Probability of Absorption by a Wetted Surface
The parameter a in Eq. (1) is the fraction of the light
incident on the surface which is absorbed. (The above
refers to a single interaction: the total probability of
absorption, allowing for reflections at the liquid-air
interface, is A.) Angstrom takes a to have the same
value for the wet as for the dry surface. We expect a,
(the value when wet), to be greater than ad (the value
when dry), since the absorbing medium will normally
have the real part of its refractive index greater than
unity. Since reflection is caused by wave vector mismatch,
and since wave vectors are determined by refractive
indices, covering the surface with a layer of
liquid (with nj > 1) results in less reflection.
The value of ad is in principle determined by the
complex refractive index nr + ins of the material, and
by the roughness of the surface (which influences the
average angle of incidence on its randomly oriented
facets, and the probability of multiple interactions, as
in a crevice). The value of a, is in addition a function
of nj, the refractive index of the liquid film covering it.
For the purpose of comparing the albedos 1 - ad and 1
- A of the dry and wetted surfaces, we estimate a, in
terms of ad, nl, and nr as follows.
For small absorption (ni << nr), ad 1 - R(n) where
R(n) is the average reflectance of an isotropically illuminated
surface, defined in Eq. (7). The assumption
made here is that the angle of incidence on facets of the
rough surface (for, say, normal illumination) has the
same distribution as would be obtained for a plane
surface illuminated isotropically. Similarly, a, - 1 -
(nr/nl) when ni << n,. Thus when the absorption is
small
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