Download 21. Specific rotation of sugar solution

21. SPECIFIC ROTATION OF SUGAR DILUTION
1. Objective
Determination of specific rotation of sugar dilution.
2. Equipment needed
Half shadow polarimeter, tube with unknown sugar dilution.
3. Theory
3.1 LIGHT POLARIZATION
Nature of light is wave-corpuscular. It is an electromagnetic wave, as well as a photon flux i.e a flow
of particles of light. The phenomenon of light manifests dualism of a physical Picture of the world –
continuous and discrete uniformity.
In this laboratory work the explanation of investigational properties of light is based on it’s
electromagnetic wave properties.
In light (as in each electromagnetic wave) both the electric field intensity vector (E-vector) as well as
the H-vector (magnetic field intensity) oscillate perpendicular to the direction of the wave
propagation, ie. the light is a transverse wave.
Light waves, taking only a minor part of the wide electromagnetic spectra are the only ones directly
observable by a human being. As in the process of interaction of light and matter the E-vector has
more important role than the H-vector, we limit ourselves only to observation of the E-vector, which
is in optics also called the light vector. As a rule, its direction is chaotic, but it always remains
perpendicular to the direction of light propagation. From the fact that light is a cross (transverse)
wave concludes its ability to be polarized which is manifested in either partial or complete order of
the oscillations of E-vector under certain conditions. For example, while reflecting from the surface
of the dielectric at a certain angle the E-vector of reflected light oscillates only in one plane.
Polarization is one of the most essential features of the lights cross wave character.
In case of non-polarized (or natural) light the oscillations of the light vector take place irregularly in
many directions, but transverse to the direction of wave propagation, whereas all directions are
equally probable. In this case the oscillations are statistically axis-symmetrical in relation to the
direction of propagation. If the light vector behaves in a certain pattern (oscillates only in one
direction), it is a polarized light. Generally, in this case the light vector oscillates asymmetrically to
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the direction axis. Cross-wave polarization in general, stands for disorder of axis-symmetry according
to the spreading direction.
Polarized light is divided into categories by the projection of the E-vector endpoint trace on the
plane, which is perpendicular to the direction of light propagation. If the endpoint of the electric
vector generates a straight line on the plane perpendicular to the direction in which light propagates,
it is linearly polarized light. If it forms a circle or an ellipse, then it is respectively either circularly or
elliptically polarized.
E-vector of the linearly polarized light oscillates on one level – called polarization level, which is
determined by the direction of the oscillations of the E-vector and direction of light propagation.
Therefore this light is called flat polarized as well.
Endpoint of the E-vector of the circularly polarized light draws a spiral with a circular cross-section,
elliptically polarized lights vectors endpoint draws an elliptical cross-section of the screw-line.
Above we described three cases of fully polarized light, all of which are reducible to merging of two
orthogonal oscillations with constant phase difference. The elliptical polarization is the most general
of the three kinds of polarization; circular and linear polarizations are its special cases.
Partially polarized light is also distinguished. In this case, one of the directions of oscillations of the Evector is preferable compared to the others. That’s why partly polarized light can to be observed as
a straight-line polarized and natural light mixture.
Natural light can be polarized by the polarizers. Plane, on which oscillates the E-vector which has
transmitted the polarizer, is called the principal plane of the polarizer. Ideal polarizer lets through
oscillations which are completely parallel to the main level and doesn’t let through oscillations which
are perpendicular to the main level. In “real life” polarizers light waves with E-vector oscillating
parallel to main level, are slightly absorbed. Also small part of light waves perpendicular to main level
is passed through.
Polarizer’s work is based on the phenomena that orientation of E-vector may change (polarization
state) in case of the reflection, refraction, birefringence and scattering of the light.
In this work polaroids are used as polarizers, whose work is based on the special case of the
birefringence – selective absorption of light. Light falling on the polaroid is distributed into two
orthogonal oscillation components (for the normal and the abnormal wave), of which one is
absorbed. Therefore, linearly polarized light exits from the polaroid. As a polaroid, for example, is a
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large number of entries applied on a celluloid film identically oriented needles of gerapatite crystals
that let in only light with E-vector oscillating in a single plane.
