Polarization EX-9958
PASPORT
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Polarization of Light
EQUIPMENT
1
1
1
1
1
1
1
1
INCLUDED:
Polarization Analyzer
OS-8533
Basic Optics Bench (60 cm)
OS-8541
Aperture Bracket
OS-8534
Red Diode Laser
OS-8525A
High Sensitivity Light Sensor
PS-2176
Rotary Motion Sensor
PS-2120
NOT INCLUDED, BUT REQUIRED:
PASPORT Interface
DataStudio Software
CI-6870
INTRODUCTION
Laser light (peak wavelength = 650 nm) is passed through two polarizers. As the second
polarizer (the analyzer) is rotated by hand, the relative light intensity is recorded as a function of
the angle between the axes of polarization of the two polarizers. The angle is obtained using a
Rotary Motion Sensor that is coupled to the polarizer with a drive belt. The plot of light
intensity versus angle can be fitted to the square of the cosine of the angle.
THEORY
A polarizer only allows light which is vibrating in a particular plane to pass through it. This
plane forms the "axis" of polarization. Unpolarized light vibrates in all planes perpendicular to
the direction of propagation. If unpolarized light is incident upon an "ideal" polarizer, only half
of the light intensity will be transmitted through the polarizer.
Figure 1: Light Transmitted through Two Polarizers
Written by Ann Hanks
Polarization EX-9958
PASPORT
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The transmitted light is polarized in one plane. If this polarized light is incident upon a second
polarizer, the axis of which is oriented such that it is perpendicular to the plane of polarization of
the incident light, no light will be transmitted through the second polarizer. See Fig.1.
However, if the second polarizer is oriented at an angle not perpendicular to the axis of the first
polarizer, there will be some component of the electric field of the polarized light that lies in the
same direction as the axis of the second polarizer, and thus some light will be transmitted
through the second polarizer.
Polarizer #1
Polarizer #2
Eo

E

E
Unpolarized
E-field
Figure 2: Component of the Electric Field
If the polarized electric field is called E0 after it passes through the first polarizer, the component,
E, after the field passes through the second polarizer which is at an angle  with respect to the
first polarizer is E0cos (see Fig.2). Since the intensity of the light varies as the square of the
electric field, the light intensity transmitted through the second filter is given by
I  I o cos 2 
Written by Ann Hanks
(1)
Polarization EX-9958
PASPORT
Page 3 of 7
THEORY FOR 3 POLARIZERS
Figure 3: Electric Field Transmitted through Three Polarizers
Unpolarized light passes through 3 polarizers (see Fig.3). The first and last polarizers are
oriented at 90o with respect each other. The second polarizer has its polarization axis rotated an


angle  from the first polarizer. Therefore, the third polarizer is rotated an angle     from
2

the second polarizer. The intensity after passing through the first polarizer is I1 and the intensity
after passing through the second polarizer, I2 , is given by
I 2  I1 cos2  .
The intensity after the third polarizer, I3 , is given by


