Download Light Polarization－Malus`s Law

General Physics Experiment Handout
Light Polarization－
－Malus’s Law
Purpose of the Experiment
To observe the transmission of linearly polarized light through a polarizer.
Experimental Principle
Light is an electromagnetic wave, and the polarization direction of an electromagnetic wave is
defined as the vibration direction of the electric field for the wave. In a vacuum or uniform medium, the
direction of polarization is perpendicular to the propagation direction of an electromagnetic wave. As
shown in Fig. 1a, an electromagnetic wave propagates along the x-axis, and the polarization direction
follows the y-axis. The direction of polarization is commonly represented as the angle between the
vibration direction of the electric field and a reference direction in a plane perpendicular to the
propagation direction of the electromagnetic wave. As shown in Fig. 1b, if the y-axis is the reference
direction, the wave has a polarization angle of 0°.
v
v
E and magnetic field B of an electromagnetic wave; and
v
(b) the vibration direction of E in a perpendicular plane (Halliday: Fundamentals of Physics).
Figure 1. (a) The correlation between the electric field
However, for any light wave (or electromagnetic wave) commonly found in nature, the polarization
direction of the electric field exists in every angle. As shown in Fig. 2a, one light beam represents a
superimposition of electric fields in various directions. The result is an “unpolarized” electromagnetic
wave, such as sunlight or light emitted from an incandescent bulb. If the electric field of a given light ray
vibrates in a certain direction at all times, this ray or beam is considered “linearly polarized light.” The
term “linearly polarized” indicates that when observing the propagation direction of linearly polarized
light, the electric field vibrates along a line over time (Fig. 1b).
v
Figure 2. (a) Vibration direction of the electric field E of an unpolarized light ray; and (b) representation of any
v
electric field E using two mutually perpendicular components (Halliday: Fundamentals of Physics).
Employing vectors for analysis, we find that the electric field of an electromagnetic wave consists
of two components that are mutually perpendicular and possess the same frequency and wavelength. In
the case of a linearly polarized wave, these two components of the electric field must have a phase
difference of 0° or 90°. An electromagnetic wave is circularly or elliptically polarized if the phase
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General Physics Experiment Handout
difference between these two components is not 0° or 90°. Consequently, the direction of the electric
field varies over time.
Polarizers are among the tools widely used to produce a linearly polarized light ray or beam. As
shown in Fig. 3a, this tool passes light of a specific polarization direction, and absorbs or reflects light of
perpendicular polarizations, by selecting a specific electric field of the incident ray or beam. Varying
polarizer forms have been created to fulfill various design principles and accommodate different
demands. The common polarizer types used in this experiment (as shown in Fig. 3b) are represented as
the “polarizing sheet” shown in Fig. 3a, where vertical lines represent the vibration directions of an
electric field that are allowed to pass the polarizer.
(a)
(b)
Figure 3. (a) The vibration directions of unpolarized light transmitted through a polarizing sheet (Halliday:
Fundamentals of Physics); and (b) common polarizers (Newport).
Fig. 4 shows an unpolarized light ray passing through two sequential polarizers. Each polarizer has
a transmission axis that designates a direction, and the polarization directions of electric fields parallel to
the designated direction can be transmitted through the polarizer. The transmission axis of the second
polarizer is set at an angle of θ to the transmission axis of the first polarizer.
The unpolarized ray is linearly polarized by the first polarizer. Additionally, we assume that the
E
electric field amplitude of the polarized ray is 0 . The amplitude of the electric field after the ray is
E cos θ
transmitted through the second polarizer will be 0
because angle θ exists between the
transmission axis of the second polarizer and the polarization direction of the incident ray.
