Here at Decoded Science, we recently received the following ‘Ask the Expert’ question:
“This question has been on my mind for a little over a week now. Imagine a hollow and airtight sphere.
Inside this perfect sphere, is an albedo of 100% (or as close to 100% as possible).
If light were introduced to the inside of this sphere for 1 second, would the inside of the sphere remain lit due to the combination of high albedo and no openings for the light to escape, or would the light die along with its source?”
As usual, we presented the question to our experts, and the following dialogue resulted.
Rather than distill the discussion into a single article, we have elected to present it, as it stands, to you, our readers.
As always, questions and comments are welcome!
Here are the experts who weighed in on the question, in the order in which their comments appeared:
Vincent Summers: It sounds like a cross between the bouncing effect of mirrored surfaces, e.g. in lasers, only involving loss… Would the light bounce around indefinitely (how could we say, psychologically, ‘The sphere is lit up,’ if no one can see any light emanating from it)? What mechanism(s) would modify that…
Paul Heckert: Good point. There would be no way to see inside. If the albedo really were 100%, ideal case not real, then it seems like the light would continue to bounce around inside. But perhaps that would make the outside surface act like a blackbody and radiate energy. I don’t know the answer to that one.
Vincent Summers: One of 3 as I see it: transmission, reflection, absorption. Absorption probably quantum, transmission obvious, reflection obvious. As you say, unreal, a mental exercise.
Mike DeHaan: Albedo=100% implies perfect reflection (within the frequency range of the light). Classic physics: endless reflection. Plus blackbody radiation (mainly infra-red photons carrying heat, emitted from the interior, and absorbed). More likely: eventually some of the light’s energy would warm up the sphere, so fewer photons of the appropriate frequencies are available. (But more infra-red, per blackbody radiation). Not sure that quantum physics would make a difference.
Easy real-world experiment: 2 nearly parallel mirrors give “endless” reflections; but are the after-many-repeats reflections dimmer than the original?
Paul Heckert: It sounds like you have it, Mike.
Vincent Summers: I hesitated on the warming thing. That implies things beyond my reach. For one thing, the possibility of photon absorption to produce the heat. Photon absorption is quantum. Now free electrons are able to absorb any quantity of energy. But bound ones are not. I’m not sure this one would be a thumbs up unless it is clearly indicated it is a mental exercise.
Paul Heckert: My take after more thought: If the albedo were really 100% inside the cavity, then the light would reflect 100% and therefore bounce around inside indefinitely. In reality the albedo can never really be 100%. In that case energy would be transferred to the surface. The outer surface would radiate energy outward as a black body radiator with the amount of energy per unit area and the wavelength of the maximum energy radiated depending on only the temperature of the black body.
This temperature would gradually increase as the energy inside decreased via less than 100% reflection. The apparatus described would meet the definition of a black body radiator because the light/energy enters and the apparatus described absorbs 100% of the light.
Mike DeHaan: This seems right. I assume that this means the interior would gradually lose photons and become darker (or go to lower frequency photons).
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