optical

paring with the appropriate formula, the temperature T of the filament may be determined.
By adjusting the electrical power delivered to the filament, different temperatures may be
measured.
(b) Using several values of T, the electrical power I dc V dc may be plotted versus T 4 , and the
slope of a fitted line may be used to determine a value for σ B .
Optical Absorbance by Light Sensitive Molecules and Beer’s Law
The Beer-Lambert Law [?], more commonly known as Beer’s law, states that the optical
absorbance by a light-sensitive molecule (e.g., a dye molecule) in a transparent solvent varies
linearly with both the sample cell path length and the concentration of the molecules in the
solvent. In practice, Beer’s law is accurate enough for a range of light-sensitive molecules,
solvents and concentrations, and is a widely used relationship in quantitative spectroscopy.
Absorbance is measured in a spectrophotometer by passing a collimated beam of light at
wavelength λ through a plane parallel slab of material that is normal to the beam. For
liquids, the sample is held in a an optically flat, transparent container called a cuvette.
Optical absorbance OA is calculated from the ratio of the spectral density transmitted
through the sample ε ′ e (λ) to the spectral density that is incident on the sample ε e (λ) (with
T = room temperature).
ε ′ e (λ)
OA = − log 10 (5)
ε e (λ)
For a sample with an optical pathlength l and a molar concentration C m [with units of
molarity (M), defined as a mole per liter (mol/L)], Beer’s law can be stated as
OA = α m (λ)lC m (6)
where α m (λ) is the coefficient of molar absorptivity (also known as the extinction coefficient)
of the molecule at wavelength λ. α m (λ) has units M −1 m −1 , and is a property of the material
and the solvent.
In an absorbance experiment, light is attenuated not only by the light-sensitive molecule
but also by reflections from the interface between air and the cuvette, the cuvette and the
sample, and absorbance by the solvent. These factors can be quantified separately, but
are often removed by defining ε e (λ) as the light intensity passing through a sample blank
or reference sample (e.g., a cuvette filled with solvent but with zero concentration of the
light-absorbing molecule).
In the optics lab, the transmitted spectral density ε e ′ (λ) of various samples with different
concentration and the sample blank spectral density ε e (λ) are measured so as to determine
the absorbance OA. By fitting the absorbance OA versus the concentration C m , which should
have linear relation, Beer’s law may be verified. The measurements will be performed on
solutions of two different dye molecules, indocyanine green (ICG) [?] and hexamethylindotricarbocyanine
tetrafluoroborate (HITC-BF4) [?] solutions.
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