Molar Absorptivity and Beer–Lambert Law

Seeing that a solution absorbs light is useful, but analytical chemistry often asks a more demanding question: how much of the absorbing substance is present? UV/visible spectroscopy can answer this because the amount of light that passes through a sample changes systematically with concentration.

The bridge between the optical measurement and the chemical concentration is the Beer–Lambert law. Once we understand transmittance, absorbance and molar absorptivity, a spectrophotometer reading can be converted into a concentration either directly from A = εcl or by using a calibration curve prepared from standard solutions.

Diagnostic Quiz

What Do You Already Know About the Beer–Lambert Law?

Try these five questions before reading the chapter. Focus on what absorbance measures, how it is related to transmitted light and how concentration enters the Beer–Lambert equation.

5 diagnostic questions
Concepts, equations and graphical reasoning
Instant explanation for every answer option

Question 1 of 5

Which expression correctly defines absorbance, A?

A = I / I₀

I / I₀ is the transmittance, T, rather than the absorbance.

A = lg(I₀ / I)

Correct. Absorbance is the base-10 logarithm of the ratio of incident intensity to transmitted intensity.

A = I₀ / I

The intensity ratio must be placed inside a logarithm.

A = lg(I / I₀)

Since I is normally smaller than I₀, this expression would give a negative value. Absorbance is defined as lg(I₀ / I).

Since T = I / I₀, absorbance may also be written A = −lg T. A larger absorbance therefore corresponds to a smaller fraction of the incident light being transmitted.

Which statement about absorbance is correct?

Absorbance is measured in mol dm⁻³.

mol dm⁻³ is a unit of concentration, not absorbance.

Absorbance has units of cm⁻¹.

Path length may be measured in cm, but absorbance itself is dimensionless.

Absorbance has no units.

Correct. It is obtained from the logarithm of an intensity ratio, and the two intensities have the same units.

Absorbance is measured in dm³ mol⁻¹ cm⁻¹.

These may be the units of molar absorptivity, ε, depending on the units chosen for concentration and path length.

The ratio I₀ / I is dimensionless, so lg(I₀ / I) is also dimensionless. Absorbance therefore has no units.

In A = εcl, what does ε represent?

How strongly the species absorbs light at the chosen wavelength

Correct. ε is the molar absorptivity of the absorbing species at the specified wavelength and under the stated conditions.

The fraction of incident light transmitted

That is the transmittance, T.

The path length of the cuvette

Path length is represented by l.

The concentration of the absorbing species

Concentration is represented by c.

A large ε means that even a relatively low concentration can produce a substantial absorbance at that wavelength.

For a single absorbing species at fixed wavelength and fixed path length, what graph is predicted by the Beer–Lambert law?

Concentration against absorbance gives an exponential curve.

Beer–Lambert predicts a linear relationship between absorbance and concentration under conditions where the law is obeyed.

Absorbance against concentration gives an inverse curve.

Absorbance increases, rather than decreases, as concentration increases.

Absorbance is independent of concentration.

Concentration is one of the factors in A = εcl.

Absorbance against concentration gives a straight line.

Correct. With ε and l constant, A = (εl)c, which has the form y = mx.

The theoretical gradient of a graph of A against c is εl. In a real calibration experiment, a small non-zero intercept may occur because of experimental background or instrumental effects.

Why is absorbance often measured near λ_max for quantitative analysis?

Because the transmitted intensity is always zero at λ_max

Maximum absorbance does not mean that absolutely no light is transmitted.

Because the absorbing species usually gives its strongest response there

Correct. A larger ε gives a larger change in absorbance for a given change in concentration, increasing analytical sensitivity.

Because ε becomes zero there

At an absorption maximum, ε is relatively large rather than zero.

Because concentration no longer affects absorbance there

Concentration continues to affect absorbance according to A = εcl.

Measurements are commonly made at λ_max because the analyte absorbs strongly there, giving high sensitivity. In a real analysis, interference from other absorbing species must also be considered.

1. From transmitted light to absorbance

Imagine monochromatic light entering a solution. Let the intensity of the incident light be I₀. After travelling through the solution, some photons have been absorbed, so the emerging light has a smaller intensity, I.

One way of describing this is through transmittance, T:

T = I / I₀

Transmittance is therefore the fraction of the incident light that emerges from the sample. If 80% of the light is transmitted, T = 0.80. If only 20% is transmitted, T = 0.20.

