# The Naked Scientists Forum

### Author Topic: How much light can you keep in a box?  (Read 7583 times)

#### goolag

• First timers
• Posts: 4
##### How much light can you keep in a box?
« on: 26/05/2011 22:04:48 »
This question is driving me insane!

If it take a box with *perfect* 100% reflective, no-loss one-way mirrors on the internal surface and I shone a bright light into the box, how much light could it contain?

If I got a really bright light and shone it for a hundred or so years, would the box continue to hold the light?

Is there a limit to how much light can be contained in one place?

If I placed the box next to a really bright star for a million years, then smashed the box, would the light all burst out at once and would it cause any damage?

Somebody please 'illuminate' me as I keep coming back to this every now and then and it's bugging me!

#### CZARCAR

• Hero Member
• Posts: 686
##### How much light can you keep in a box?
« Reply #1 on: 27/05/2011 01:41:09 »
i dont think 100% reflective is possible so the box would heat up

#### Supercryptid

• Hero Member
• Posts: 606
##### How much light can you keep in a box?
« Reply #2 on: 27/05/2011 02:33:53 »
I can take a stab at the question.

Light is composed of particles called photons, and photons are bosons. The funny thing about bosons is that you can have as many of them in the same quantum state as you want to. This is in contrast to fermions such as electrons, which must all occupy different quantum states. The consequence of this is that you can have a whole bunch of photons in one place at one time.

Relativity teaches us that not only matter generates a gravitional field, but so does energy. As you add more and more light to the mirrored sphere, the gravity increases. At some point, the amount of energy inside of the sphere will become so great that the light will collapse into a black hole. That would take a lot of light energy to accomplish, however. Perhaps something else would limit how much light you could put in the sphere, but I'm not aware of any such thing.

Oh...wait...I just thought of another possible limiting factor; radiation pressure. It is known that light exerts a pressure on objects. That is the principle behind the solar sail spacecraft concept. I imagine with enough light energy in the sphere, there would be so much radiation pressure that the sphere would break apart. Every material has some limit on how much pressure it can withstand.

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### How much light can you keep in a box?
« Reply #3 on: 27/05/2011 06:02:29 »
I think Supercryptid has excellent points there.  And CZARCAR has good a good point as well: no matter how good your mirrors are, they absorb or transmit a tiny percentage of the light.  But when you have enough light, a tiny percentage becomes a huge amount of energy, so a lot will be lost or it will heat up the mirrors until they melt.

I think we can confidently say that no physical mirrored box would ever be able to contain all this light.  I think the only thing that could really trap light like that would be a black hole.  Light would go in, but not come out again.  The effect of adding more light would be to add mass to the black hole and increase it's size.  But even a black hole slowly radiates away energy due to Hawking radiation, so it doesn't store the light energy forever.

By the way, you mention using "no-loss one-way mirrors."  One-way mirrors actually transmit the same percentage of light in both directions, but when they're used (in interrogation rooms, for example), one side is brightly lit and the other is dimly lit.  The person on the brightly lit side can't see the light coming from the dark side since his own reflection is much brighter than the dim scene coming through the mirror.  In your case, the inside of the one-way-mirror box would be sending the same percentage of light out as was sent in.  As soon as it got bright enough, it would be losing light as fast as it gained light from the outside.

#### Geezer

• Neilep Level Member
• Posts: 8328
• "Vive la résistance!"
##### How much light can you keep in a box?
« Reply #4 on: 27/05/2011 06:07:04 »

when they're used (in interrogation rooms, for example), one side is brightly lit and the other is dimly lit.  The person on the brightly lit side can't see the light coming from the dark side since his own reflection is much brighter than the dim scene coming through the mirror.

You seem to have a lot of first hand knowledge in this field JP.

#### JP

• Neilep Level Member
• Posts: 3366
• Thanked: 2 times
##### How much light can you keep in a box?
« Reply #5 on: 27/05/2011 06:15:48 »

when they're used (in interrogation rooms, for example), one side is brightly lit and the other is dimly lit.  The person on the brightly lit side can't see the light coming from the dark side since his own reflection is much brighter than the dim scene coming through the mirror.

