After passing through 20 mm of liquid, where 50% of light is absorbed every 7.5 mm, the intensity of light is approximately 5.17% of the initial intensity, not matching any of the multiple-choice options provided.
The question asks us to calculate the intensity of light after passing through a certain thickness of a liquid which absorbs 50% of light every 7.5 mm. Since the sample thickness is 20 mm, we need to determine how many times the light's intensity is halved.
The calculation is as follows: Every 7.5 mm halves the light's intensity. First, we find out how many times this occurs within a 20 mm thickness:
20 mm / 7.5 mm = 2.67 times.
However, we cannot have a fraction of an absorption event, so we consider 2 full events and calculate the remaining distance: 20 mm - (2 x 7.5 mm) = 5 mm. Now, for those 5 mm, it will be less than a 50% reduction. We calculate the percentage absorbed in 5 mm by scaling the 50% proportionally:
5 mm / 7.5 mm = 2/3, and so the light will be (1 - (1/2)^(2/3)) * 100%.
Therefore, the final intensity is 1/2 (after the first 7.5 mm) x 1/2 (after the second 7.5 mm) x (1 - (1/2)^(2/3)) after the remaining 5 mm. In numerical terms, this is:
Answer: 0.5 x 0.5 x (1 - (1/2)^(2/3)) = 0.5 x 0.5 x 0.2067 = approximately 0.0517 or 5.17%.
The intensity of the light after traveling through the 20 mm of liquid, as a percentage of the initial intensity, is approximately 5.17%, which means the correct multiple-choice answer is not listed among the options (a to d).