# How far does light penetrate water?

1. Nov 22, 2008

### benbenny

Hi, cant figure this out:

1. The problem statement, all variables and given/known data

" 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."

2. Relevant 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

3. The attempt at a solution

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

Thanks for any help!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 22, 2008

### 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.