Let’s assume we have ideal mirrors that reflect 100% of the photons incident on them, and also that there will be a vacuum between the mirrors, then yes, indeed, in this scenario, the photons between the mirrors will fly almost forever.
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However, in the real world, perfect mirrors do not exist. The better the mirror is polished, the higher its reflection coefficient, and the closer it is to the ideal. But for real mirrors consisting of atoms it is impossible to achieve this since at the atomic and molecular level, the roughness will inevitably occur, even if we manage to smooth out all micro and nano roughness.
As a result, some of the photons will be reflected from the surface of the mirrors not at right angles to the surface of the mirror, which will lead to scattering and leakage of photons beyond the boundaries of the pair of mirrors. Today, there are mirrors with a reflection coefficient equal to 99.9999%, however, given the tremendous speed of light and the small distance between the mirrors, photons will stop running even between such mirrors in very small fractions of a second.
A more effective trap for photons could be a reflective sphere. Similar devices are used to simulate a black body. Such spheres release outward no more than one ten-millionth percent of the photons that have entered.