I 3  I 2 cos 2      I1 cos 2 
2


 cos  2    
2



(2)
Using the trigonometric identity, cos     cos cos   sin  sin  , gives
1




cos     cos cos   sin sin   sin  . Therefore, since cos  sin   sin 2  ,
2
2
2
2

I3 
I1 2
sin (2 )
4
(3)
Because the data acquisition begins where the transmitted intensity through Polarizer 3 is a
maximum, the angle () measured in the experiment is zero when the second polarizer is 45o
from the angle . Thus the angle  is related to the measured angle  by
(4)
  45o  
This equation is entered into the DataStudio calculator to compensate for measuring  instead of
measuring  directly.
Written by Ann Hanks
Polarization EX-9958
PASPORT
Page 4 of 7
SET UP
Figure 4: Equipment Separated to Show Components
1.
Mount the aperture disk on the aperture bracket holder.
2.
Mount the High Sensitivity Light Sensor on the Aperture Bracket and plug the sensor into
the PASPORT Interface. Select the “Sun” (0-10,000) setting on the side of the sensor.
3.
Rotate the aperture disk on the light sensor to the open circular aperture (see Fig.5).
Figure 5: Use the open circular aperture as shown.
4.
Mount the Rotary Motion Sensor on the polarizer
bracket. Connect the large pulley on the Rotary
Motion Sensor to the polarizer pulley with the plastic
belt (see Fig.6).
5.
Plug the Rotary Motion Sensor into the PASPORT
Interface.
Figure 6: Rotary Motion Sensor
Connected to Polarizer with Belt
Written by Ann Hanks
Polarization EX-9958
6.
PASPORT
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Place all the components on the Optics Track as shown in Fig.7.
Figure 7: Setup with Components in Position for Experiment
SOFTWARE SET UP
Start DataStudio and open the file called "Polarization_PASPORT.ds".
PROCEDURE FOR 2 POLARIZERS
In the first two procedure steps, the polarizers are aligned to allow the maximum amount of light
through.
1.
Since the laser light is already polarized, the first polarizer must be aligned with the
laser's axis of polarization. First remove the holder with the polarizer and Rotary Motion
Sensor from the track. Slide all the components on the track close together and dim the
room lights. Click Start and then rotate the polarizer that does not have the Rotary
Motion Sensor until the light intensity on the digits scale is at its maximum. Press Stop
and leave the polarizer in that position. From the Experiment menu select “Delete Last
Data Run”.
2.
To allow the maximum intensity of light through both polarizers, place the holder with
the polarizer and Rotary Motion Sensor back on the track, press Start, and then rotate the
polarizer that does have the Rotary Motion Sensor until the light intensity on the digits
scale is at its maximum and press Stop (see Fig. 8). From the Experiment menu select
“Delete Last Data Run”.
Written by Ann Hanks
Polarization EX-9958
PASPORT
Page 6 of 7
Figure 8: Rotate the Polarizer That Has the Rotary Motion Sensor
3.
Press Start and slowly rotate the polarizer which has the Rotary Motion Sensor through
360 degrees. Then press Stop. Keep this data.
ANALYSIS
1.
Click on the Fit button on the graph and select User-Defined Fit. Double-click the UserDefined Fit box on the graph and write an equation (Acos(x)^2) with constants you can
adjust to make the curve fit your data. Make sure to select the DEG box for degrees.
2.
Try a cos3() fit and then try a cos4() fit. Does either of these fit better than your
original fit? Does the equation that best fits your data match theory? If not, why not?
Written by Ann Hanks
Polarization EX-9958
PASPORT
Page 7 of 7
PROCEDURE FOR 3 POLARIZERS
NOTE: This section is optional if you do not have a third polarizer. Perhaps another lab group
may have one you can share.
1.
Now repeat the experiment with 3
polarizers. Place one polarizer on the track
and rotate it until the transmitted light is a
maximum.
2.
Then place a second polarizer on the track
and rotate it until the light transmitted
through both polarizers is a minimum.
3.
Then place a third polarizer on the track
between the first and second polarizers.
Rotate it until the light transmitted through
all three polarizers is a maximum (see Fig.9).
Figure 9: Setup with a Third Polarizer (#2)
between the Rotary Motion Sensor and the
Light Sensor
4.
Press Start and record the Intensity vs. angle for 360 degrees as you rotate the third
polarizer that has the Rotary Motion Sensor.
5.
Select your data from 2 polarizers and from 3 polarizers. What two things are different
for the Intensity vs. Angle graph for 3 polarizers compared to 2 polarizers?
6.
Click on the Fit button and select the User-Defined Fit. Double-click the User-Defined
Fit box on the graph and enter the equation that you had for two polarizers. Then change
the equation until it matches your data for the 3 polarizers.
QUESTIONS
1.
For 3 polarizers, what is the angle between the middle polarizer and the first polarizer to
get the maximum transmission through all 3 polarizers? Remember: In the experiment,
the angle of the middle polarizer automatically reads zero when you start taking data but
that doesn't mean the middle polarizer is aligned with the first polarizer.
2.
For 3 polarizers, what is the angle between the middle polarizer and the first polarizer to
get the minimum transmission through all 3 polarizers?
Written by Ann Hanks