The brightness of a ray or beam is related to its power density, which is the power per unit time and
per unit area transmitted by the ray (or electromagnetic wave). The power transmitted by an
v 1 v v
S=
E×B
µ0
. During experiments,
electromagnetic wave is represented using the Poynting vector
as
v
S avg
light is measured as the time-averaged Poynting vector (
), which is known as the intensity of light
(I).
cε 2
I 0 = 0 E0 2
2
Thus, the intensity of the ray transmitted through the first polarizer is
. After the ray
passes through the second polarizer, which has a transmission axis that creates an angle of θ with the
cε 2
I (θ ) = 0 E0 2 cos 2 θ
2
first polarizer, the intensity is
, or
2
I (θ ) = I 0 cos θ
(1)
which is Malus’s law.
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General Physics Experiment Handout
Figure 4. Schematic diagram of Malus’s law (Serway: Fundamentals of Physics).
Laboratory Instruments
1.
2.
3.
4.
5.
6.
Laser diode (LD) (including a power supply and a support frame, as shown in Fig. 6)
Two polarizers 5 cm in diameter fixed on a support frame with a nonadjustable angle
One polarizer 2.5 cm in diameter fixed on a support frame with an adjustable angle (Fig. 8)
Slide rail with five platforms
Five support rods and support bases
Photodiode (power supply included, as shown in Fig. 7) and electricity meter mounted on a table
Figure 5. Experimental instruments
Figure 7. Photo diode (PD). A piece of paper is taped onto
the detector to reduce the intensity of the laser
beam on the light receiving area. This prevents the
PD from becoming saturated if the incident laser is
too intense.
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Figure 6. Laser diode (LD)
Figure 8. The markings or divisions on Polarizer III. The
outer ring is the main scale, and the inner ring is
the auxiliary scale, which rotates with the
polarizer.
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Notes
※
The power of the LD is approximately 5 mW. To protect your eyes, do not look directly at the laser
beam or any reflection of the laser.
※
The markings on Polarizer III consist of a main scale (outer ring) and an auxiliary scale (inner ring).
The main scale has a minimum increment or division of 2°; thus, every mark represents 10°.
The 30 measurements on the auxiliary scale cover the range of 29 measurements (58°) on the main
scale.
The angle of the auxiliary scale is read similarly to how a vernier scale is read.
1. Identify the two measurements on the main scale, between which the zero measurement of the
auxiliary scale is located. The smaller of the two measurements is A.
2. Find the measurement on the auxiliary scale that aligns with a measurement on the main scale.
The measurement on the auxiliary scale is B.
B
3. Thus, the rotation angle of the polarizer is θ = A + 2 ×
(degree).
30
Experimental Procedure
A.
Instrument Setup
Fig. 5 shows the experimental setup. The relevant details are provided below.
1.
2.
3.
Component positions and heights
PD and LD are separately placed on the slide platforms on the outermost slide bases of the
slide rail.
Use the height of the LD-emitted beam as the standard for other components. Align the
components and ensure that the beam hits the center of the PD detector through the
centers of the three polarizers. The direction of the beam should be parallel to the slide rail.
PD setup
Connect the PD power supply to a power extension cord of 110 VAC.
Connect the two voltage output cables to the electricity meter on the table. The black
cable is the ground cable, and the red cable is used for voltage signals. Set the electricity
meter to DCV.
The measured light intensity is output by the PD in analog voltage signals. Higher
intensities produce higher voltages.
LD
Connect the LD power supply to a power extension cord of 110 VAC. When switched on,
the LD emits a laser beam.
Caution!!
Use a paper or your palm to block the laser output before the LD is switched on to ensure
the beam is not directed to unexpected areas.
B.
Measuring the Polarizations of Components
In this experiment, components such as the LD and polarizers have specific polarization angles.
Polarizers I and II have fixed polarization angles, and their transmission axes are horizontal and vertical,
respectively. The beam or ray produced by the LD possesses greater amplitude in one of the polarization
directions, which is set as approximately 45° to the horizon.
Polarizer III (2.5 cm in diameter), which has an adjustable angle, should be employed for this
experiment. Use the angle graduations or increments on the support frame (Fig. 8) to measure and record
the polarization direction of the LD laser beam and the directions of the transmission axes of the other
polarizers.
The measurement procedures for above instruments are as follows:
1. Ensure that the beam hits the detector in the PD.
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General Physics Experiment Handout
2.
