Can light continue without a light source? If you have 2 mirrors over for each other placed exactly so they face each other perfectly, and then use a laser light pen as the source into one of the mirrors so it bounces to the other mirror and back again:


*

*Would the laser light line continue to exist between the 2 mirrors if the source of the laser stopped?

*If so, how long could the laser light continue to be between the mirrors without a source?

*Would it just continue existing between the mirrors using itself as the source or is this not possible for light?


Note: It doesn't have to be only 2 mirrors. It could be any amount of mirrors if that would change the outcome.
 A: We recieve light from far away stars even they are dead when the signal reached to earth. So, the source is not there when we actualy see it (capture the light with space telescopes).
A: A quick calculation which I heard of sometime ago (I don't remember where, I just remember the concept).
The only datum I found (ok, I looked only for a few minutes, so forgive me) on mirrors is on wikipedia. A dielectric mirror can reflect up to 99.999%. Pretty impressive, isn't it? Only 10 parts per million are lost every "bounce". 
Now, how many "bounces" are needed so that the intensity is 1 millionth of the original source? Well, math says that it is about 1.38 million bounces.
Now, imagine the mirrors are 1 meter one from the other. The light will travel 1.38 million meters before degrading to 1/1000000 of its original intensity. How long does it take? Well, 4.6 ms.
So, with an almost perfect mirror and being able to detect until 1 millionth of the original light, will you see the light slowly dimming off? Well... No. A common camera acquiring at 25fps has one frame every 40 ms.
So even with an almost perfect mirror and an almost perfect detector, I'm afraid light is so damn fast..
A: Assuming ideal experimental conditions (using a perfect, or spherical mirror, for example) the laser light wouldn't reflect forever. This is because photons have momentum, $p = h/\lambda$, which means that each reflection will transfer momentum to the mirror, i.e.
\begin{align}
\Delta p \, &= \, 0 \>\> \text{(conservation of momentum)}                   \\
         \, &= \, \Delta p_{_{photon}} \, + \, \Delta p_{_{mirror}}          \\
         \, &= \, \big[ - p_{_{photon}} \, - \, ( + p_{_{photon}} ) \, \big]
         \,  + \, \big[ \>\, p_{_{mirror}}^{^{final}}
         \,  - \> ( \> p_{_{mirror}}^{^{initial}} = 0 \, ) \>\, \big]      \\\\
         \, &\implies p_{_{mirror}}^{^{final}}
         \, = \, 2 \, p_{_{photon}}
\end{align}
This transfered momentum will heat up the mirror, after which the energy will be lost as thermal radiation, and the laser light will gradually decohere.
I believe that the calculation for the lifetime of the original laser photons might depend on variables such as the wavelength of the light, $\lambda$, the size, shape, and material of the mirror, and the temperature of the room. This might be helpful:
https://en.wikipedia.org/wiki/Thermal_radiation
A: Yes, it would continue. But not forever, for two reasons. One is that no mirror is perfect, so a bit of light is lost at each bounce. The other is that no beam of light is perfectly parallel ("collimated"), so that the light spreads out over time, and light eventually falls outside the mirror. 
Edits after comments
Spherical mirrors will help, but they will not eliminate the problem at hand, which is diffraction. A perfectly collimated beam is not possible, but as a corollary to that it is also not possible to produce a beam with a finite cross section. Some portion of the beam always falls outside of the next mirror.  
Using beams that are approximately Gaussian (perfect Gaussian beams are impossible) and spherical mirrors the amount of energy that misses the next mirror is small, but not zero.  
The OP's question #3 is new.  I don't quite know what you mean by "itself as the source". If you can somehow get the light going, it will continue for a while after you turn off the source. The decay, as others have pointed out is (approximately) exponential as roughly the same fraction is lost on each bounce. It's approximately exponential because the beam shape will change as bits are diffracted away, so the fraction lost changes slightly from bounce to bounce.
How long the light will persist depends entirely on the quality of the set up. The surface quality of the mirrors, their surface figure, the atmosphere, the materials used, the rigidity of the mounts ...  It's probably possible to estimate the longest possible persistence time taking into account effects that others have mentioned in other answers:  scattering, heating, momentum transfer, ... I don't know what the "theoretical" maximum would be, or the practical limit. A quick search on Fabry-Perot interferometers finds finesse values in the $10^6$ ball park, which would imply a persistence time for a 30 cm cavity of about 1 ms, but that's a very rough estimate.
A: 
would the laser light line continue to exist between the 2 mirrors if the source of the laser stopped. 

As DJohnM commented,


light travel to the moon and back, even though the laser source is off for most of the round trip.


This happens because any light source emits photons. They are indivisible packages of energy and they are traveling as long as they not get absorbed by an obstacle or - more precise - by a subatomic particle.

Would it just continue existing between the mirrors using itself as the source or is this not possible for light?

As told above, once emitted, the photon is on it own and don’t anymore care about the source.
But where is another point about the mirrors. What garyp told you in his answer is about the technical imperfection. Beside this, any reflection process of photons is accompanied at least with the transfer of a momentum to the mirror. Every photon pushes the mirror a little bit and any photon - due to energy conservation - leaves the mirror with a lower frequency. So the light dies a infrared death and the mirror gains velocity, or the temperature raises. 
A: With a perfect laser and perfect mirrors yes it would and this is provable from the conservation of energy.
If you turn on a one watt laser for 1 second it will use on joule of energy. That energy must exist after the light is turned off. If it has not been absorbed by the mirror in heat then it must still exist as light.
In reality as pointed out the light will scatter and be absorbed very quickly so this effect can't be observed.
A: well, light is both a radiation and a particle , in this case we'll consider it as a particle from the moment it got out of the source and started it's ongoing travel through space time , the particle of light will continue traveling until it hits the mirrors , and then there are two cases : 
-light will be 100% reflected by the mirror ,  if the mirror is considered as a perfect conductor 
-it'll be99% reflected by the not so perfect mirror and will vanish within 100 or so ..reflections 
so once a photon is thrown away by a source it'll continue it's journey forever until it reaches something , and  no we can't consider a light wave a light source ,a light source is in brief something that radiates (emits energy ) energy to get rid of some "excess" in energy , while a light particle is just a finite quantity of energy , quantum, traveling through space-time .
