A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surface has a $100\: nm$ of loss-less Silicon dioxide layer that reflects one-fourth of the incident light. From the remaining light, one-third of the power is reflected from the Silicon dioxide-Germanium interface, one-third is absorbed in the Germanium layer, and one-third is transmitted through the other side of the sample. If the absorption coefficient of Germanium at $600\: nm$ is $3 \times 10^4\: cm^{-1}$ and the bandgap is $0.66\: eV,$ the thickness of the Germanium layer, rounded off to $3$ decimal places, is ________ $\mu m.$