Percentage transmittance is %T = 100(I / I₀).

Absorbance

Spectroscopic calculations usually use absorbance, A, rather than transmittance directly. Absorbance is defined by

A = lg(I₀ / I)

Since T = I / I₀, the same relationship can be written as

A = −lg T

Here, lg means logarithm to base 10.

High transmittance: most of the incident light passes through the sample, so absorbance is low.

Low transmittance: a smaller fraction of the incident light emerges, so absorbance is high.

Why absorbance has no units

I₀ and I are both intensities measured using the same units. Their ratio therefore has no units. Taking the logarithm of this ratio also produces a dimensionless quantity.

Therefore, absorbance has no units.

Example: Suppose the incident light intensity is I₀ = 100 arbitrary units and the transmitted intensity is I = 25.0 arbitrary units.

T = 25.0 / 100 = 0.250
A = −lg(0.250)
A = 0.602

Only 25.0% of the incident light is transmitted, corresponding to an absorbance of 0.602.

2. The Beer–Lambert law

The key quantitative relationship in absorption spectroscopy is the Beer–Lambert law:

A = εcl

The symbols represent:

Symbol	Meaning	Typical units
A	Absorbance	No units
ε	Molar absorptivity	dm³ mol⁻¹ cm⁻¹ when c is in mol dm⁻³ and l is in cm
c	Concentration of the absorbing species	mol dm⁻³
l	Path length travelled by the light through the solution	cm

What does the equation tell us?

At a particular wavelength, ε is fixed for a given absorbing species under specified conditions. If the same cuvette is used throughout an experiment, l is also fixed.

Beer–Lambert then becomes

A = (εl)c

A ∝ c

This is the crucial result for quantitative spectroscopy: doubling the concentration ideally doubles the absorbance, provided the system remains within the range over which the Beer–Lambert relationship is obeyed.

At fixed wavelength and path length, absorbance is directly proportional to the concentration of the absorbing species.

Path length also matters

A more concentrated sample contains more absorbing particles per unit volume, but concentration is not the only factor. Increasing the distance travelled by the light also gives photons more opportunity to encounter absorbing species.

At fixed ε and c:

A ∝ l

Standard UV/visible cuvettes commonly have a path length of 1.00 cm, which is one reason calculations often appear to simplify to A = εc. However, l should not simply be omitted unless its value is known to be 1.00 cm.

3. Molar absorptivity, ε

The quantity ε is called the molar absorptivity, also known as the molar absorption coefficient. It tells us how strongly one mole per unit concentration of a particular species absorbs light over a stated path length.

A substance with a large ε at a particular wavelength gives a large absorbance even when its concentration is relatively low. A substance with a smaller ε absorbs more weakly at that wavelength.

Large ε: strong absorption at the selected wavelength; a small concentration can produce a readily measurable absorbance.

Small ε: weaker absorption at that wavelength; a larger concentration may be needed to obtain the same absorbance.

ε depends on wavelength

It is important not to think of ε as a single universal number belonging to a molecule. The value depends on the wavelength at which the measurement is made.

This makes sense when we remember what an absorption spectrum represents. Different wavelengths correspond to different photon energies, and the probability of absorption changes across an absorption band. ε therefore changes with wavelength and reaches a relatively large value near an absorption maximum.

A quoted value of ε is meaningful only when the wavelength and chemical form of the absorbing species are understood.

Units of molar absorptivity

Absorbance has no units, so the units in εcl must cancel.

c is in mol dm⁻³ and l is in cm

then ε must have units

dm³ mol⁻¹ cm⁻¹

because

(dm³ mol⁻¹ cm⁻¹)(mol dm⁻³)(cm) = 1

Worked example: A solution has an absorbance of 0.620 at a particular wavelength. At that wavelength, ε = 1.55 × 10⁴ dm³ mol⁻¹ cm⁻¹ and the cuvette path length is 1.00 cm.

A = εcl

c = A / (εl)

c = 0.620 / [(1.55 × 10⁴)(1.00)]

c = 4.00 × 10⁻⁵ mol dm⁻³

4. Calibration curves and unknown concentrations

In practice, an analyst does not always need to know ε independently. Instead, a series of standard solutions of known concentration can be measured under the same experimental conditions.

Their absorbances are plotted against concentration to produce a calibration curve.

Why is the calibration graph linear?

