Inverse square law. Light decreases at the square of the distance. If your light source is 1000 lumens at 10', it'll be 100 lumens at 20'. Light can travel arbitrarily long distances (literally across the universe), albeit decreasing in strength. Additionally, typical mirrors are only 90% reflective, so that's additional loss with each mirror you add. Human visual acuity varies by wavelength. It's best for blue-green light, worst for red. For ideal wave lengths, humans can detect as little as 1 photon. There's also some scattering based upon atmospheric density (pressure) and particulate matter (smoke, haze, etc). The TLDR is that your light will be visible in any real cave no matter how faint. Setting aside hypotheticals like 100 light year long caves with single photon light sources at one end.