but the light will loose the energy it has as it bounces off the mirriors walls through friction and heat, this heat would be released out of the back of the mirriors slowly so thus if a jolt of energy was produced in the form of light, it would reflect untill the energy is completely disipated. you could test this by creating a enclosed room of mirriors with a light then create an apperatus to measure the energy released from the sphere and compare its levels after an hour to the set amount of energy that was sent into the sphere by the light... Thus if it is a lower amount of energy is recorded after the hour this means the light would be dimming or non existant inside the mirrior coated shere.

Let me know your thoughts =)