For every standard solution, measurements are made at the same wavelength and using the same path length. Therefore ε and l are constant:

A = εlc

Comparing this with

y = mx

gives

y = A, x = c, gradient = εl

For an ideal Beer–Lambert plot of A against c, the gradient is εl. If l = 1.00 cm, the numerical value of the gradient corresponds to ε when the stated concentration units are used consistently.

Must the line pass exactly through the origin?

The theoretical Beer–Lambert relationship predicts A = 0 when c = 0. However, a real experimental calibration may show a small non-zero intercept because of background absorbance, imperfect blank correction, instrumental offsets or other experimental effects.

Therefore, it is better to use the experimentally determined best-fit line rather than automatically forcing every calibration graph through the origin.

Finding an unknown concentration

After producing the calibration line:

Measure the absorbance of the unknown under the same conditions.
Locate that absorbance on the calibration graph.
Read the corresponding concentration from the concentration axis.

If the best-fit equation has been calculated, the concentration can instead be obtained algebraically.

Example: A calibration line is described by

A = (1.50 × 10⁴)c + 0.010

An unknown gives A = 0.460.

0.460 = (1.50 × 10⁴)c + 0.010

0.450 = (1.50 × 10⁴)c

c = 3.00 × 10⁻⁵ mol dm⁻³

Notice that the small intercept has been included rather than ignored.

5. Choosing the wavelength for analysis

Absorbance depends on wavelength because ε depends on wavelength. For quantitative measurements, the wavelength must therefore be kept constant for all standards and unknown samples.

Measurements are commonly made at or near the wavelength of maximum absorbance, λ_max.

Why λ_max is useful

At λ_max, the analyte absorbs strongly. In Beer–Lambert terms, ε is relatively large, so a small change in concentration produces a relatively large change in absorbance.

This gives greater sensitivity.

Large ε: the calibration graph has a steeper gradient, so small concentration differences produce larger absorbance differences.

Small ε: the calibration graph is shallower, so the same concentration difference produces a smaller absorbance difference.

λ_max is often a good analytical wavelength because it gives strong absorption, but selectivity also matters. If another species absorbs strongly at the same wavelength, a different wavelength may be preferable.

6. Carrying out a quantitative UV/visible measurement

A successful Beer–Lambert analysis depends on keeping experimental conditions consistent. The standards and unknown must be measured in a way that makes concentration the variable responsible for the observed change in absorbance.

Step 1: Prepare standard solutions

Prepare several solutions containing known concentrations of the species to be measured. Their concentrations should span the range expected for the unknown.

Step 2: Select the wavelength

Choose an appropriate analytical wavelength, commonly λ_max, and keep it unchanged for all measurements.

Step 3: Use a blank

Before measuring the analyte solutions, the spectrophotometer is normally referenced using a blank containing the solvent and other components of the measurement system but not the analyte being determined.

This allows the measurement to focus on absorbance attributable to the analyte rather than absorption caused by the solvent, cuvette and background components.

Step 4: Measure the standards consistently

Use the same cuvette path length and the same wavelength. Cuvettes should be clean and appropriately filled, with fingerprints or droplets removed from the optical faces.

Step 5: Construct the calibration graph

Plot absorbance on the y-axis against concentration on the x-axis and obtain a suitable best-fit line over the linear region.

Step 6: Measure the unknown

Measure the unknown in the same way and use its absorbance to determine its concentration from the calibration relationship.

Standards and unknowns must be compared under the same wavelength, path-length and chemical conditions.

7. When the Beer–Lambert relationship deviates from linearity

Beer–Lambert behaviour is an ideal relationship. A straight-line calibration is expected only while the assumptions underlying the measurement remain sufficiently valid.

Concentration effects

At sufficiently high concentrations, absorbing particles are close enough that interactions between them and changes in the optical properties of the solution can cause deviations from simple proportionality.

It is therefore more accurate to say that Beer–Lambert behaviour is generally best for sufficiently dilute solutions rather than memorising one universal concentration cut-off. The usable linear range depends on the chemical system and instrument.

Chemical changes in the absorbing species

Beer–Lambert calculations assume that the same absorbing species is being compared throughout the concentration range.

If changing concentration alters an equilibrium, causes association or dissociation, changes protonation state, or produces another chemical species, ε may no longer remain effectively constant.

The calibration may then cease to be linear even though the instrument itself is functioning correctly.

