Chapter 13, Problem 13.46P

In Problems 12.20 and 12.25, we estimated the earth’s surface temperature, assuming the earth is black. Most of the earth’s surface is water, which has a hemispherical emissivity of $\epsilon =0.96$ . In reality, the water surface is not flat but has waves and ripples.
(a) Assuming the wave geometry can be closely approximated as two-dimensional and as shown in the schematic, determine the effective emissivity of the water surface, as defined in Problem 13.43. for $\alpha =3\pi /4$ .
(b) Calculate and plot the effective emissivity of the water surface, normalized by the hemispherical emissivity of water $\left({\epsilon }_{\text{eff}}/\epsilon \right)$ over the range $\pi /2\le \alpha \le \pi$ .