# The Naked Scientists Forum

### Author Topic: Does light remain in containers?  (Read 8792 times)

#### chiralSPO

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##### Re: Does light remain in containers?
« Reply #25 on: 23/07/2015 22:07:32 »
Thanks all for your contributions. Of course I neglected to say that all internal surfaces are perfectly reflective, but I think most of you realised my intent.
As to the calculation of how long it would take for the box to empty of light via the one-way hole (again, of course, a hypothetical construct), I'm afraid the responses assumed a level of knowledge I don't have. Does anyone have a simple explanation? Or perhaps an explanation of why a simple explanation of the solution isn't possible?
With perfectly reflecting walls, if you neglect the radiation emitted thermically by the container and you neglect the thermal radiation outside the container, the solution is simple: the time needed to empty the container is infinite.
You can see it from the equation I wrote:

E = E0e-c*s*t/V

Solving from t you get:

t = (V/c*s) log(E0/E)

and if you put E = 0, you get t = oo.

But as you saw from the simple computation I made in my previous thread, in a very short time (of the order of microseconds) the energy inside the container is almost reduced to zero. So if you intended to use that system to store energy...it's not very useful.

In a more realistic situation, essentially because of not perfectly reflecting walls, visible radiation will be lost quicker; furthermore, since the outside environments cannot be at a temperature less than 2.75 K (cmbr radiation) the container will stop losing radiation in a finite time, when it will have reached thermal equilibrium with the environment.

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lightarrow

The time is only infinite if photons are infinitely divisible, which they are not. One only has to solve the equation for the time required to get to less than 1 photon to find the answer (assuming a long list of things you have already pointed out...) One thing I do not see in this equation, is a reference to the size of the hole, or the surface area of the box--these will certainly have an effect on the rate of photons leaving.

#### Bored chemist

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##### Re: Does light remain in containers?
« Reply #26 on: 23/07/2015 22:14:13 »
Thanks all for your contributions. Of course I neglected to say that all internal surfaces are perfectly reflective, but I think most of you realised my intent.
As to the calculation of how long it would take for the box to empty of light via the one-way hole (again, of course, a hypothetical construct), I'm afraid the responses assumed a level of knowledge I don't have. Does anyone have a simple explanation? Or perhaps an explanation of why a simple explanation of the solution isn't possible?
With perfectly reflecting walls, if you neglect the radiation emitted thermically by the container and you neglect the thermal radiation outside the container, the solution is simple: the time needed to empty the container is infinite.
You can see it from the equation I wrote:

E = E0e-c*s*t/V

Solving from t you get:

t = (V/c*s) log(E0/E)

and if you put E = 0, you get t = oo.

But as you saw from the simple computation I made in my previous thread, in a very short time (of the order of microseconds) the energy inside the container is almost reduced to zero. So if you intended to use that system to store energy...it's not very useful.

In a more realistic situation, essentially because of not perfectly reflecting walls, visible radiation will be lost quicker; furthermore, since the outside environments cannot be at a temperature less than 2.75 K (cmbr radiation) the container will stop losing radiation in a finite time, when it will have reached thermal equilibrium with the environment.

--
lightarrow

The time is only infinite if photons are infinitely divisible, which they are not. One only has to solve the equation for the time required to get to less than 1 photon to find the answer (assuming a long list of things you have already pointed out...) One thing I do not see in this equation, is a reference to the size of the hole, or the surface area of the box--these will certainly have an effect on the rate of photons leaving.

I don't understand why you don't see a reference to the size of the hole- it's "s".
The area of the box is a bit more obscure but it's in there. It has been combined with the length of the box (which is also important) to get a volume.

#### chiralSPO

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##### Re: Does light remain in containers?
« Reply #27 on: 24/07/2015 15:51:09 »

I don't understand why you don't see a reference to the size of the hole- it's "s".
The area of the box is a bit more obscure but it's in there. It has been combined with the length of the box (which is also important) to get a volume.

My mistake then. It would help though, to have a definition of terms to make it easier to interpret these equations.

#### Bored chemist

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##### Re: Does light remain in containers?
« Reply #28 on: 24/07/2015 18:35:13 »
Something like this?
"... the energy escaping the hole in the unit time at a certain instant of time t is proportional to the energy density inside the box at that instant t, to the area s of the hole's surface and to c:"

#### chiralSPO

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##### Re: Does light remain in containers?
« Reply #29 on: 24/07/2015 19:13:29 »
Something like this?
"... the energy escaping the hole in the unit time at a certain instant of time t is proportional to the energy density inside the box at that instant t, to the area s of the hole's surface and to c:"

precisely!

#### Bored chemist

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##### Re: Does light remain in containers?
« Reply #30 on: 25/07/2015 01:06:23 »
Now all I need to do is perfect my time-travel device...

#### lightarrow

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##### Re: Does light remain in containers?
« Reply #31 on: 25/07/2015 08:59:35 »
Something like this?
"... the energy escaping the hole in the unit time at a certain instant of time t is proportional to the energy density inside the box at that instant t, to the area s of the hole's surface and to c:"

precisely!
What is not clear to me is if you realized that Bored Chemist here quoted my first post of this thread.