Polychromatic radiation

The simple Beer–Lambert treatment assumes light of a sufficiently narrow wavelength range. If a broad range of wavelengths reaches the sample, each wavelength may have a different ε value, making the overall behaviour less ideal.

Scattering and turbidity

Suspended particles can scatter light away from the detector. The instrument may interpret this loss of transmitted light as additional absorbance even though it was not caused purely by molecular absorption.

Instrumental and cuvette effects

Stray light, dirty optical surfaces, fingerprints, bubbles, mismatched cuvettes and inconsistent positioning can all alter the measured transmitted intensity.

True molecular absorption: light intensity decreases because photons are absorbed by the species being measured.

Experimental loss of light: scattering, dirt or instrumental effects can also reduce the light reaching the detector and may therefore create an apparent increase in absorbance.

Common Mistakes

Common mistake	Why it is wrong	Better approach
Writing A = I / I₀	I / I₀ is transmittance, not absorbance.	Use T = I / I₀ and A = lg(I₀ / I) = −lg T.
Giving absorbance a unit	Absorbance is the logarithm of a ratio of two intensities with the same units.	State that A is dimensionless.
Treating ε as one universal constant for a substance	ε varies with wavelength and can also depend on the chemical form and measurement conditions.	Associate a quoted ε value with the specified wavelength and species.
Forgetting l in A = εcl	A 1.00 cm cuvette is common, but path length is still part of the Beer–Lambert relationship.	Substitute the stated l before simplifying.
Assuming every experimental calibration must pass exactly through the origin	Real data may have a small intercept because of background or instrumental effects.	Use the appropriate best-fit calibration relationship unless the question specifically establishes an ideal line through the origin.
Using an unknown whose absorbance lies well outside the calibration range	This requires extrapolation beyond the concentrations experimentally established by the standards.	Dilute the sample where appropriate and measure it within the linear calibration range, then account for the dilution.

What you should be able to do

Relate intensity, transmittance and absorbance

Use T = I / I₀ and A = lg(I₀ / I) = −lg T correctly.

Apply the Beer–Lambert law

Use A = εcl to calculate absorbance, concentration, molar absorptivity or path length.

Interpret molar absorptivity

Explain why a larger ε means stronger absorption at the specified wavelength.

Interpret a calibration graph

Recognise that a plot of A against c is linear under Beer–Lambert conditions and that its theoretical gradient is εl.

Determine an unknown concentration

Use either A = εcl or an experimentally determined calibration line.

Recognise limitations

Explain how chemical changes, excessive concentration, scattering, polychromatic radiation and experimental errors can cause deviations.

Mastery Quiz

Can You Apply the Beer–Lambert Law?

These ten questions test whether you can move confidently between intensity, transmittance, absorbance, concentration, calibration graphs and experimental reasoning.

10 mastery questions
Calculations and experimental interpretation
Instant explanation for every answer option

Question 1 of 10

Light enters a solution with intensity I₀ = 1.00 and leaves with intensity I = 0.250, measured in the same arbitrary units. What is the absorbance?

0.250

0.250 is the transmittance, T = I / I₀.

0.602

Correct. A = lg(1.00 / 0.250) = lg 4.00 = 0.602.

4.00

4.00 is I₀ / I, but the logarithm of this ratio must be taken.

−0.602

This would result from taking lg(I / I₀) rather than lg(I₀ / I).

A = lg(I₀ / I). When only one quarter of the light is transmitted, A = lg 4 = 0.602.

A solution has absorbance A = 0.301. Approximately what percentage of the incident light is transmitted?

30.1%

Absorbance is logarithmic, so 0.301 does not mean 30.1% absorption or transmittance.

70.0%

Transmittance must be calculated using T = 10⁻ᴬ.

20.0%

This would correspond to a larger absorbance than 0.301.

50.0%

Correct. T = 10⁻⁰·³⁰¹ ≈ 0.500, so %T ≈ 50.0%.

From A = −lg T, rearrange to T = 10⁻ᴬ. An absorbance of 0.301 corresponds approximately to a transmittance of 0.500.

At a particular wavelength, ε = 1.40 × 10⁴ dm³ mol⁻¹ cm⁻¹. A 1.00 cm cuvette gives A = 0.420. What is the concentration?