You seem to have a lot of first hand knowledge in this field JP.

Whatever are you talking about.  By the way, Geezer, if you could just step this way, I'd like to ask you a few questions...

#### CliffordK

• Neilep Level Member
• Posts: 6321
• Thanked: 3 times
• Site Moderator
##### How much light can you keep in a box?
« Reply #6 on: 27/05/2011 08:10:23 »
I think we can confidently say that no physical mirrored box would ever be able to contain all this light.  I think the only thing that could really trap light like that would be a black hole.  Light would go in, but not come out again.

Would the event horizon of a black hole be equivalent to a perfect mirror?  The point where the light is forced into a circular orbit around the black hole.  At which point, the event horizon would become infinitely bright.

#### goolag

• First timers
• Posts: 4
##### How much light can you keep in a box?
« Reply #7 on: 27/05/2011 08:22:59 »
Thanks and interesting!

I appreciate you cannot have a 100% reflective 1 way mirror, but I was talking theoretically

Also, if the box was unbreakable and the pressure element thus eliminated, what are we talking about then?

would i just be creating a black hole? i thought photons had no mass, so if no mass why would the gravity increase?

#### imatfaal

• Neilep Level Member
• Posts: 2787
• rouge moderator
##### How much light can you keep in a box?
« Reply #8 on: 27/05/2011 10:47:31 »
would i just be creating a black hole? i thought photons had no mass, so if no mass why would the gravity increase?
They have energy - energy is equivalent to mass.  too much energy in one place you have same result as too much mass

I am probably making a horrible faux pas which someone will delight in pointing out
you can take the formula showing the schwarzchild radius

rs=2GM/c2
as inertial mass = gravitational mass switch in E/c2 for M
calling number of photons N you can switch in Nhν for E

You would then have a formula in terms of Number of photons of certain frequency that you could put in a certain radius - also bearing in mind that your wavelength is constrained by the containment as well (max wavelength in a box is 2*length).  To be honest the above looks very hooky to me - but what the hell...

#### Phractality

• Hero Member
• Posts: 523
• Thanked: 1 times
##### How much light can you keep in a box?
« Reply #9 on: 27/05/2011 20:27:23 »
This question is driving me insane!

If it take a box with *perfect* 100% reflective, no-loss one-way mirrors on the internal surface and I shone a bright light into the box, how much light could it contain?

If I got a really bright light and shone it for a hundred or so years, would the box continue to hold the light?

Is there a limit to how much light can be contained in one place?

If I placed the box next to a really bright star for a million years, then smashed the box, would the light all burst out at once and would it cause any damage?

Somebody please 'illuminate' me as I keep coming back to this every now and then and it's bugging me!

EDIT: If the opening in the box faces a uniformly bright surface in all directions that can be seen from the opening, the brightness inside will immediately become the same as the brightness outside.

Assuming you shine a laser thru a small opening in the box, it would bounce around inside the box until it eventually returns to the opening and excapes. The number of internal reflections would depend on the shape of the box and the direction of the beam as it enters. There would be special cases, where the beam reflects only once before leaving. I doubt if there is any real geometry which would result in infinite reflections, but there could be special cases where it reflects billions of times. I think the upper limit depends on the size of the opening in proportion to the size of the box.

On the other hand, since you are starting with the impossible assumption of 100% reflectivity, I suppose you could also postulate a one-way opening, which allows light to enter but never to leave. Since light has momentum, and the act of reflecting involves force, you would also have to assume that your box is infinitely strong. Otherwise, the outward pressure of light reflecting back in would eventually explode the box.

