Answer to Question #139352 in Physics for vhee

Question

Find the optical density and transmittance of 0.04% -lactose solution, if 1/8 of initial light intensity is absorbed in it.

Answer 1

By definition, transmittance is:

$$T = \dfrac{F_t}{F_i}$$

where $F_t$ is the radiant flux transmitted by that material and $F_i$ is the radiant flux received by that material. If 1/8 of initial light intensity is absorbed in the material, then the transmited ratio is:

$$T = \dfrac{F_t}{F_i} = 1-\dfrac18 = \dfrac{7}{8}\approx 0.875$$

The optical density (or absorbance) is then:

$$D = -\log_{10}T = -\log_{10}0.875 \approx 0.058$$

Answer. Transmittance: 0.875. Optical density: 0.058.