A radiation detector has an aperture of area \(A_{d}=10^{-6} \mathrm{~m}^{2}\) and is positioned at a distance of \(r=2 \mathrm{~m}\) from a surface of area \(A_{s}=10^{-4} \mathrm{~m}^{2}\). The angle formed by the normal to the detector and the surface normal is \(\theta=25^{\circ}\).

The surface is at \(500 \mathrm{~K}\) and is opaque, diffuse, and gray with an emissivity of 0.8 . If the surface irradiation is \(2500 \mathrm{~W} / \mathrm{m}^{2}\), what is the rate at which the detector intercepts radiation from the surface?

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