It is quite an intriguing question, and a lot of possibilities come to mind. The room could become a light storage device that continues to get brighter with time. Will the room stay bright even after the light is switched off? How would the room look like after continuous total internal reflection of light by mirrors?
For such a hypothetical scenario, let us consider a situation with a 60-watt bulb lit inside a perfectly sealed room where the light cannot escape. A 60-watt bulb means an energy of 60 Joules per second. In such a scenario, when we consider the specific heat of air and assume that there are about 45 moles of air per cubic meter; a total energy of about 900 Joules per cubic meter will raise the temperature of air by one Kelvin.
So, the effects will primarily depend on the size of the room. If the chamber is a little box of 1 cubic meter, it will take about 15 seconds to raise the temperature by 1 Kelvin. For a bigger room of dimensions 3x4x5, the temperature would rise by a Kelvin in 900 seconds.
We are considering that the mirrors reflect perfectly, so a 100% reflection will result in absorption of this light energy by the air. The amount of energy absorbed will also depend on the attenuation coefficient and thickness of the air.
So, a bulb in a room full of mirrors will eventually become a heater. Air also has a significant absorption and emission spectrum in the visible light region. The air will continue to absorb and convert some energy to heat and radiate some amount of energy as electromagnetic radiation. The bulb also gets heated by absorbing the light reflected off the mirrors. If an ideal bulb is used that never melts, the temperature will continue to increase as long as the bulb is powered, eventually getting so hot that it begins to emit ultraviolet rays, X-rays, and gamma rays.
The same technique is used in Rapid Thermal Processing (RTP) furnaces to manufacture semiconductor wafers. The walls of these furnaces have gold coated interiors, and the setup typically uses 20 halogen lamps of 2 kW. The wafer gets heated to 1100 degree Celsius in just a few seconds.
If you just want to see how beautiful the scene would become when the light is reflected off multiple mirrors, look at these Yayoi Kusama infinity mirror rooms.
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