My answer is not much different from the other ones, but it is based on my personal experience. For several years I have been using Cavity ring-down spectrosopy(CRDS) - the method to measure very weak light absorption that is based on building such optical cavity and placing an absorbing sample inside. The light pulse will pass through the sample thousands of times, thus greatly enhancing its absorption. For highly reflective mirrors the formula given by Colin K can be approximated as $$ \tau_0=\frac{L}{c\left ( 1-R \right )} $$ State-of-the art mirrors for CRDS in the visible range can have reflectivity up to 99.999% (link) resulting in a decay time of $167 \mu s$ for $L=0.5m$. During this time the light travels 50000 km which means that it is reflected 100000 times.

My answer is not much different from the other ones, but it is based on my personal experience. For several years I have been using Cavity ring-down spectrosopy(CRDS) - the method to measure very weak light absorption that is based on building such optical cavity and placing an absorbing sample inside. The light pulse will pass through the sample thousands of times, thus greatly enhancing its absorption. For highly reflective mirrors the formula given by Colin K can be approximated as $$ \tau_0=\frac{L}{c\left ( 1-R \right )} $$ State-of-the art mirrors for CRDS in the visible range can have reflectivity up to 99.999% (link) resulting in a decay time of $167 \mu s$ for $L=0.5m$. During this time the light travels 50000 km which means that it is reflected 100000 times.

PS: This experiment is done in vacuum (below 1 mbar). At atmospheric pressure the decay time is reduced to a couple of microseconds due to Rayleigh scattering (or absorption by dust particles).