3.00 × 10⁻⁵ mol dm⁻³

Correct. c = A / (εl) = 0.420 / [(1.40 × 10⁴)(1.00)] = 3.00 × 10⁻⁵ mol dm⁻³.

5.88 × 10³ mol dm⁻³

This comes from multiplying rather than dividing by εl.

3.33 × 10⁴ mol dm⁻³

The Beer–Lambert expression has not been rearranged correctly.

1.40 × 10⁴ mol dm⁻³

This simply repeats the numerical value of ε, which has different units and meaning.

Start from A = εcl and rearrange before substituting: c = A / (εl).

A plot of absorbance against concentration has a gradient of 2.50 × 10⁴ dm³ mol⁻¹. The path length is 1.00 cm. What is ε?

4.00 × 10⁻⁵ dm³ mol⁻¹ cm⁻¹

This incorrectly takes the reciprocal of the gradient.

2.50 × 10⁴ mol dm⁻³

These are concentration units, not molar absorptivity units.

2.50 × 10⁴ dm³ mol⁻¹ cm⁻¹

Correct. Gradient = εl, so with l = 1.00 cm, ε = 2.50 × 10⁴ dm³ mol⁻¹ cm⁻¹.

2.50 × 10⁴ cm

The gradient is not a path length.

A = εlc has the form y = mx. Therefore the gradient of A against c is εl.

The same solution is measured at the same wavelength first using a 1.00 cm cuvette and then using a 2.00 cm cuvette. Assuming Beer–Lambert behaviour, what happens to its absorbance?

It is halved.

A is directly, not inversely, proportional to path length.

It doubles.

Correct. With ε and c unchanged, A ∝ l.

It remains unchanged.

Path length is explicitly included in A = εcl.

It becomes four times as large.

A varies linearly with l, not with l².

Doubling the path length doubles the number of absorbing particles encountered along the light path on average, giving twice the absorbance under Beer–Lambert conditions.

What is the main purpose of using a blank before measuring the absorbance of an analyte solution?

To account for background absorption from the solvent, cuvette and other non-analyte components

Correct. The blank establishes a reference so the measurement can focus on the analyte's contribution.

To increase the analyte concentration

A blank contains no analyte being determined and does not increase the sample concentration.

To make ε independent of wavelength

ε remains wavelength-dependent.

To increase the cuvette path length

Blanking does not alter the physical path length.

A blank provides the background reference against which the analyte solution is measured.

A calibration graph begins to curve at its highest concentrations. Which explanation is most appropriate?

Absorbance must always be inversely proportional to concentration at high concentration.

There is no general inverse Beer–Lambert relationship at high concentration.

Molar absorptivity must become exactly zero.

Curvature does not imply that ε suddenly becomes zero.

The path length must be decreasing as concentration rises.

The same cuvette can maintain a constant path length while non-ideal solution behaviour causes deviation.

The solution may be leaving the concentration range over which simple Beer–Lambert proportionality is valid.

Correct. Interactions between absorbing species, chemical changes or optical effects can produce deviations at sufficiently high concentrations.

Beer–Lambert behaviour should be verified experimentally over the concentration range being used rather than assuming unlimited linearity.

Why does measuring near λ_max often increase the sensitivity of a concentration measurement?

Because the path length becomes larger at λ_max

Cuvette path length is a physical dimension and does not increase because wavelength changes.

Because concentration becomes larger at λ_max

Changing wavelength does not itself increase the analyte concentration.

Because ε is relatively large, giving a larger change in A for a given change in c

Correct. Since the calibration gradient is εl, a larger ε gives a steeper response when l is fixed.

Because absorbance is independent of concentration at λ_max

Beer–Lambert proportionality still links absorbance to concentration.

At λ_max, strong absorption generally makes concentration changes easier to detect as absorbance changes.

A calibration line is A = (1.50 × 10⁴)c + 0.010. An unknown has A = 0.460. What is its concentration?

3.07 × 10⁻⁵ mol dm⁻³

This results from dividing 0.460 directly by the gradient and ignoring the intercept.

3.00 × 10⁻⁵ mol dm⁻³

Correct. c = (0.460 − 0.010) / (1.50 × 10⁴) = 3.00 × 10⁻⁵ mol dm⁻³.

6.90 × 10³ mol dm⁻³

The calibration equation has not been rearranged correctly.

1.50 × 10⁴ mol dm⁻³

This repeats the gradient rather than calculating the concentration.

