Using Beer-Lambert law to calculate light intensities 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
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
$$\ln\left(\frac{I_0}{I}\right) = 0.8 l.\tag{2}$$
And, if $\displaystyle\frac{I}{I_0} = 0.5,$ the corresponding depth is
$$l = \frac{\ln 2}{0.8} = \pu{0.846 m}.\tag{3}$$