How far does light penetrate water?

[benbenny]

Hi, can't figure this out:

Homework Statement

" Seawater has a conductivity of 5 seimens/meter. Calculate the depth so that the wave is 1/1000 of the entering power at a frequency of 10 khz."

Homework Equations

I was thinking to use the beer-lambart law: frac{I}{I(0)} = 10^-/alpha*L
(l=depth, alpha= coeficiant of absorption)
To find alpha from the info in the question I thought to use

/alpha = frac{(/sigma*/omega*frac{mu}{mu(0)}}{k*c^2}

where: /sigma = 5 siemens/meter /omega = angular frequency mu= permeability mo(0) = permeability of vacuum

The Attempt at a Solution

My idea was to try to find the intensity using the black body laws (weins law and the stefan Boltzmann law) so that I get intensity as a function of wavelength but I am quite sure that this is incorrect because a radio transimetter does not emit light through thermionic radiation. I've read around and found that amplitude and intensity are not related to frequency at all and so I am stuck.

Thanks for any help!

 

[fikus]

from Maxwell equations and Ohm's law you can derive that conducting materials have complex index of refraction. The solution for propagating wave (exp(i*omega*x/c, where c is c_0/n) then gets a damping factor from the complex part of n. So you can easily find that depth. Complex part of n depends on omega and conductivity.