely flawless. If it is warped in places but not actually broken, you would be able to see distortions, a little bit like immobile heat haze. If it was cracked, you could see the cracks.

The takeaway here is that glass is sufficiently transparent that you don't really see glass - you see the discontinuities between glass and air, or between sections of glass with different properties. (In technical terms, you see the difference in the refractive index of the materials.) With only the one, highly regular surface, there won't be anything to see.

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    With any glass that could be made in such quantities, it would absorb most of the light you shine into it. Also, it would have to be old or otherwise it would still be hot -- it would take many, many years to cool down from molten. – Mark Olson Aug 13 at 21:58
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    I hadn't really considered how the glass sphere came to be; I just assumed it was magic. Otherwise I have several questions. ("Why" being the foremost.) – Cadence Aug 13 at 23:24
  • This is good information, but "there simply won't be anything to see" isn't really an answer. A person is looking at a thing: unless that person is vision-impaired, they must see something. Do you mean to convey that the glass would be completely dark? Would the glass appear as black obsidian? Would the proximity of the light source have any effect? – Pink Sweetener Aug 13 at 23:33
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    If there's only light in the room, the sphere would be perfectly reflective, like a normal window with house lights and a dark night outside but moreso. If there's light inside the sphere, it would look very much like a sphere full of air, although the light would fall off more quickly (it wouldn't be as bright) and it would probably diffuse more quickly (it would turn hazy at a shorter distance). – Cadence Aug 13 at 23:54
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    @EricDuminil Even if the surface I am describing absorbs all incoming light and emits nothing in return, not a single photon hitting my eyeballs, one could still describe that surface as "completely pitch black, 100% void of all light and color". I need to describe this thing to my D&D party; I can't tell them that the wall "looks like nothing". And as it so happens, the wall is apparently somewhat reflective, so it does look like something. – Pink Sweetener Aug 14 at 15:53

What would the sphere look like to someone standing in this room holding a pitch torch?

A flat wall, because the deviation of the surface of a sphere that size is 1/1382nd of an inch per foot (the diameter of such a sphere being 1 mile x 5280 feet/mile x pi = 16588).

Please feel free to assume whatever type of glass makes answering this question easiest.

The type of glass has nothing to do with the fact that it will look flat when looked at up close. (It's the same reason the Earth looks flat when you're in Kansas.)

  • It will also be reflective, like windows viewed from inside a lit room at night. – intrepidhero Aug 13 at 20:31
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    @intrepidhero good point. Unless it's dusty and all scratched up. Whatever you see... "solid glass sphere that is 1 mile in diameter" won't be the first -- or tenth -- thing that comes to mind... :) – RonJohn Aug 13 at 20:39
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    "A flat wall" I guess I was hoping for a little more than this. I understand the geometry of the wall, but what does it look like? – Pink Sweetener Aug 13 at 23:38
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    Take your phone, turn it off, now look at the screen... It'll look pretty much like that, but covering an entire wall from floor to ceiling. No light is coming from inside it, so the effect will be of light falling into it because it is. Light will be lost to the Great Orb and scattered across a mile of glass. The only light from it will be the partial reflection off its surface. The nearest thing to this in real life is probably the behaviour of light in a glacier. – Ruadhan Aug 14 at 10:34

Unless the glass is quite extraordinarily pure, it will look the same as a one-mile obsidian sphere. Jet black, with some reflection from the surface. Impurities in any ordinary glass will absorb all the light you might see before it reaches the far side of the sphere. If you look at the side of an ordinary pane of window glass, it is dark turquoise-green, and that's under two feet of glass.

But it is possible to make ultra-pure glass that will transmit light over tens to hundreds of kilometers. This is what long-distance fibre-optic cables contain. So if you want an "inexplicable" object, it can be transparent enough to see internal reflections of your torch without violating the laws of physics as we know them. It's just a technological issue.

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    It hadn't occurred to me to look sideways at a pane of glass to see what it would be like if it were thicker. Interesting. I suggested in my answer that there would be some absorption (it's a mile across!) but this seems to indicate I was drastically underestimating how much. Unless, as you say, the sphere is absolutely pure as well as flawless. – Cadence Aug 14 at 16:31

What would the sphere look like to someone standing in this room holding a pitch torch?

I'll go ahead as mentioned in the comments (and approved by the asker) and relax that "pitch torch" restriction. Also, this answer is based on your statement that the room is built, if the room is a natural occurrence, other workarounds must be found.

From your comments to Draconis' answer, I gather that you were hoping for a more "scenographic" result than a "simple" mirror.

There are ways in which (I think, but I am open to corrections) you could achieve that.

You say that

one small room that is built adjacent to the sphere. One of the four walls of this room is the surface of the sphere.

you can position along the sides of this "glass wall" a series of strong LEDs, these will emit enough (exact quantity TBD) lumens so that:

  • the inverse square law will bring the intensity of the light after a round trip to observable levels (we are speaking of a maximum distance of 2 miles, that's quite a lot for a pitch torch)
  • will project enough light in all directions so that internal reflection will be affecting a noticeable fraction of the light

How to achieve this?

Between the LEDs and the sphere there must be as little space as possible, and possibly a material with the same refractive index of glass (so that all light from the LEDs ends up into the sphere)

What will a person in the room see?

Good question, this is the part I am least sure. I think it would be reasonable to say that they would perceive diffuse light from the far side of the sphere (coming from those internal reflections).
It is possible that they could also perceive the rocks behind the sphere (light leaving the sphere, reflected by the rocks, and re-entering the sphere), but I am not too confident about this.

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