The Refractive Index of a Solid

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The Refractive Index of a Solid

• An unusual application of spectroscopy

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Background
The goal of this experiment is to obtain the
optical dispersion of a solid using a reference
liquid of known optical dispersion at various,
but specific, temperatures. The distortion
polarizability and molar refraction of a solid
will be calculated as a function of the
wavelength of light. Determination of the
optical properties of solids is not only of
scientific interest but has a wide range of
applicability from telecommunications to the
design of optical components.
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The refractive index of a solid is defined as the
ratio of the speed of light of a specific
wavelength in a vacuum to its speed in the solid.
The change of the refractive index with
wavelength is called the dispersion. In a solid,
the refractive index may also be dependent on the
direction the light takes through the
material. It is relatively easy to measure the
refractive index of a fluid and many instruments
exist for that purpose. It is significantly more
difficult to measure the refractive index for a
solid. Regardless of the medium, a light beam
entering a medium of higher refractive index (the
more optically dense medium) will bend toward
the normal to the surface. This is described by
Snells Law.
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Snells Law is given by
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Most materials of interest to the chemist are
dielectrics, substances that do not conduct
electrical charge. When an electrical potential
is applied to them the electrons in the medium
shift toward the positive electrode and positive
charges shift toward the negative electrode.
Thus, the applied electric field induces a dipole
in the medium. The dipole moment per unit volume
is called the polarization, P. It can be seen
this motion of charges will decrease the size of
the electric field in the medium from that in the
vacuum. Electric Field in vacuum Eo 4ps (s
surf. chg. density) Electric Field in medium E
4ps/e Division is by a constant, the dielectric
constant (e), so the magnitude of the field in
the medium is decreased.
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The value of e is specific to the material.
Since the polarization partially cancels the
electric field in the medium, the field may be
represented as E 4p(s P) or 4pP (e
1)E. The polarization can be related to the
dielectric constant of the material and the
external (vacuum) electric field by
The number of molecules of molecular weight, M,
in the unit volume that contribute to the
polarization is No?/M where ? is the density.
If the average dipole induced in each molecule is
µ then the dipole in a cm3 of material is µNo?/M
P.
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The polarization can now be abandoned for an
expression in terms of the microscopic quantity,
µ
And since µ a Eo the Clausius-Mossotti
equation is derived
Where it is explicitly noted that both the
polarizability and the dielectric constant depend
upon the frequency of the field.
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At optical frequencies, it can be shown that e(v)
n(v)2 so that
R is the molar refraction which is characteristic
of a material. However, it is found that
different functional groups and types of bonds
may be assigned partial molar refractions that
are approximately additive and from them the
molar refraction of a material can be estimated.
Finally, the polarizability can be obtained from
quantum mechanics
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The determination of the refractive index of the
solid is based on the fact that a solid suspended
in a liquid cannot be seen when its refractive
index equal to that of the liquid. When
the refractive indices of the two media differ,
then light is reflected from the interface
between the two. This reflected light Appears
as an absorption from the beam of light traveling
directly through the sample, i.e. it looks like
an absorption. The refractive index of a liquid
is temperature dependent as well as frequency
dependent
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The refractive index of a solid is only weakly
dependent on the temperature. The dispersion of
a solid can be expressed by the Cauchy equation
Where A, B and C are specific to the
material. The specular reflection that occurs
when two media have different refractive indices
is expressed by the Fresnel equation
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The light beam traveling through the suspension
of solid particles will undergo a large number (
N) of reflections that cause the beam to be of
diminished intensity and, therefore, decreased
transmittance T ( 1 R)N When the
refractive indices of the liquid and solid match
then T 1. The refractive index of the liquid
can be made to match that of the solid by varying
the temperature. Thus, by measuring the
transmission spectrum at several temperatures,
the optical dispersion of the solid can be
obtained.
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Procedure

• Allow cell to be used to equilbrate to 25 C while
  the sample is being prepared.
• Fill a cuvette with pure toluene, the index
  matching liquid.
• Samples will be of KCl, KSO4 or KClO3 or other
  related salts.
• Grind samples separately to very fine powder.
• Allow sample to equilibrate to 25 C.

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• Sprinkle a small amount of the solid onto the
  liquid in the cuvette but only so that it remains
  suspended without much sinking.
• Measure the transmission spectrum from 350nm to
  700nm with a UV-Vis spectrophotometer at 1 nm
  resolution.
• Measure subsequent transmission spectra at by
  increasing by 5 C degrees until the last
  measurement is made at 70 C. Measure the
  tranmission of a blank at each temperature.

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• Sprinkle more material at each temperature to
  assure material is always in suspension.
• It is vital that the sample is equilibrated at
  each temperature.
• At conclusion clean cuvettes and dispose of
  sample as instructed.

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Data Analysis

• Obtain the temperature dependence of the
  refractive index of toluene from the literature.
• Fit the data with an equation that gives the
  refractive index of toluene as a function of
  temperature and light wavelength.
• Calculate the toluene dispersion curves from
  350nm to 700nm for each temperature.

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• Mark the wavelength on the dispersion curve where
  the corresponding transmission spectrum had its
  peak transmittance (both curves for the same
  temperature).
• Connect the marks to obtain the dispersion curve
  of your solid over the measured wavelength
  region.
• Obtain the Cauchy relations for each of the
  samples.
• Plot the wavelength dependence of the
  polarizability and the molar refraction for your
  samples.