3.2 POLARIMETER
Polarizer can also be used for identifying light polarization, as an analyzer. A device consisting of two
sequence polarizers, which is supplied with a circular scale, is called polarimeter. The light sourceside polarizer changes natural light into linearly polarized light. By turning the second polarizer,
called the analyzer, the position of the polarization plane of light can be determined. The point is that
the intensity of the light transmitted through the analyzer I depends on both the intensity of the
fallen light on the analyzer I0 and on the angle γ between principal planes of the analyzer and
polarizer.
Light intensity characterizes the amount of energy which is carried forward by electromagnetic wave,
and it is equal to the energy propagated through the perpendicular surface of a unit size in an
average time interval. Thereat 𝐼0 ~ 𝐸𝐴2 , where 𝐸𝐴 is the amplitude of the electric field strength.
Dependence of the intensity of light transmitted through the analyzer on the angle γ is described by
the Malus’ law:
𝐼 = 𝐼0 𝑐𝑜𝑠 2 𝛾
(1)
where γ is the angle between the main levels of the polarizer and the analyzer,
I – intensity of the light that had passed through the analyzer and 𝐼0 is the intensity of light fallen on
the analyzer. It is seen that the intensity of light is maximum when 𝛾 = 0. If the principal planes of
𝜋
the polarizer and analyzer are orthogonal to each other (𝛾 = 2 ), then the ideal analyzer will not let
the light through. For all the intermediate angles the light will be partially quenched. As a zero
position of such a polarimeter could be taken perpendicular or parallel position of the polarizer and
analyzer. Outgoing light intensity then is either zero or a maximum.
Measurement accuracy of a polarimeter consisting only of the polarizer and analyzer, however, is
small. In case of the angles 𝛾 = 0 and 𝛾 =
𝜋
2
, the speed of changing of intensity of the light
transmitted through the analyzer (intensity change of angle per unit) is
𝑑𝐼
𝑑𝛾
= 𝐼0 sin 2𝛾 = 0.
𝜋
If the analyzer is rotated a few degrees by the angles 𝛾 = 0 and 𝛾 = 2 , intensity of light in the field
of sight remains practically unchanged. Rather, the eye does not notice the change. The eye,
however, is capable to record very accurately the intensity difference or equality of the two areas
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situated side by side, compared to the darkening or brightening of the same. The accuracy is highest
if both sides of the field of view are faintly illuminated.
Therefore, the field of view is divided into two halves by an appurtenance. So a half shadow
polarimeter has been built. As a zero position is taken the position, in which both sides are equally
slightly illuminated. In this position the angle 𝛾 is a few degrees smaller than a right angle, and
𝑑𝐼
therefore, 𝑑𝛾 is different from zero, and in addition, with different signs in the opposite halves of the
visual field. When the intensity in one half of the visual field grows, it shrinks in the second half.
Hence, here comes the name of the half shadow polarimeter from.
Figure 21.1
Figure 21.2
In the physics lab half shadow polarimeters CM-2 and CM-3 are used. Their optical scheme is
presented in figure 21.1. Light from the light source S first passes the filter F, which separates the
sodium D-line from the spectrum. Next, before reaching the eye, the light passes the condenser K,
polarizer (polaroid) P, the phase plate FP which divides the field of view into two parts, the test cell
KL filled with liquid, analyzer (polaroid) A and a spyglass PS. The phase plate is an optical device
which separates the light into two partial waves with different speeds, causes the phase difference
(gearchange), and then interfers them. In polarimeters the half-wave plate (with gearchange
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𝜆
2
(2𝑘 + 1) ), which is oriented so that the polarization plane of the polarized light is rotated by a
relatively small angle.
The telescope's field of view of the polarimeter which is divided into two halves by a phase plate, at
different positions of the main plane of the analyzer AA is shown in the figure 2.21.
Since the phase plate FP covers the left side of linearly polarized light coming out from the polarizer,
only right half of the light falls directly on the analyzer (if there is no cuvette with a liquid solution).
The left side of the beam passes the half-wave plate before reaching the analyzer. The half-wave
plate rotates the oscillation plane of the E-vector anticlockwise by the angle 2𝛿 = 7° (Figure 21.2). In
the uncovered half of the field of view, the oscillation plane of the E-vector remains unaffected.
