Fakultät für Physik und Geowissenschaften
Physikalisches Grundpraktikum
O11e „Polarisation and Optical Activity“
Tasks
1. Determine the specific rotation and the concentration of three sugar solutions of a specific type of
sugar using a half-shade polarimeter.
2. Using the solution with the highest concentration from task 1 measure the dependence of the
rotation angle on the wavelength. Plot the data and determine the exponent of the power law.
3. Qualitatively, using the dispersion of the optical rotation, check whether quartz plates are left- or
right-rotating.
4. Measure the intensity I(α) of a linearly polarized laser beam as a function of the rotation angle of
a polarizer. The measurement should be done with a λ/4-plate in the angle settings 0°, 30° and
45°. Plot I(α) in a cartesian coordinate system and evaluate the curves using the law of Malus.
Further plot the data in a polar diagram. Discuss the graphs and the results of the fitting
procedure.
Literature
Physikalisches Praktikum, 13. Auflage, W. Schenk, F. Kremer (Hrsg.), Optik, 4
Physics, P. A. Tipler, 3rd Edition, Vol. 2, Chap. 30-6
University Physics, H. Benson, Chap. 38.9
Accessories
Half-shade polarimeter with sodium lamp (λPeak = 590 nm), polarimeter with halogen lamp, set of
interference filters, test tubes with liquids, quartz plates, diode laser
, polarizer, photodiode,
digital multimeter
Keywords for preparation
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Light as an electromagnetic wave
Linear, circular and elliptical polarized light
Generation of polarized light (birefringence, reflexion, absorption, scattering)
λ/4 wave plate
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Optical activity, rotation dispersion
Principle setup of a polarimeter
Law of Malus, Fresnel equations
Visual perception of illumination levels, Weber-Fechner law
1
Remarks
In task 1 perform at least three measurements of the rotation angle for each test fluid. The
concentration of one solution (standard solution) is known. From this the specific rotation can be
determined for the given experimental conditions (ϑ, λ).
Fig. 1. Half-shade polarimeter (L-light source, P-polarizer, H-prism, K-test tube of length l, A-analyzer).
The mode of operation of a polarimeter is shown in Fig. 1. The light rays emitted by the
monochromatic light source (L) are collimated by a lens before being linearly polarized by the
polarizer (P). The plane of polarization of a part of the light beam is turned by a few degrees by the
prism (H). The test tube (K) of length l = 200 mm contains the solution under study. By turning the
analyzer (A) the rotation angle of the polarization plane can be determined.
Fig. 2. Adjustment and reading of the angle (ϕ) at the half-shade polarimeter.
The measurements should start with a check of the zero point of the polarimeter without test tube.
To this end the different brightness of the inner and outer areas (Fig. 2a) of the half-shade
polarimeter has to be compensated by turning the analyzer (Fig. 2b). Note that in a full 360° turn of
the analyzer there are four settings with areas of equal brightness, two of these sensed dark and two
of these sensed bright (compare with the law of Malus). Use the darker setting, since this allows the
eye a more sensitive comparison of the brightness of the areas (Weber-Fechner law). The reading of
the values is made with a degree scale divided from 0 to 180° with nonius. For the measurement of
the rotation angle the test tube is brought into the light path and by turning the analyzer equal light
intensities are adjusted in both areas (Fig. 2c). Note that only samples with a rotation angle -90°< ϕ <
90° can be measured with this polarimeter.
In the investigation of the dispersion of the optical rotation in task 2 a relationship between the
angle of rotation ϕ and the wavelength λ of the form ϕ∼λn is assumed. A plot of the ϕ - λ - diagram
on a double logarithmic scale will lead to a straight line with a slope corresponding to the exponent
n. The measurement is performed with a white-light polarimeter equipped with colour filters.
Task 3 is carried out with the white-light polarimeter. Since the specific rotation depends on the
wavelength (dispersion of the optical rotation), specific wavelength ranges of the white light are
extinguished, depending on the setting of the analyzer (crossed). In case of left-rotating substances
(mathematically positive direction of rotation) during leftward rotation of the analyzer the light is
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extinguished in the colour series red – yellow – green – blue. The colour impression during this
analyzer rotation corresponds to the series of complementary colours (subtractive mixture of colour)
blue – green – yellow – red.
