Only if

1: The mirrors are perfect (and we don't get such)

and

2: The air in the space between the mirrors is perfectly transparent (and we don't get such)

In practice such a reflection is doing well if it can last for microseconds.

As Jon says, the mirrors and the air have loss and so the answer is that the light would be converted to heat. However, you would not really know the anser until you open the box to look. So, before you open the box it is both light and dark.

Even with perfect mirrors and a perfect vacuum

the will be no "infinit" radiation.

A radiation field in such a cavity has a temperature,

which is the color temperature of the torch.

(Look up blackbody radiation, Kirchhoffs law,

Planks formula, the laws of thermodynamics etc)

Georg

No, The light will be reflected back onto the source. Absorption at the source will limit the the luminance in the box.

The radiance in the box can never exeed that of the source.

If you put a normal torch into an actual mirrored box the radiance will not even come close to that of the source, i.e. the filament or LED die, because of absorption in the casing, the bulb and of course the mirrors.

Oh blast!!!

I misread the question again! Uninfinitely silly me!

On rereading the responses of my companions, I retract my answers. I meant that that what we could not do was to trap light for illumination of infinite duration, not of infinite qunatity or intensity.

Sorrrryyyy about that!

I have reservations about HU's answer in that I find it hard to believe that all incident light would have to enter by routes that would permit light to exit again. For one thing, we could surely generate light by external inductive means. For another, we could generate light internally by permitting the mutual annihilation of particles and antiparticles.

However, no, we could not ever achieve infinite light or light intensity. Even if we could, an amount of light far short of infinity even for a nanosecond, in any compact reflecting cavity would blast any containing structure apart. And it would take the destruction of more matter than the observable universe. And it would collapse into a black hole.

We keep saying this: Even the smallest infinity isn't big; it is beyond big. Even the largest observable universe is not big, it is negligibly small in mathematical terms.