Theory of Colorimetry
UNDERSTANDING LIGHT AND COLOUR
Before we can discuss the technique of colorimetry it is
important to understand and to differentiate this technique
and others which involve measuring electromagnetic
radiation from various parts of the spectrum.
The following table should clarify the types of radiation
that constitute the electromagnetic spectrum.
For those who are unfamiliar with the definition of
wavelength and its units here is a brief guide:
Radiation may be considered as a wave. The
wavelength is the distance between two successive peaks
of that wave.
The wavelengths in the table are expressed in
nanometers (nm) these are related to metres thus:
1 nanometer = 10-9 metre
Colorimetry is just one of the types of photometric analysis
techniques i.e. it is a light measuring analytical procedure.
Colorimetric measurements are made using a white light
source which is passed through a colour filter or alternative
wavelength selection device. This incident light then passes
through a cuvette containing a chemical compound in
solution. The intensity of the light leaving the sample will be
less than the light entering the cuvette. The loss of light or
absorption is proportional to the concentration of the
Colorimetry however only applies to measurements
made in the visible region of the electromagnetic spectrum
e.g. (380 - 780 nm). The extent to which light is absorbed by a
sample is dependant upon many factors. The main general
contributors are the wavelength of the incident light and the
colour of the solution.
Each compound in solution has a typical (and usually
unique) absorption spectrum, an example is shown in fig. 4.
The spectrum is a pattern of the amount of light absorbed by the substance in the solution plotted against the wavelength of the light
In most cases the spectrum will have a peak i.e. a
wavelength at which absorption is at a maximum. This is often
referred to as the max for the compound in question.
If the absorption is being quantified it is essential that it is
measured as close as possible to the max. Sensitivity is
reduced at any other wavelength.
From the example our sample has a max at about 460
nm in the blue part of the spectrum. So what colour will it
appear to be?
Well the answer is yellow!
Confused? Well here is the explanation:
Inert materials whether solid or liquid appear coloured due
to the way they modify light illuminating the object. Thus
different objects absorb some wavelengths and reflect
If white light passes through a yellow solution, it absorbs all
colours except yellow.
Similarly, a book cover appears red since it absorbs all
colours except red.
If a solution is clear and colourless it has not absorbed any
visible radiation and therefore all the white light is transmitted ie. it is transparent.
See the example of the spectral distribution curve
solution in figure 5. The solution absorbs blue light strong
a max at 460nm and therefore appears yellow.
If the concentration of the yellow solution is reduced by half the two solutions will give curves shown. Therefore for greatest sensitivity and linearity it is essential to limit the measuring wavelength to the area of highest absorption.
Figure 5 shows that the correct wavelength at which to measure a solution is the one which gives greatest absorption.
The wavelength or colour filter that will produce the maximum absorbance can be selected in two ways:
1. Take readings throughout the spectrum on a typical standard solution of the substance under investigation and establish the peak wavelength
2. Choose a filter of the complementary colour to the standard solution. Figure 6 shows the basic relationship between colours
There are several options open to the manufacturer of a
colorimeter when deciding how to select the wavelength i.e.
produce monchromatic radiation (one wavelength band)
from polychromatic radiation (white light).
These basic options are-
a. Gelatin filters
b. Interference filters
c. Grating monochromators
These are low cost selection devices which produce or transmit a wide band of radiation usually ± 20 nm.
Fortunately most colorimetric analyses have a wide
absorption band which allows excellent results to be
obtained from a simple colorimeter.
The most common type of gelatin filter is constructed by
sandwiching a thin layer of dyed gelatin of the desired colour
between two thin glass plates.
There are two drawbacks which can be encountered
using gelatin filters:
1. They have a wide bandpass, see Fig 15, which can lead to non
linearity in standard curves
2. They absorb approximately 30-40% of all incident
radiation thereby reducing energy throughput to the
However these filters are eminently suitable for most
(Glass Filters Coloured glass filters are now more or less historical selection devices in colorimeters and have very wide
bandposses often up to 150nm. Specific wavelengths can
however be achieved by using a combination of glass filters.)
To ensure all wavelengths in the visible spectrum are catered for approximately 8 Gelatin filters are required.
A typical range of filters will have the following transmission
These are used to select wavelengths more accurately by
providing a narrow bandpass typically of around 10nm. The
interference filter also only absorbs approximately 10% of the
incident radiation over the whole spectrum thereby allowing
light of higher intensity to reach the detector.
The theory of operation of an interference filter is fairly
complicated but has been simplified below.
An interference filter comprises of several highly reflecting
but partially transmitting films of silver separated by thin layers
of transparent dielectric material (often magnesium fluoride
(MgF2) This is also referred to as an MD or metallic dielectric
filter). When white (polychromatic) light passes through the
dielectric layers multiple reflections appear between the
semi-transparent mirrors. However some energy from the
light beams passes straight through the filter. It is this
wavelength which is desired for analysis. If the dielectric layer
thickness is altered slightly the resultant wavelength is
Before the analyst attempts to perform quantitative colorimetric
analysis it is important to understand the theoretical aspects of
The relationship between concentration and the light
absorbed is the basis of the following theoretical consideration;
The seemingly obvious way of taking readings on a
colorimeter is to measure % transmission and adjust the
'blank" to 100%.
For example, consider a situation where a blank is
measured followed by three standard solutions having
concentrations of 1, 2 and 3 units respectively. Ideally, a
colorimeter should be giving concentration readings directly,
but consider the above solutions when analysed.
The solution with a concentration of 1 unit reduces the light
to 50% therefore, the solution with a concentration of 2 units will
reduce the light to 25% and the solution with a concentration
of 3 units will reduce the light to 12.5%.
Therefore if the colorimeter is calibrated using a
transmission scale, the following graph is produced.
The calibration in %T has the drawbacks of being non-
linear and readings decreasing with increasing concentration.
Bonguer first investigated this type of relationship for
changes in thickness of solid materials. His work was followed
by Lambert and Beer in 1852, who extended the studies to
solutions. All three investigators contributed what is universally
known as The Beer Lambert Law.
This states that:
The light transmitted through a solution changes in an
inverse logarithmic relationship to the sample concentration.
In order to take measurements both directly and linearly in
terms of concentration, %T readings must be converted into
an inverse logarithmic form which are called optical density
units (OD) or absorbance (A).
The formula is: = OD = log10100/%T
Therefore, for the given example, the relationship of OD to
concentration is shown in the table below.
A calibration curve of OD against concentration
linear and directly proportional.
Optical density (absorbance) is used for colorimetric
analysis so that readings relate directly to concentration.
Similarly, optical density changes directly with sample path
length. Thus we arrive at.
Abs = E x c x l
Abs = Absorbance
E = Extinction coefficient or molar absorbtivity
c = Concentration
l = Path length
l is fixed by the pathlength of the cuvette (usually 10mm) and E is a constant for each chemical species hence