In task 4 the intensity of linearly polarized
monochromatic light is measured with a photo diode as
a function of the angular setting between the direction
of polarization and the direction of the analyzer. The
intensity of the light passing a polarizer is proportional
to the square of the cosine of the angle α between the
direction of the polarization and the polarizer (law of
Malus,
see
Fig.
3):
cos2 (α − α0 ) = I (α ) / I 0
(I0: maximum intensity at α = α0).
Fig. 3. Law of Malus
With a λ/4-plate three measurement series should be performed with the angle between the optical
axis of the λ/4-plate and the direction of polarization of the linearly polarized light set to 0°, 30° und
45°, respectively.
A λ/4-plate is a thin layer made from an optically anisotropic material; in this material the speed of
light (resp. the refractive index) depends on the direction of the polarization. Often materials with a
unique optical axis are used that can be characterized by two refractive indices (for polarization
directions parallel and perpendicular to the optical axis). Polarized light propagating through this
uniaxial optical crystal can be decomposed into two electric field components, parallel and
perpendicular to the optical axis. The velocities of light, v and v ⊥ , corresponding to these two
electric field components are conventionally related to the extraordinary (e) and the ordinary (o) ray
of light with principal refractive indices: ne = c0 / v , no = c0 / v⊥ . c0 denotes the speed of light in
vacuum. The refractive index difference Δn = ne − no is a measure of the birefringence and
determines its character, i.e. whether the crystal is optically negative or positive uniaxial. The
following table shows a few examples.
Material
no ( ⊥ )
ne (⏐⏐)
Δn
calcite
1,6584
1,4864
-0,1720
turmaline
1,669
1,638
-0,031
quartz
1,5443
1,5534
+0,0091
(E. Hecht, Optik, 4. Auflage)
Table 1. Refractive indices of selected uniaxial birefringent crystals at λ = 589 nm
In case of optically positive uniaxial crystals, e.g. quartz (crystalline silicon dioxide, Δn > 0 ), one has
v ⊥ > v , i.e. the ordinary ray propagates faster than the extraordinary ray. In case of calcite, being an
optically negative uniaxial crystal, v is larger than v ⊥ (ne- no =-0,172). After passing through the
crystal plate a phase shift of Δϕ =
2π
λ
d ( ne − no ) has developed between the two components. d
denotes the geometrical thickness of the plate and λ the wavelength of the incoming light. Both rays
interfere when leaving the crystal. In this way a new kind of polarization state of the light beam is
generated (frequency and wavelength are unaffected). Consequently, a λ/4-plate is made for a
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specific wavelength with the value of the phase shift Δϕ being determined by the thickness d of the
plate. Depending on the amplitudes of the ordinary and extraordinary ray one obtains linearly
polarized light (in case one ray has vanishing amplitude), elliptically polarized light or circularly
polarized light (in case both rays have the same amplitude). The ratio of the amplitudes of both rays
can be modified by the angle settings of the optical axis of the λ/4-plate with respect to the axis of
polarization of the incoming linearly polarized light.
As shown in Fig. 4 for the study of the polarization state of the incoming light a linear polarizer is
used as analyzer. The transmitted intensity is measured by a photo diode.
Fig. 4. Schematical setup for the law of Malus and the action of a λ/4-plate
Instead of a λ/4-plate a (less expensive) λ/4-foil is used in the experiment. These wave plates are
clear transparent foils with a thickness of 0.8 mm. There action corresponds to that of conventional
gypsum or mica plates. Their use as λ/4-foil is appropriate in the wavelength range of 480-640 nm.
For the intensity I = I(α) of the transmitted light behind the analyzer one obtains in dependence of
the parameter θ (angle between the E-vector of the linearly polarized light and the optical axis of the
λ/4-foil):
I (α ) =
E02
[cos 2 θ cos 2 (α − θ ) + sin 2 θ sin 2 (α − θ )] .
2
This equation may be derived by vector decomposition and the use of the law of Malus (a favoured
question at the beginning of the laboratory session). Further rearranging leads to:
I (α ) =
I0
[1 + cos 2θ cos 2(θ − α )]
2
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