Answer to Question #139350 in Physics for victory

Question

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

Answer 1

According to Beer-Lambert law for both cases:

$$\frac{I_1}{I_0}=e^{-kl_1}=\frac{3}{8}.\\\space\\ \frac{I_2}{I_0}=e^{-kl_2}=\frac{1}{3}.$$

Our goal is to find l₂:

$$\frac{e^{l_2}}{e_{0.02}}=\frac{9}{8},\\ l_2=13.7\text{ cm}.$$