Thus, the oscillation plane of the E-vector is different in the left and right half of the field of view. (In
figure 21.2 ⃗⃗⃗⃗
𝐸1 is the amplitude of the E-vector in the left half, and ⃗⃗⃗⃗
𝐸2 on the right.)
According to the Malus’ law, the light intensity of the left side of the field of view (with index 1) and
the right side (with index 2) manifest as follows:
𝐼𝑡 = 𝐼0 𝑐𝑜𝑠 2 𝛾 ,
𝐼2 = 𝐼0 𝑐𝑜𝑠 2 (180° − 𝛾 − 2𝛿) = 𝐼0 𝑐𝑜𝑠 2 (𝛾 + 2𝛿).
(2)
(3)
Here 𝐼0 is light intensity falling on the analyzer in each half of the field of view. On the left diagram of
figure 21.2 𝛾 = 90°, 𝛾 = 90° − 𝛿 on the central and 𝛾 = 90° − 2𝛿 on the right diagram.
According to formulas (2) and (3) the condition of 𝐼1 = 𝐼2 is fulfilled only in two cases: first, when
𝛾 = −𝛿 and, second when 𝛾 = 90° − 𝛿. In the first case, both sides of the field of vision are of
maximum brightness, in the second case the minimum. Both states can be considered as zero
positions of the polarimeter. However, considering characters of the eye together with the changing
𝜋
light intensity, the measurements (rotating the analyzer's main plane AA) are made nearby 𝛾 = 2 .
Rotating the analyzer by a small angle near 𝛾 =
𝜋
2
, there will be a considerable change of intensity
in the halves of the field of vision (once the left, once the right side darker, as it is shown in figure
21.2).
Based on the foregoing rotation angle of the analyzer is always measured in the polarimeter zero
position (Figure 21.2 Average share), where both sides of the field of view are equally weakly lighted
(𝐼1 = 𝐼2 ). Then the analyzers main plane AA is perpendicular to the bisector O of the angle 2δ. In the
future we will name this position – the zero position.
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Angle readings are taken from two symmetrically placed circular verniers of the polarimeter. One of
them is shown with a main scale in the Figure 21.3. From the main scale grades and half-grades are
taken, smaller parts from the vernier. It is important that readings must be taken with accuracy of
the vernier. In the figure 21.3 we can see the reading 2,24°.
Figure 21.3
3.3 OPTICAL ACTIVITY
Many crystals and dilutions have the ability to rotate the plane of the linearly polarized light which is
spreading through them. Such substances are called optically active. This property comes from
unsymmetrical structure of the molecule or the crystal lattice. Rotation of the polarization plane
occurs in the substances where crystal lattice or molecules cannot mirror image of one match. Such
objects are called chiral. Their asymmetry is resulting from a lack of mirror symmetry. (Of everyday
things have a chiral structure for example a bottle screw, as well as a one hand glove. Optically active
substances are quartz crystals, sugar, camphoric and nicotine dilutions, etc.
These substances usually occur in two different forms where the crystal of one modification or a
molecule is a mirror image of the other. One modification turns then the light oscillation plane in one
direction, another in the opposite direction. That is the situation in case of quartz which rotates the
light oscillation plane to the right and to the left. The sugar molecule is asymmetric (screw shaped
model) due to configuration of carbon atoms. There has been found 16 different forms of this
molecule. They band together into 8 left-right pairs.
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Rotation of light polarization plane in optically active substances can be explained by the model of
classical physics. According to that in optically active substance (screw-shaped) molecules oscillating
electric and magnetic dipoles are formed, which oscillations of the field strength vectors are
⃗ ). Polarization plane
perpendicular to the initial (falling) field strength corresponding vectors (𝐸⃗ and 𝐻
turns as a result of accession of the initial and induced electromagnetic fields.
Phenomenological explanation to the phenomenon of the optical activity was given by Fresnel in
19th century, based on the separation of the polarized light into two in the opposite directions
circularly polarized lights and assuming different refractive indexes in case of the right and left
circularly polarized light.