When a calibration line has an experimentally determined intercept, include it in the calculation rather than automatically assuming it is zero.

A fingerprint is left on the optical face of a cuvette. If this causes less light to reach the detector, what is the likely effect on the calculated concentration when a normal calibration curve is used?

The measured absorbance becomes smaller and the concentration is underestimated.

Reducing the transmitted intensity increases rather than decreases the apparent absorbance.

The measured absorbance is unchanged because fingerprints cannot affect light.

Contamination on an optical surface can alter the light reaching the detector.

The molar absorptivity of the analyte becomes exactly zero.

The problem is an experimental optical error, not the disappearance of the analyte's absorption.

The measured absorbance becomes artificially high and the concentration may be overestimated.

Correct. A smaller transmitted intensity gives a larger apparent absorbance, which a calibration curve may interpret as a higher analyte concentration.

Beer–Lambert analysis assumes that the measured loss of light reflects the intended absorption process. Dirty cuvettes can introduce an additional loss of transmitted light and therefore systematic error.

Frequently asked questions

Questions students often ask about the Beer–Lambert law

The equations are short, but several details — especially logarithms, units, λ_max and calibration graphs — can cause confusion. These questions connect the ideas together.

What is the difference between transmittance and absorbance?

Transmittance, T = I / I₀, is the fraction of incident light that passes through the sample. Absorbance expresses the same information logarithmically: A = −lg T = lg(I₀ / I). High transmittance therefore corresponds to low absorbance, while low transmittance corresponds to high absorbance.

Why do we use absorbance rather than transmittance for concentration measurements?

The transmitted light intensity itself does not decrease linearly with concentration. Converting the intensity ratio into absorbance gives the Beer–Lambert relationship A = εcl, so absorbance is directly proportional to concentration under the appropriate conditions. This is why a calibration graph of A against c can be linear.

Why does absorbance have no units?

Absorbance is calculated from lg(I₀ / I). I₀ and I have the same units, so their ratio is dimensionless. The logarithm of that ratio is therefore also dimensionless.

What exactly does a large molar absorptivity mean?

A large ε means that the species absorbs strongly at the specified wavelength. According to A = εcl, a large ε produces a larger absorbance for the same concentration and path length. This also produces a steeper calibration graph of A against c.

Is molar absorptivity a fixed constant for a molecule?

Not as one wavelength-independent number. ε depends strongly on wavelength and is associated with a particular absorbing chemical species under specified conditions. A value of ε should therefore be interpreted together with the wavelength at which it was measured.

Why is λ_max commonly chosen for quantitative measurements?

At λ_max, the analyte has strong absorption and therefore a relatively large ε. This gives a larger absorbance change for a given concentration change and usually improves sensitivity. However, if another species interferes strongly at the same wavelength, another analytical wavelength may be more selective.

Must a Beer–Lambert calibration graph pass through the origin?

The ideal equation A = εcl predicts zero absorbance when the analyte concentration is zero. Real calibration data, however, may have a small non-zero intercept because of background absorbance, instrumental offsets or imperfect blank correction. Unless the problem specifically assumes an ideal line, use the experimentally determined best-fit relationship.

Why can concentrated solutions stop obeying the Beer–Lambert law?

At sufficiently high concentrations, interactions between absorbing particles and changes in the optical properties or chemical speciation of the solution can make absorbance no longer directly proportional to concentration. There is no single concentration boundary that applies to every substance; the linear range should be established for the system being studied.

Why should an unknown be measured within the range of the standards?

A calibration curve demonstrates experimentally that the relationship is reliable over the concentration range covered by the standards. Using an unknown far outside this range requires extrapolation and may enter a region where Beer–Lambert behaviour is no longer linear. Dilution is often preferable when an unknown is too concentrated.

How can a dirty cuvette affect the calculated concentration?

Dirt or fingerprints can reduce the light reaching the detector. Since A = lg(I₀ / I), an artificially low I gives an artificially high absorbance. If that absorbance is interpreted using a normal calibration curve, the analyte concentration may be overestimated.

The central idea is simple but powerful: molecular absorption changes the intensity of transmitted light, absorbance converts that change into a useful logarithmic quantity, and the Beer–Lambert law then connects absorbance to concentration. Once A = εcl is understood together with calibration curves and experimental limitations, UV/visible spectroscopy becomes a quantitative analytical technique rather than merely a way of observing an absorption spectrum.