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lightarrow

#### lightarrow

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##### Re: Does light remain in containers?
« Reply #32 on: 25/07/2015 09:31:41 »
The time is only infinite if photons are infinitely divisible, which they are not. One only has to solve the equation for the time required to get to less than 1 photon to find the answer (assuming a long list of things you have already pointed out...)
This is true, my was just a classical description. But what you say is not "immediate" as it seems. I'd like to see how you would perform the computation.

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lightarrow

#### chiralSPO

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##### Re: Does light remain in containers?
« Reply #33 on: 25/07/2015 13:39:54 »
Something like this?
"... the energy escaping the hole in the unit time at a certain instant of time t is proportional to the energy density inside the box at that instant t, to the area s of the hole's surface and to c:"

precisely!
What is not clear to me is if you realized that Bored Chemist here quoted my first post of this thread.

--
lightarrow

Sorry, I guess this is the problem with trying to keep up with posts that are so far apart--by the time I read the last post on your equation, I had forgotten the one with the definitions (posted 9 days later, and 20 posts down). My bad! [:I]

#### Bored chemist

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##### Re: Does light remain in containers?
« Reply #34 on: 25/07/2015 14:16:27 »
I strongly suspect that Lightarrow's expression is incorrect since it doesn't depend on the geometry of the box, only the volume.
It's complicated.

#### lightarrow

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##### Re: Does light remain in containers?
« Reply #35 on: 25/07/2015 21:56:30 »
I strongly suspect that Lightarrow's expression is incorrect since it doesn't depend on the geometry of the box, only the volume.
It's complicated.
And why should depend on geometry, given the assumptions I made (e.g. that the energy is redistributed instantly inside the box) and the macroscopic dimensions of the box I used in my example? Do you relate to the cavity geometry when you derive the black body spectrum of emission? Remember that we are talking of light here, that is em radiation with a wavelength enormously shorter than the box dimensions. Furthermore the OP didn't say that a thin ray of light enters the box or something like that, he generically talked of "light" out of the box which entered through a lid, so through a macroscopic aperture. In this conditions the radiation fills the box homogeneously and in the end it's not geometrical optics that you have to use, but em field description.

Anyway, as I wrote when I derived my expression, it was just an approximate computation because of the many assumptions made (implicitly or not).

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lightarrow

#### lightarrow

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##### Re: Does light remain in containers?
« Reply #36 on: 25/07/2015 22:02:28 »
Sorry, I guess this is the problem with trying to keep up with posts that are so far apart--by the time I read the last post on your equation, I had forgotten the one with the definitions (posted 9 days later, and 20 posts down). My bad! [:I]
No problem, sometimes I make the same mistake  .

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lightarrow

#### Bored chemist

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##### Re: Does light remain in containers?
« Reply #37 on: 25/07/2015 22:33:38 »
I strongly suspect that Lightarrow's expression is incorrect since it doesn't depend on the geometry of the box, only the volume.
It's complicated.
And why should depend on geometry, given the assumptions I made (e.g. that the energy is redistributed instantly inside the box) and the macroscopic dimensions of the box I used in my example? Do you relate to the cavity geometry when you derive the black body spectrum of emission? Remember that we are talking of light here, that is em radiation with a wavelength enormously shorter than the box dimensions. Furthermore the OP didn't say that a thin ray of light enters the box or something like that, he generically talked of "light" out of the box which entered through a lid, so through a macroscopic aperture. In this conditions the radiation fills the box homogeneously and in the end it's not geometrical optics that you have to use, but em field description.

Anyway, as I wrote when I derived my expression, it was just an approximate computation because of the many assumptions made (implicitly or not).

--
lightarrow
Granted, you wrote "Assuming ... that energy is redistributed instantly inside the box and ... ".
But I don't think that assumption is valid.
In particular if the box is very long and thin (as CRDS systems generally are) the decay time along the length will be a lot longer than the decay time across the width.
Explicitly including the length and area allows for that factor.

#### lightarrow

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##### Re: Does light remain in containers?
« Reply #38 on: 27/07/2015 13:18:36 »
I strongly suspect that Lightarrow's expression is incorrect since it doesn't depend on the geometry of the box, only the volume.
It's complicated.
And why should depend on geometry, given the assumptions I made (e.g. that the energy is redistributed instantly inside the box) and the macroscopic dimensions of the box I used in my example? Do you relate to the cavity geometry when you derive the black body spectrum of emission? Remember that we are talking of light here, that is em radiation with a wavelength enormously shorter than the box dimensions. Furthermore the OP didn't say that a thin ray of light enters the box or something like that, he generically talked of "light" out of the box which entered through a lid, so through a macroscopic aperture. In this conditions the radiation fills the box homogeneously and in the end it's not geometrical optics that you have to use, but em field description.

Anyway, as I wrote when I derived my expression, it was just an approximate computation because of the many assumptions made (implicitly or not).

--
lightarrow
Granted, you wrote "Assuming ... that energy is redistributed instantly inside the box and ... ".
But I don't think that assumption is valid.
In particular if the box is very long and thin (as CRDS systems generally are) the decay time along the length will be a lot longer than the decay time across the width.
Explicitly including the length and area allows for that factor.
Granted, that assumption is wrong in the case you write
When I made the example of box, I had in mind something compact, like a sphere or a cubic box, but I forgot to write it explicitly.
Thanks for correction.

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lightarrow

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##### Re: Does light remain in containers?
« Reply #38 on: 27/07/2015 13:18:36 »