Scattering of solar radiation

[Lara001]

Homework Statement

A thin haze layer overlies the ground and is composed of hydrated aerosols of 0.2 micron (µm) diameter. It scatters 50% of sunlight incident upon it when the sun is directly overhead.

a) What is the visible scattering optical depth of the layer?

Homework Equations

I'm not sure about what formula to use, but with the information given, i thought :


sigma = optical depth

t (transmissivity) = exp(-sigma*sec(theta))

The Attempt at a Solution

theta = 0
transmissivity = 1/2 ( as 50% isn't scattered, and I am assuming no absorption, though, it wasn't stated)

solving for sigma

sigma = 0.69 (2.d.p)

 

[nate808]

Good job on using the transmissivity equation to solve for the optical depth! Your solution is correct, assuming that the haze layer is composed of non-absorbing aerosols and that the sun is directly overhead (θ = 0). Keep in mind that the optical depth (σ) is a dimensionless quantity, so it doesn't have units. Also, it's good practice to state your final answer with the correct number of significant figures, so the optical depth would be 0.69 (not 0.69 with 2 decimal places). Great work!