*Harry Audus asked the Naked Scientists:*

On the subject of light, a hypothetical question. Suppose I had a perfectly light-tight box with a lid that was perfectly light-tight when closed. The box is standing in a light environment with its lid open. If I close the lid, will the inside of the box stay forever just as light as it was before I closed the lid?

By definition: you wrote that the box is "perfectly light-tight" and this means that it doesn't absorb light. Of course there isn't only the light that has entered, inside of it, but also the radiation the box emits itself because of its temperature. However I don't grasp the exact meaning of the phrase "will the inside of the box stay forever just as light as it was before I closed the lid?" I hope to have given the answer you were looking for.

Now suppose the box has one very very very tiny hole in it. This is a magic hole that allows light to travel through it in one direction only, from the inside to the outside.

And not from outside to inside? Physically impossible.

Is it possible to calculate how long it would take for the box to lose all its light (i.e. become completely dark)? What sort of function would the rate of loss follow?

A lot of assumptions are missing.

Assuming we could neglect the radiation emitted thermically by the box and the radiation which is present outside of it when you open the hole, that energy is redistributed instantly inside the box and ... some othe things, the energy escaping the hole in the unit time at a certain instant of time t is proportional to the energy density inside the box at that instant t, to the area s of the hole's surface and to c:

dE/dt = - c*s*E/V where V is the box' volume.

Integrating:

Integral dE/E = - Integral c*s/V dt

E = E

_{0}e

^{-c*s*t/V}where E

_{0} is the total energy of light at t = 0.

Example.

V = 1 litre = 10

^{-3} m

^{3}s = 1 mm

^{2} = 10

^{-6} m

^{2}the interval of time t needed to halve the energy inside the box is:

t = ln(2)*V/c*s ≈ 2.3*10

^{-6} s = 2.3 μs.

But this equation would be approximately true only at the beginning, at least because of the assumptions I talked about.

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