Re: if light entered a light-proof box of mirrors- would the light intensify?

Jonathon, 
The short answer to your question is "No".  The reason is that you have 
presented a design for a perpetual motion machine in which energy (e.g., 
light amplification) gets created from nothing.  Science has proven that 
perpetual motion machines are an impossibility and even the US Patent Office 
has declared that PMMs will not be considered.  The technical reason is that 
light loses some of its energy each time it bounces (i.e., some of the light 
gets absorbed by the mirror and the air in the box).  Because of the loss, 
the light cannot "amplify".  Amplification always requires one to add 
energy.

On a more technical note, what you describe is akin to a laser.  Lasers 
operate on the principle that light can be amplified by beaming it into a 
solid, liquid, gas, or plasma with a mirror at both ends.  The matter in 
between is designed to be excited by the wavelength of the light which then 
emits light of the same wavelength, etc., etc. As the light passes through the 
matter and bounces off of the mirror on the other end, it increases (amplifies). 
 The light exits through a small hole in one of the mirrors creating a very high 
intensity laser "beam".  Usually all of the light exiting the laser is of one 
wavelength (i.e., color) and in-phase.   The high energy density is attributed 
to Light Amplification through Stimulated Emission of Radiation (or LASER, for 
short - did you know that was the acronym?).  Unfortunately, there is always a 
source of energy that fuels the amplification.  I'd encourage you to look at 
Laser's though, for they are fascinating machines.

This is all not to say that your idea of improving the efficiency of Solar 
Cells could not be accomplished by utilizing light energy that is initially 
rejected by solar cells.  I would think that looking at the profile of what 
light is rejected and how it could be used to improve efficiency.  We know 
that mirrors can be used to focus more light onto solar cells to increase power 
output, but at the expense of more area covered by mirrors.  In particular, you 
might look at the sensitivity of solar cells to wavelength, since the sun 
contains all wavelengths and there may be some that are not utilized as well in 
typical solar cell structures.  

Good luck with your endeavors.  You may email directly at tjamison@observera.com 
with any further questions.

Todd Jamison