Chapter 12, Problem 12.55P

A diffuse, opaque surface at 700 K has spectral emissivities of ${\epsilon }_{\lambda }=0\text{ for 0}\le \lambda \le 3\mu m,{\epsilon }_{\lambda }=0.5\text{ for 3}\mu \text{m,and }{\epsilon }_{\lambda }=0.9for10\mu m<\lambda <\infty$ for. A radiant flux of $1000W/m^2$ , which is uniformly distributed between $\text{1 and 6}\mu \text{m }$ , is incident on the sur- face at an angle of ${\text{30}}^{\circ }$ relative to the surface normal.

Calculate the total radiant power from a ${10}^{-4}{m}^2$ area of the surface that reaches a radiation detector positioned along the normal to the area. The aperture of the detector is ${10}^{-5}{m}^2$ , and its distance from the sur- face is 1 m.