Physic 214 Polarization of Light
Theory: The direction of the electric vector of an electromagnetic wave defines the
direction of polarization of the wave. Light that is unpolarized is light that has electric
vectors randomly distributed and pointing in all directions (but still in the plane
perpendicular to the direction of propagation of the light). Unpolarized light with an
intensity Io that is passed through a polarizing sheet will emerge with an intensity I =
(1/2) Io , and will be polarized along the direction of the polarizing sheet. If this
polarized light is incident upon another polarizing sheet that is at an angle  relative to
the polarized light, it will emerge with an intensity I ' = I cos2 .
Thus, for unpolarized light that passes through a polarizing sheet, the light will emerge
with an intensity
I
1
I0 .
2
(1)
And, polarized light that passes through a polarizing sheet with an angle  relative to
the polarized light, will emerge with an intensity
I   I cos 2  .
Malus’s Law (2)
Procedure and Calculations: A series of polarizers are set up on an optical bench.
White light, which is unpolarized, shines through the series of polarizers, and its
intensity is recorded using a light sensor. One of the polarizers is attached to a rotary
motion sensor, which records the polarization angle. The light intensity and the angle
on the rotating polarizer are recorded by data studio. We will use this device to study
polarization and equation (2).
Figure 1 The optical bench with the polarization apparatus in place.
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I). For the first experiment, we will study equation (2). White light will be shown
through a polarizer. Place this polarizer so its polarization angle is zero. The second
polarizer should be attached to the rotary motion sensor, and should also be set to a
polarization angle of zero. (Remove the third polarizer, if there is one on the optical
bench.) The gain on the light sensor should be set to 10. Turn on the Data Studio
computer box, and then turn on the computer.
1). Turn on the science workshop box first, and then start up the computer. Go to
Start, click on physics, then on Data Studio, then on Create Experiment. Select the
Light Sensor, and drag it to port A. Click on the Rotary Motion Sensor, and drag it to
ports 1 and 2. Double click on the Rotart motion sensor icon. Click on the General, and
change the frequency to 50 Hz. Click on the Rotary Motion Sensor tab and select 1440
in the Divisions/Rotation box. Click on Measurements, and select Position. Save these
settings.
Click and drag a graph to "Light Intensity." Click and drag the angular position to the
x axis and release to create a graph with "Light Intensity" on the y-axis, and "angular
position" on the x-axis. Now, you are ready to take data. The best data will be obtained
if the light source, polarizers, and light sensor are as close together as possible.
2). Be sure that each polarizer is set to an angle of zero. Click on Start (you are now
recording the light intensity and the polarization angle). Turn the polarizer that is
attached to the angular motion sensor slowly through 360o. Then, click on Stop (so you
stop recording data).
3). We will verify equation (2) by fitting the intensity to the function
Acos(x+B)cos(x+B)+C, where and x is the angle between the first and second polarizers,
and A, B, and C are constants. A represents the amplitude of the cosine squared
function, B is a phase angle correction because our data may not start with the cosine
of the angle x being exactly zero, and C represents a constant “background” value. To
do this, click on the "scale to fit" icon on the graph, located in the top left hand corner
of the graph. There are two fitting functions, one called "Curve Fit," and one called
"Fit." We will use the first to define the fitting function, and the second to fit the data
using this fitting function. First, click on "Fit" and select "User-Defined Fit." Then,
click on "Curve Fit." Select New, select User-Defined Fit, and make sure that this
appears in the two boxes in the upper left hand corner (the first box should not say "Fit
1"). Type in the fit given above, using the "scientific" tab to select the function "cos."
Click on Accept. You will need to select values for A, B, and C. Choose values that you
think are reasonable choices. Click on "Accept." Click on "Fit," and select "UserDefined Fit." You may have to click on "Light Intensity Run 1" to have the fit applied to
your data. Print out the graph and fit, along with your initial values of A, B, and C.
The fit may not be very good on this first try; that's OK. Now, go back and change the
values of A, B, and C until you have a good fit. Print this graph out including raw data,
the fit, and the values of A, B, and C. When you are done, you should have at least two
graphs each with different values of A, B, and C.
4). Discuss and compare the expected values of A, B, and C with those you determined
experimentally, and discuss the accuracy of equation (2).
5) What is the angle between the maxima and minima for this graph?
II). Now, we are ready for the second part of the experiment. Clear the data from the
graph, but leave the graph set up.
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1). Reset the angles on the first and second polarizers to zero. Place a third polarizer
between the second polarizer and the light sensor. Set the third polarizer to an angle of
90o.
2). Start to record data, and slowly turn the (second) polarizer that is attached to the
rotary motion sensor through an angle of 360 o. Click on Stop.
3). Click on "scale to fit." Print out a copy of the graphs. Record the angles at which
the intensity has maxima, and those at which the intensity has minima, and indicate
the positions of these on the graph. Compare the results with I step 5. Why are they
different?
4). Calculate the angles at which you expect the light intensity to have maxima and
minima. Compare your observations and predictions, and discuss your results.
Figure 2. Calcite Crystal placed over the word ‘Lab’
III. Birefringence in calcite. Study the behavior of a dot on a piece of white paper
transmitted by a calcite crystal using a polarizer. Draw diagrams of your observations
with and without the polarizer. If you rotate the crystal without the polarizer what
happens? If you rotate the polarizer what happens? Is there a polarization to the two
distinct images? What are they? Attempt to identify the o-ray and the e-ray.
IV. (Optional) Study the polarization of light reflected from the floor or table. What is
the orientation of the polarizer when the light is “cancelled”? What polarization is
reflected? For what range of angle do you observe cancellation? Try to measure them by
measuring the horizontal distance from reflection to you; then measure the vertical
distance above the floor that you are holding the polarizer. Use the tangent function for
p to determine a range for the index of refraction for the reflecting surface. Within this
range of indices of refraction, what do you think the index of refraction is most likely to
be?
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