A diffuse radiation flux is incident on a dielectric medium having an absorption coefficient ? and…

A diffuse radiation flux  is incident on a dielectric medium having an absorption coefficient κ and a simple index of refraction . The air–medium interface is slightly rough so that it acts like a diffuse surface. It has a directional–hemispherical reflectivity of  that is assumed to be independent of θ. Derive a relation to determine the amount of incident energy directly absorbed per unit volume, , in the medium as a function of depth x from the surface. For  1.52, obtain an estimate for the surface reflectivity for diffuse incident radiation by using Figure 3.3. Using this value and the other conditions as in Example 17.2, compute . How does the result compare with that in Example 17.2 and what is the reason for the difference?

Figure 3.3