system
Given the following post, respond as if you're commenting on Reddit:
human
If I were to stand in the middle of a completely sealed, spherical mirror with a light bulb in the middle, would the light build up to blinding levels, or just remain as bright as the bulb?

Title basically says it all, but I imagine if you have a box full of bouncy balls, and you keep throwing them in there with infinite energy, adding more and more would increase the density of the balls in the box, so would the same thing happen with light?
gpt
Short answer:  for perfectly reflecting walls, it's gonna get hecka bright.

Let's start with what determines the brightness of an incandescent bulb.  You've got some electrical power P being deposited in the resistive filament.  The filament heats up to the point where that input power is matched by all the power it loses to conduction and radiation.  The radiation it puts out is that of a rather imperfect blackbody... but let's just pretend it's a perfect little blackbody whose radiation is given by its surface area and temperature, T (maybe in the neighborhood of 4500F = 2500C).

As the hot filament fills the sphere with light, the energy density of that light grows, dE/dt = P, assuming you're not conducting any energy out of the sphere.  Some of the light traversing the sphere impinges on the little filament, and is absorbed.  That means the filament has to heat up so it can radiate more power (to balance the new input of absorbed light).   Indeed, if you managed to fill up the sphere to just the right energy density (that associated with the temperature of the filament) you could turn off the electrical power and the filament (and radiation) would remain forever at the temperature T.

But, if you keep pumping in electrical power, the filament will heat up, the radiation energy density will increase... until something gives.  For a practical filament, the material will fail when it gets too hot, opening the circuit... but then of course the whole system will remain at some high temperature, forever.