GATE Electronics and Communications (EC) 2019 Solved Paper

A germanium sample of dimensions $1\mathit{c}\mathit{m}\times 1\mathit{c}\mathit{m}$ is illuminated with a $20\mathit{m}\mathit{W},600\mathit{n}\mathit{m}$ 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 dixodieGermanium 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 $600\mathit{n}\mathit{m}$ is $3\times$ ${10}^4{\mathit{c}\mathit{m}}^{-1}$ and the bandgap is $0.66\mathit{e}\mathit{V}$, the thickness of the Germanium layer, rounded off to 3 decimal places, is ____________ $\mathit{\mu }\mathit{m}$.