---
title: "Measuring a Solution’s Concentration with Light"
description: "Equal layers multiply transmission. Absorbance turns that into a concentration scale, whose useful range depends on blanks, standards and stray light."
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Inside the instrument

# Measuring a Solution’s Concentration with Light

A darker solution may contain more dye, or the light may simply travel through more liquid. A spectrophotometer fixes that distance, selects a narrow wavelength band and compares the transmitted signal with a blank. Under dilute-solution absorption conditions, the comparison can become a concentration measurement.

Sandbox Physics · 2026-11-03

## What happens in a second layer?

Send green light through a one-centimetre cell. The solvent alone gives a thousand detector counts; a dye solution gives four hundred. The dye transmits forty percent of the blank signal. This fraction is called transmittance. Comparing the two readings removes factors shared by both, including the lamp brightness and detector sensitivity. Now place an identical layer behind the first. It receives only the light that survived, and passes forty percent of that remainder. The detector gets one hundred and sixty counts: sixteen percent of the original blank. Each equal layer removes the same fraction of the light reaching it. The absolute number removed becomes smaller with each layer.

In a sufficiently dilute solution, molecules have little influence on one another. Doubling the concentration then gives light twice as many absorbing molecules to encounter, much as doubling the liquid thickness would. A concentration measurement therefore needs a known path length: the distance through the solution between the cell’s inner windows.

Sources: [1] [2]

## A logarithm supplies an additive scale

Take the base-ten logarithm of transmittance and reverse its sign. The resulting quantity is absorbance. Forty percent transmission gives about 0.398; sixteen percent gives about 0.796. Two identical layers now add. Transmission of one tenth gives absorbance 1, and one hundredth gives absorbance 2. Absorbance is a logarithmic ratio.

Write absorbance as $A$ and transmittance as $T$. Concentration $c$ and path length $\ell$ determine how many absorbers the light encounters. The molar absorption coefficient $\varepsilon$ describes how strongly that molecular species absorbs at the selected wavelength. Its value depends on conditions including solvent, wavelength and molecular form.

For an unknown solution, prepare several standards with known concentrations and measure them under matching conditions. Plot their absorbance against concentration. An unknown between the standards can be read from this working curve. Departures from a straight line provide a warning that the simple absorption relation is failing under the current conditions.

$$
A=-\log_{10}T=\varepsilon c\ell
$$

With concentration in moles per litre and path in centimetres, molar absorptivity has units of litres per mole per centimetre. The right-hand equality assumes a uniform dilute solution and a sufficiently narrow wavelength band.

Sources: [1] [2]

## The blank has its own optical path

Cell windows reflect some light, and the solvent may absorb some too. Even with the light blocked, a detector can accumulate dark counts. Measure that dark signal first, then measure the solvent in a matched cell. The blank supplies the container-and-solvent comparison needed to interpret the added dye.

A lamp that weakens after the blank measurement makes the sample appear to absorb more. A double-beam instrument divides the same source between a sample path and a reference-solvent path. Simultaneous readings can cancel a brightness change common to both. Separate detector drift or a changing optical path still requires attention.

The selected light occupies a finite band. A wider slit admits more neighbouring wavelengths, some of which pass through the dye more readily. Their photons are added before absorbance is calculated. The observed peak becomes lower, and the working curve may bend. Narrowing the slit reduces this mixing but sends fewer photons to the detector.

Sources: [2] [4]

## Why a dark sample can reach a plateau

Suppose the dye almost blocks the chosen band, but a little light at other wavelengths leaks through the instrument and passes through this dye. As concentration rises, the intended signal falls until those unwanted photons dominate. The detector signal approaches a floor, and the calculated absorbance approaches a plateau. Further solute becomes difficult to distinguish.

This stray component arrives when the lamp is on, so a shuttered dark measurement does not measure it at its illuminated level. Repetition does not remove the resulting systematic bias. Diluting the solution or using a shorter cell can bring the intended transmitted signal above that floor; matching standards then establish the useful range again. Suspended particles and molecules that change form with concentration can alter the same measurement. One wavelength may leave several possible causes of a darker signal. A useful concentration scale combines matched chemistry and optical paths with readings inside a range that known standards have tested.

Sources: [3] [2]

## [Measure concentration with blanks and standards](https://sandboxphysics.com/labs/uv-vis-spectrophotometer/)

Move the cell window, save matching standards, then compare a wide slit and a stray-light floor.

A synthetic-dye count model with finite bandwidth, simultaneous double detection, dark counts and simplified source stray light.

## Sources and further reading

1. [Shimadzu, The Structure of a Spectrophotometer](https://www.shimadzu.com/an/service-support/technical-support/uv/overview/structure.html)

   Measurement Principle (solution samples), Configuration and Sample Compartment: solvent comparison, absorbance, path length, finite band and sample/reference optical paths.

2. [Agilent, The Basics of UV-Vis Spectrophotometry, 5980-1397EN (August 19, 2025)](https://www.agilent.com/cs/library/primers/public/primer-uv-vis-basics-5980-1397en-agilent.pdf)

   Printed pp. 4, 9–12, 18–19 and 22–23: cells, optical paths, absorbance and concentration standards. The worked numbers here are independent teaching examples.

3. [Shimadzu Scientific Instruments, How does stray light influence high absorbance measurements?](https://www.ssi.shimadzu.com/service-support/faq/uv-vis/resolution-and-stray-light/4/index.html)

   Manufacturer explanation of the absorbance plateau and downward bias caused by stray radiation; no commercial performance is assigned to the teaching model.

4. [Shimadzu Scientific Instruments, How are single beam and double beam instruments different?](https://www.ssi.shimadzu.com/service-support/faq/uv-vis/instrument-design/20/index.html)

   The single path and the physical sample/reference split. The linked Lab chooses simultaneous separate detectors.

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