If we may return closer to reality for a moment, you should consider a silver-lined box with no opening, floating in space. Silver reflects approximately 90% of visible light on each reflection. Assume you have a point source of light floating inside the box and not absorbing any light. The total brightness at an average point inside the box would be approximately 20 times brighter than the case in which the inside surface is perfectly black. (Based on adding the infinite sequence, 1 + .9^1 +.9^2 + .9^3... +.9^n.)
« Last Edit: 27/05/2011 20:31:15 by Phractality »

#### yor_on

• Naked Science Forum GOD!
• Posts: 11697
• Thanked: 1 times
• (Ah, yes:) *a table is always good to hide under*
##### How much light can you keep in a box?
« Reply #10 on: 28/05/2011 09:11:51 »
You could also apply chaos theory to it :)

Assume that the box is a mystical attractor, and that light doesn't propagate. How does it get into the box? Do you really need a 'opening' then? Where does the limit goes for pair productions, will the box 'expand' as seen from the inside as it gets filled with 'energy'?

And yes, it's just for fun.

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How much light can you keep in a box?
« Reply #11 on: 28/05/2011 19:48:48 »
There is no need of silver or other material for a perctly reflecting mirror: you only need to inject a leser light inside a glass fiber at the right angle (total internal reflection).

#### Phractality

• Hero Member
• Posts: 523
• Thanked: 1 times
##### How much light can you keep in a box?
« Reply #12 on: 28/05/2011 20:32:14 »
There is no need of silver or other material for a perctly reflecting mirror: you only need to inject a leser light inside a glass fiber at the right angle (total internal reflection).

Total internal reflection eliminates one problem and introduces several others. Real optical fibers attenuate the light intensity between 1 and 10 db/km. That translates to between 300,000 and 3,000,000 db/s. So you can't store light in an optical fiber more than a few microseconds.
« Last Edit: 28/05/2011 20:34:12 by Phractality »

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How much light can you keep in a box?
« Reply #13 on: 30/05/2011 21:37:26 »
Ok. Then I propose to use a normal cavity with internal reflecting walls, but very tiny in diametre as a glass fiber, so that the incidence angle of the injected laser light is near 90°. The reflection coefficient is much higher in this conditions.
This fiber-like cavity could be wrapped in many loops.
« Last Edit: 30/05/2011 21:39:16 by lightarrow »

#### syhprum

• Neilep Level Member
• Posts: 3770
• Thanked: 16 times
##### How much light can you keep in a box?
« Reply #14 on: 04/06/2011 02:38:29 »
If you used a box of one cubic meter capacity with perfectly reflecting walls and exposed it to sunlight at the surface of the Earth that has an intensity of 1300 Joules per second per square meter moving at c it would collect 1300/c joules.

1300/3*10^8 = 4.33*10^-6 J  with a mass equivalent of 4.33*10^-6/c^2 = 4.8*10^-26 Kg

Post by cherrypink27 click to view.

#### cherrypink27

• First timers
• Posts: 1
##### How much light can you keep in a box?
« Reply #15 on: 04/06/2011 02:46:05 »
Shrunk
hello,im interested in studying about astronomy.

#### CZARCAR

• Hero Member
• Posts: 686
##### How much light can you keep in a box?
« Reply #16 on: 05/06/2011 00:12:14 »
wOULD THE BOX GET LIGHTER?

#### syhprum

• Neilep Level Member
• Posts: 3770
• Thanked: 16 times
##### How much light can you keep in a box?
« Reply #17 on: 05/06/2011 00:47:16 »
nO IT WOULD BE A LITTLE BIT HEAVIER

#### CZARCAR

• Hero Member
• Posts: 686
##### How much light can you keep in a box?
« Reply #18 on: 05/06/2011 01:00:23 »
nO IT WOULD BE A LITTLE BIT HEAVIER
light has no mass, only energy?

#### lightarrow

• Neilep Level Member
• Posts: 4586
• Thanked: 7 times
##### How much light can you keep in a box?
« Reply #19 on: 05/06/2011 19:00:57 »
nO IT WOULD BE A LITTLE BIT HEAVIER
light has no mass, only energy?
The system: (Box + Light inside) has a mass variable according to the amount of light's energy inside. If the amount of energy is not given by light but something else (anything else) it's the same.
« Last Edit: 05/06/2011 19:04:03 by lightarrow »

#### The Naked Scientists Forum

##### How much light can you keep in a box?
« Reply #19 on: 05/06/2011 19:00:57 »