Using Beer-Lambert law to calculate light intensities

Question

Supposing the mean absorption coefficient of seawater in the visible region is $pu{0.8 m-1}$, calculate the depth at which a diver will experience half the surface light intensity.
I know that you have to use $A = -log left(dfrac{I}{I_o}right) = epsilon cl$ but I'm not sure how to proceed

Maurice · Answer

In my opinion, Beer–Lambert law is no use. I would rather write
$$frac{mathrm dI}{I,mathrm dl} = pu{0.8 m^-1},tag{1}$$
which leads to the integrated formula
$$lnleft(frac{I_0}{I}right) = 0.8 l.tag{2}$$
And, if $displaystylefrac{I}{I_0} = 0.5,$ the corresponding depth is
$$l = frac{ln 2}{0.8} = pu{0.846 m}.tag{3}$$

Using Beer-Lambert law to calculate light intensities

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