How Does Water Affect Solar Radiance Observed Underwater?

[cpmiller]

Homework Statement

An underwater observer is looking directly into the sun. His head is near, but below the surface, and he is not wearingsun glasses. Let L_s(x) be the solar radiance at the water surface, on the air side, when the sun is at a zenith angle x. What is the ratio of the solar radiance at the observer's eye to the solar radiance just above the water surface?

Homework Equations

Here's where I'm having trouble. I'm not sure which equation is relevant. Is this simply a Fresnel transmission problem? I have equations for vertical and horizontal polarization

Rh = [sin²(x_a - x_w)]/[sin²(x_a + x_w)]

But I also have a solid angle formula for radiance at the air water boundary. It is labeled "From Snell's law and flux conservation" $$\Omega$$_a = n² [cos x_w/ cos x _a ] $$\Omega$$ _w

Where the $$\Omega$$s are solid angle. The subscript a one is subtended by L_s in the accompanying diagram. And the subscript w by L_d (downwelling) so I'm not sure if this ratio would be what I need.

Any thoughts?

Thanks for your help!

 

[BigJDubs]

The Attempt at a SolutionI'm not sure what equation would be appropriate to solve this problem. I have equations for vertical and horizontal polarization, as well as a solid angle formula for radiance at the air water boundary. However, I'm not sure which equation would be relevant. Any help would be greatly appreciated!