Angle α of the rotation of the polarization plane of the light transmitted through an optically active
substance is dependent on the layer thickness of the substance 𝑙, the wavelength of light λ , the
temperature t and in case of dilutions, also on concentration c. It turns out that in case of a given
temperature and wavelength angle of the rotation of the polarization plane α in dilutions is
proportional to the thickness of the dilution and concentration of the optically active substance in it:
∝= [∝]𝑡𝜆 𝑙𝑐.
(4)
The physical quantity [∝]𝑡𝜆 is called a specific rotation of an optically active substance. It indicates the
angle by which turns the polarization plane in case the light with wavelength λ passes through a layer
with a unit thickness and a unit concentration, the temperature of which is t.
In operational manuals specific rotation is usually given at wavelength of D-line of sodium
(𝜆̅ = 589.3nm) and at temperature 𝑡 = 20 °C. Corresponding specific rotation is marked as [∝]20
𝐷 .
Hence:
𝛼
[∝]20
𝐷 = 𝑙𝑐 .
(5)
Equation (5) shows that for designation of the specific rotation of the dilution it is necessary to know
the concentration of the dilution c, the thickness of the layer of dilution 𝑙 and the rotation angle of
the polarization plane α. In this work, dilution with a certain concentration, has been poured into the
cuvette cast. The length of the cuvette is written on it. The angle of rotation is measured with the
help of a polarimeter.
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4. WORKING PROCEDURE
1. Acquaint yourself with the construction of the polarimeter and its adjustment opportunities.
Read and write into your protocol accuracy of the polarimeters vernier.
2. Turn on the polarimeters lamp and focus the telescope's field of vision by turning the ocular.
In this case intensities of the different parts of the field of view must be different: 𝐼1 ≠ 𝐼2
(see the left or the right part of the Figure 21.2). In case of the focused image, the bright and
the dark side are clearly separated.
3. Scroll to the zero position of the polarimeter. For that purpose turn the analyzer to a position
where the entire field of view of the telescope is illuminated uniformly weak, ie, 𝐼1 = 𝐼2 (see
the middle part of Figure 21.3). Note down to the scale reading 𝛼0 .
4. Ask the practicum supervisor to check the zero position and specify the task.
5. Place the tube filled with the test dilution into the polarimeter. Focus the telescope's field of
vision again (𝐼1 ≠ 𝐼2 ). Locate the position of the analyzer, in which a total field of view of the
spyglass is evenly poorly lit (𝐼1 = 𝐼2 ). Note the corresponding reading 𝛼1 . Now one
measurement is done.
6. Repeat measurements of the angle with and without a dilution for 5 ... 10 times. Write
results in a table 21.1.
Table 21.1
Determination of the natural reversal of the light polarization plane in the sugar dilution
Mass concentration of the sugar dilution
Thickness of the dilution
Smallest basic scale interval
Number of sections of the vernier
Accuracy of the vernier
Test №
1
∝0
∝1
∝
…
10
̅ =. …
∝
7. Find the optical rotation angle ∝=∝1 −∝0 for each test. Calculate their arithmetic average
̅.
value ∝
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8. Calculate the reversal of the light polarization plane of the sugar by the means of formula (5).
9. Evaluate the uncertainty of the result, using A-type uncertainty for the angle, B-type
uncertainty for the concentration and thickness of the dilution. (As the dependence of the
specific rotation of the dilution on temperature is generally weak, the correction arising from
the fact that the temperature of the dilution is not exactly 20 °C, is quite small and doesn’t
need taking into account).
10. Comparing your results to the table in the workplace (or data from internet) determine type
of sugar dilution used in experiment.
5. Questions and Tasks
1. What is a light wave?
2. What is polarized light?
3. How is it possible to polarize the light?
4. What is a polaroid and Nicol prism?
5. What is the intensity of the light?
6. Formulate Malus’ law and substantiate it.
7. What is the construction and work principle of a half shade polarimeter?
8. What is specific rotation of a dilution?
9. What does the specific rotation depend on?
10. Give the physical explanation to the rotation of the plane of polarization in an optically
active substance.
6. Literature
1. Halliday D., Resnick, R., Walker, J. Fundamentals of Physics. - 6th ed. New York, John
Wiley & Sons Inc., 2001, § 34-6.
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