The relative positions of the components can be located using the beam propagation direction
(Fig. 4).
LDtest polarizer (Polarizers I or II) adjustable angle Polarizer IIIPD
3. Test and adjust the intensity of the beam illuminating the PD. Changes in intensity must be
measured accurately.
If the beam is too intense, the PD becomes saturated and cannot correctly measure the
voltage for higher light intensities.
If the beam is too weak, the PD and electricity meter measurements will be too imprecise
to reflect minor changes in intensity.
Rotate Polarizer III (approximately 180°) and assess whether the PD is saturated by
observing the meter reading. In addition, observe the maximum voltage.
When the angle is within a certain range and the PD is saturated, the meter reading will
remain fixed at the maximum. This implies that the intensity of the incident beam
projected into the detector is excessive and must be reduced.
Tape a piece of paper or a thin black film to the front of the detector to reduce the
intensity of the beam illuminating the detector.
4. Record the background signal measured by the PD.
Block the laser beam to enable the PD to measure only the light within the room.
Subtract the background signal from the measured light intensity for correction.
5. Alter the angle of Polarizer III and record the electricity meter readings measured at various
angles.
Let the angle be represented as a horizontal axis and output voltage be represented as a
vertical axis, and plot a data graph.
The range of angle alteration should be approximately 360°.
6. According to the data graph, calculate the polarizations of the LD laser and the angles of the
transmission axes for Polarizers I and II.
C.
A System Composed of Three Polarizers
Position Polarizers I and II, which are used in several parts of Procedure B, between the LD and the
PD. A phase difference of 90° exists between the transmission axes of Polarizers I and II; thus, the
intensity measured by the PD should be extremely minor. Place the adjustable angle Polarizer III
between Polarizers I and II for most of the experiments. Change the angle of Polarizer III. As shown in
Fig. 9, observe and record the changes in light intensities measured by the PD.
Figure 9. Schematic diagram of Procedure C (Halliday: Fundamentals of Physics)
Procedures
1. Ensure the PD detector is directly illuminated by the laser beam.
2. Test and adjust the laser intensity to ensure accurate PD laser measurements.
Adjust the intensity according to Procedure B.
3. Record the intensity of background light signals measured by the PD.
4. Alter the angle of Polarizer III and record the electricity meter readings measured at various
angles.
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General Physics Experiment Handout
Let the angle be represented as a horizontal axis and voltage be represented as a vertical
axis, and plot a data graph.
The range of angle alteration should be approximately 360°.
D. Examine the Effects of Stress
1. Fig. 10 shows the instrument setup.
In addition to the setup in Procedure C, a light source with a larger range is required. Such
a source can be an LCD screen, sunlight, a flashlight, or a fluorescent light.
Remove the laser, Polarizer III, and the PD used in Procedure C, and move the entire setup
in front of the light source with a larger range. Allow the light ray or beam radiated from
this source to pass through Polarizers I and II in the same incident direction as the laser
beam.
2. Position the test object between Polarizers I and II.
Test objects must be transparent, such as an acrylic plates, spectacles, or glass.
3. Observe and record images behind Polarizer II with your naked eyes or a camera. Fig. 10b shows
the image that should be observed.
Caution
A laser cannot be used as the light source in this experiment because the power
density is too high and can damage your eyes.
(a)
(b)
Figure 10. (a) Schematic diagram of Procedure D; and (b) regions on the test object where stress is applied allow
light to pass through this system, which comprises two polarizers. (Photograph by Spigget: “Stress in a
pair of plastic glasses made visible by placing it between two polarizers,” obtained from
http://en.wikipedia.org/wiki/File:Polarized_Stress_Glasses.jpg)
Questions for Reflection
1.
2.
3.
Identify various types and principles of polarizers.
Derive the relationship formula of PD-measured light intensities that change with the angle of
Polarizer III in Procedure C.
Carefully describe the phenomenon observed in Procedure D. Explain why a ray is allowed to pass
through two mutually perpendicular polarizers after being transmitted through certain objects.
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