Answer to Question #185458 in Physics for Praise

Question

3/8 of light initial intensity is absorbed in the beaker with length of 2cm filled with 9% solution. Find the length of beaker that should be used to get transmittance 1/3 for the same solution.

Answer 1

According to Beer-Lambert law for both cases:

$$\frac{I_1}{I_0}=e^{-kl_1}=\frac{3}{8}\\\frac{I_2}{I_0}=e^{-kl_2}=\frac{1}{8}\\\frac{e^{kl_2}}{e^{0.02}}=\frac{9}{8}\\l_2=13.7\ cm$$