Using Beer-Lambert law to calculate light intensities
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
$$l = \frac{\ln 2}{0.8} = \pu{0.846 m}.\tag{3}$$