Is it possible to build a mirror cage in order to catch light in it? Let's assume the surface of the mirror reflects absolutely 100% of the light. Which shape of cage is the best to do this? Is it also possible to "fill" up the cage with light?
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It may stretch the parameters of your question but I believe a combination of slowing the speed of light and capturing it in a lossless optical fibre system could do this.
The speed of light is normally about 186,000 miles per second, or fast enough to go around the world seven times in the wink of eye.
Scientists succeeded in slowing it down to 38 mph.
They did this by shooting a laser through extremely cold sodium atoms, which worked like “optical molasses” to slow the light down.
By transforming the optical fiber span into an ultralong cavity laser, we experimentally demonstrate quasilossless transmission over long (up to 75 km) distances and virtually zero signal power variation over shorter (up to 20 km) spans, opening the way for the practical implementation of integrable nonlinear systems in optical fiber. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.96.023902
The device could consist of an incredibly long coil of optical fibre rolled into a ball and placed into your cage. Light would be fed into one end of the fibre-optic cable until it was 'full'. It would then emerge from the other end over a period of hours.
If the light was to be kept for longer, the end of the cable could be connected back to the input. The light would go around the circuit until required.
100% reflective mirrors do not exist in reality. The best we can get is dielectric mirrors, with reflectivity around 99.9% at specific wavelengths.
That aside, if you want to trap light, just shape the mirror as a sphere with perfectly reflective surfaces. Any photon inside the sphere will keep bouncing in the sphere.
A similar concept is employed in the making of the integrating sphere (the only difference being that it is not perfectly reflective)
An integrating sphere (also known as an Ulbricht sphere) is an optical component consisting of a hollow spherical cavity with its interior covered with a diffuse white reflective coating, with small holes for entrance and exit ports. Its relevant property is a uniform scattering or diffusing effect. Light rays incident on any point on the inner surface are, by multiple scattering reflections, distributed equally to all other points. The effects of the original direction of light are minimized. An integrating sphere may be thought of as a diffuser which preserves power but destroys spatial information. It is typically used with some light source and a detector for optical power measurement. A similar device is the focusing or Coblentz sphere, which differs in that it has a mirror-like (specular) inner surface rather than a diffuse inner surface.
I have not been able to find any reference to the cited Coblentz sphere, though.
Not with conventional mirrors: Even with something like 99.9999999...% reflection, there are losses. The light is reflected back-and-forth a trillion times inside a box, which causes the seemingly insignificant loss to accumulate fast enough and the light fades almost instantly, in human perception.
Edit: Based on SpoonMeiser's comment, the optic fiber has a bulge somewhere along the fiber. The light is trapped and spirals back-and-forth along the bulge. The length of the bulge determines the frequency of the light it can trap. The article has no mention how light is caught and then released on command.
A resonance bottle is a very small molecular structure
No, because light moves at the speed of light. That means it can cover the circumference of Eart multiple times in a second. You will let all the light out before you can close the lid.
Also each photon will impart momentum to the walls upon hitting them, even if they are magically 100% reflective. Over finite time they will lose energy and become non-visible radiation.
You can get more kick for your money by buying a battery and a flashlight.
Q1: Is it possible to build a mirror cage in order to catch light in it?
Yes in fact there is an existing term for this in physics and engineering: The Optical Cavity https://en.wikipedia.org/wiki/Optical_cavity
An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light. hey are also used in optical parametric oscillators and some interferometers. Light confined in the cavity reflects multiple times producing standing waves for certain resonance frequencies.
Optical cavities are literally a pair of mirrors or other material that reflects light. They are configured so that a light wave reflecting on either mirror will keep the same frequency and overlap strongly with the other light waves in the cavity. When this happens the totality of light waves in the cavity will 'constructively interfere' and add up thereby forming a single more powerful light wave of the same frequency. As you pump more light waves into the cavity, by keeping the same frequency on each reflection, you may continue to add up more light waves thereby forming an extremely energetic light wave. This behavior is called resonance. Consequently, when you remove one of the mirrors after doing this for some time, the cavity will emit the powerful resonant light wave. The light wave emitted will carry the total energy of all light put into the cavity but as a single wave (boom laser).
Errata: * Photons and Light Waves are the same thing (per wave-particle duality). I call them light waves here to drive home the wave mechanics that make this work. * When the constructive interference occurs, the two waves are essentially adding together. Since mirrors are not perfect, or their placement might not per perfect, said interference will not be perfect either. Consequently that means the waveform after interference will carry sub frequencies or nodal pairs. This will change the overall resonance behavior or may cause issues with the cavity as a whole (heating it up or light escaping) * Resonance is occurring because multiple waves will constructively interfere over time forming a more powerful photon or set of photons. Since interference is not perfect, ultimately you can get close to resonance but not perfect. Ideally the cavity should be adjusted or automatically adjusted to keep as close to resonance as powerful and to emit the wave before the cavity fails or becomes permanently damaged.
Q2 Which shape of cage is the best to do this?
According to the stability diagram for a two mirror cavity, the most stable configurations are plane-parallel and concentric (upper right and bottom left of the linked diagram).
Q3 Is it also possible to "fill" up the cage with light?
Yes. See above.
Without assuming an extremely (and unreasonably) fast means of replacing the entry aperture with a (perfect) mirror, or and extremely (and unreasonably) large cage, even if you grant perfect mirrors it won't work.
Regardless of mirror geometry, the fact that any beam of light will spread ensures that eventually all of the light will bouncing around with essentially uniform dispersion, and some of that will hit the entry aperture and exit the cage. This process will automatically self-regulate, so that the power exiting the aperture will equal the input power.
For "reasonable" cage sizes, as you close the aperture the input power must drop to zero, so the exit power must drop to zero as well, and the energy content of the cage must drop to zero.
The obvious way around this is to make the cage very big. Then the speed of light will allow you to close the aperture fast enough to allow some light to remain within the cage.
If you have a mirror that can reflect 100% of the photons that land on it, it doesn't matter what shape you use. As long as the container the light is placed into is perfectly sealed and the inside is a vacuum, you will be able to store it in the cage forever.
Why? because your material is 100% (not 99.9999%, 100%) reflective, it will absorb no energy and shoot out as many photos as it receives with the same velocity. Light is never absorbed so just keeps bouncing around. The shape only matters if you want to store more energy, because you will need to increase the length the light bounces before it exits the box. I would recommend a very long and straight box, shoot the light in almost parallel (the closer to parallel the better) to the entrance and let it bounce all the way down and out. Seal the Box and you have the light trapped inside.
Now you need a vacuum. If there is anything else inside except a vacuum you will lose energy. Why? because your photos are going to hit the molecules inside the box and be absorbed by it in the form of heat energy. So even if the outside is perfectly insulated and reflects 100% of the energy, eventually all your photos will have hit that one special molecule that is still inside the box and you will just have one super fast molecule bouncing around inside.
Finally you can't exactly fill up a shape with light. Light has no mass and doesn't take up space. It can interfere with itself, but thats about it.
If you don't need mirrors you could convert (compress?) light into matter for easier storage and then back again when needed.