Can light be trapped theoretically? My question is a little silly I know, but I'm curious to know if a particle of light can be theoretically trapped between two reflective screens. 
For example once the particle of light has left it's source, and is reflected against a mirror (assuming there is no loss of energy) and you immediately replace the source of light with another mirror. Would the light beam bounce in between the sheets endlessly?
 A: The best complex dielectric mirrors, see

http://en.wikipedia.org/wiki/Perfect_mirror

may reflect up to 99.999 percent of the incident energy. The loss is about 1/100,000, so after 100,000 reflections, the total intensity decreases $e=2.718$ times or so. If the distance between the mirrors is 3 meters, the light travels 3 meters times 100,000 = 300,000 meters before it gets diluted $e$ times, and it takes 1/1,000 of a second. So within one millisecond, most of the light is absorbed, anyway.
The time may be extended by increasing the distance between the (great) mirrors.
In principle, if the mirrors got better, a photon could be trapped. Its phase would be changing by the gravitational field – the photon would literally start to accelerate downwards. With the realistic mirrors described above, this acceleration downwards is pretty much unobservable.
More generally, the absorption by the inevitably imperfect mirrors is still the fastest process that makes the vision about the trapped photon impossible. Within the time scale before the light gets absorbed, the photon may be considered almost perfectly trapped because all other effects that violate it are negligible in comparison.
A: From your question, I guess the double mirror configuration is just an example you thought of. I suppose your question actually is about if a photon can be trapped. Then basically yes. A device able to confine electromagnetic wave or light or photon is called cavity. You should understand a photon does not necessarily means a propagating plane wave. It can be in fact an excitation of cavity modes. Of course in practice there doesn't exist perfect cavity. The figure of merit used to measure how long a cavity can keep a photon is quality factor Q. The capability of holding a photon for long time is important for many real life applications, so much effort has been made in pursuit of higher and higher Q value. 
A: Yes & No, You can however create an perfect mirror, which does not absorb any of the photons energy however its simply not possible or even feasible at this time to create such a device without energy being conserved in the photon, but it will however it will loose its energy due to Gravitational red shift after a long-time or Red shift due to moving in expanding space. Therefore it is possible to trap a photon however as time-passes the energy of the photon will be lost to space.
To conclude, a photon can be "trapped" however its initial energy cannot be trapped as it will be lost, but you could create a pair of photon then smash them together to create  electron-positron pair which could be saved without loss of energy. 
Read: http://en.wikipedia.org/wiki/Pair_production
Then to change them back into photons simply take the electron-positron and smash them to create 2 photons thus you can trap photons in a different state. 
A: As everybody says, we don't have perfectly reflective mirrors so light that is reflected many times will eventually be absorbed.
I read an article dated some time before 1990 that described the shape for a curved mirror that would trap light. Light that enters the mirror gets bounced at increasing angles until it is reflected back and forth at a ninety degree angle from the entrance. To get that effect the hole in the mirror that light enters can't be much over 40% the area of the cross-section of the mirror. (The mirror is a 3D structure and the inside is a mirror surface; light that enters the hole must be reflected at a big enough angle to miss the hole but instead hit another mirror on the inside. Think of an egg shape.)
So you start with light entering across an area, and you end with light reflecting from a mirror basicly along a line. The article did not include an estimate of how big a mirror like that would have to be,before it could collect enough sunlight to melt itself along the line that the reflections converged to.
The article was either in the American Mathematical Society bulletin or in American Mathematical Monthly. I don't remember which and a moderately thorough search just now didn't find it.
A: The issue with perfect mirrors is the false assumption that the surface is without defect.  This is of course impossible and the scale of the defects is on an order of magnitude several times larger than a photon; ergo the light will diffuse rapidly.  Think of it like trying to bouncing a pea sized ball straight up and down in a gravel pit.  Even if it were possible to encase a beam of light within a reflective sphere, the light would diffuse until the entire volume of the sphere appeared to glow dimly as opposed to a clean crisp beam endlessly bouncing around inside.  Of course this is not observable.  Perhaps someone would like to experiment with the fiber optic loop suggested above and light slowed through a Bose-Eisenstein condensate.  It might be possible to actually trap a beam observably for a short period of time. 
