# Why is there a log relationship between absorbance and transmittance

### Spectrophotometry: Transmittance and Absorbance | cell biology olm

That is, it's absorbance which is used in Beer's law: Taking the negative log is just another trick to make things work out reasonably: it's more. Describe the relationship between Absorbance and Transmittance and the 20 ™, the absorbance is displayed on the bottom scale, which is logarithmic. This value when compared with varying concentrations of the sample is non- linear, whereas the log of the transmittance (the absorbance) becomes linear when.

The explanation of why absorbance is additive falls out of the derivation of Beer's law.

The official derivation relies on calculus, but you can get a sense of things by thinking of the solution not as a single thing, but as a succession of "slabs": Take a single thin slab of a colored material. This absorbs a certain amount of light at a given frequency.

But it doesn't absorb a fixed amount of light. Instead, each photon that passes through has a certain probability of encountering an absorbant molecule and being absorbed.

**Light Absorption, Reflection, and Transmission**

The more light, the more absorbed. But what happens if you start varying the width of the material. Or equivalently, if you stack several of such slabs together. The second slab would only "see" half the original light, and would then absorb half of that light. So the amount being transmitted out the back of the second slab would be only 0.

### Beer's Law - Theoretical Principles

Note the necessity of converting from percentages to fractions to do the calculation here. Now for the fun part! Using the calibration plot that YOU made from the data two pages ago. We are going to determing the concentration of an unknown solution.

Make sure you have your plot ready, because here we go! Here's a typical problem. You take 3mL of your unknown sample and 7mL water and mix them together.

### Chem - Experiment II

The dilluted sample gives an absorbance of 0. What is the concentration of the initial unknown? Where do you begin?! You have an absorbance, and you have a straight line equation that relates absorbance to concentration.

This is the line of best fit through your data. Remember you dilluted it once, so you can use the Dilution Equation Ready to try one on your own? Here are a few more problems.