A small surface of area $A_s={10}^{-4}{m}^2$ is irradiated from an external source of radiation with $G=2000\frac{W}{m^2}.$ The surface is gray, opaque, diffuse, and has an emissivity of $=0\mathrm{.}7.$ Another small surface $(A_c)$ is positioned at a distance of $r=0\mathrm{.}5$ m away and has an area of $A_d=3{10}^{-6}{m}^2.$ The geometry of the problem is shown below, where ${}_l=30$ and ${}_2=40.$ If the surface $(A_s)$ is maintained at a temperature of $600$ K $,$ what is the rate at which the surface $A_c$ intercepts radiation from the surface?