Physics 220 General Physics II
Grist
Laboratory Exercise: Polarization
Object
In this experiment you will study the relationship between the intensity of a transmitted beam
of light through two polarizers and the angle θ between their two axes. You will also confirm
Malus’ Law of Polarization.
Introduction
A polarizer, or Polaroid, is a type of filter. It can be a plastic sheet or a thin film on a lens. The
Polaroid filter only allows light that is vibrating in a particular plane to pass through it. This
plane is called the ‘axis’ of the Polaroid. An electromagnetic wave, such as light, vibrates in all
planes perpendicular to the to the direction of its propagation. We call this unpolarized light.
When unpolarized light is incident on an ‘ideal’ polarizer, only half the light will be transmitted.
As no Polaroid is ideal, less than half is typically transmitted.
The polarized light is transmitted in one plane, parallel to the axis of the Polaroid. Now let’s
look at a two special cases when we have a second Polaroid, which is sometimes called an
analyzer:
1) Our second Polaroid is in line with our first and the second polarizer is rotated 90°, so that it’s
axis is perpendicular to the axis of the first Polaroid. Now we send some unpolarized light
through the first Polaroid, it becomes polarized and we lose half the intensity, because we lose
half the light, really more if it’s not ‘ideal’. Now that same polarized light passes through the
second Polaroid, except it doesn’t pass through because it is absorbed by the second Polaroid!
Why?
2) Our second Polaroid is in line with our first and the second polarizer is rotated some angle
less than 90° relative to the first Polaroid. That is, it’s axis is neither perpendicular nor parallel
to the axis of the first Polaroid. Now we send some unpolarized light through the first Polaroid,
it becomes polarized and we lose at least half the intensity, again because we lose at least half
the light. Now that same polarized light does pass through the second Polaroid, well at least
some of it does and its intensity is dependent on the angle between the axes of the two
polarizers. Why?
http://www.olemiss.edu/courses/phys319/Polarization_ex_1.pdf
Polarization 1
Physics 220 General Physics II
Grist
Now to answer the why. Remember that the electromagnetic wave is a set of vectors
perpendicular to it’s propagation. Let’s suppose that the first Polaroid has its axis aligned with
the Y axis. It will absorb the X components of the electromagnetic wave. The Y components are
the ones that pass through. If the second Polaroid is rotated 90°, so that it’s axis is
perpendicular to the axis of the first Polaroid (case 1), then it will absorb all of the Y components
and there will be nothing left. If the second polarizer is rotated some angle less than 90° relative
to the first Polaroid (case 2), then some amount will get through that depend on the angle
between the axes of the two Polaroids. If it is closer to being parallel, then more will get
through and if it is closer to perpendicular, well then less will get though all the way up to
nothing if they are 90° relative to each other.
Now we know that the electric field goes as
E  Eo cos 
and that the intensity of light goes as the square of the electric field, so the intensity of light
through the second polarizer is
I  I o cos 2 
This is Malus’ Law of polarization, which describes the relationship between the intensity of
transmitted light and the rotational angle of the polarizersangle .
Procedure
I. Physical Observation of the Polarizers
Hold a pair of Polaroids together and look through them at various light sources. Observe how
the intensity of the light changes as you rotate the Polaroids. The Polaroids have degree marks
on the outer edge. Using the marks, can you determine the orientation of the axes?
II. Intensity as a Function of Angle
PASCO
scientific
You have a set up that is similar to the one shown below.
The computer system will map the data as you take it on two graphs. One graph of relative
intensity vs. angular position, and the second one of relative intensity vs. cos2 θ.
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Physics 220 General Physics II
Grist
Start the data collection software with the polarizers at 0°. Very slowly rotate the polarizer
closest to the light sensor in a clock-wise direction. This is the polarizer with the belt connecting
it to the position sensor. Rotate it over a range of 360°, then click the stop button.
III. Analysis
The Pasco software creates two graphs for you, one graph of relative intensity vs. angular
position, and the second one of relative intensity vs. cos2 θ. The second graph is hidden behind
the first. Just drag the first graph top the side and click the second to bring it to the front. Click
the “scale-to-fit” button on both graphs before proceeding. Sketch both graphs on your data
sheet in the space provided.
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Physics 220 General Physics II
Grist
Data Sheet
Relative Intensity vs. Angular Position
Name_____________________________
Relative Intensity vs. Cos2 θ
Questions
1) If the transmitted light is at maximum intensity when the two polarizers are parallel, and
minimum intensity when the two polarizers are perpendicular, what is the relationship of the
intensity of transmitted light to the angle of the polarizers between 0 and 90 degrees?
2) What is the shape of the graph of the Light Intensity versus the Angular Position?
3) What is the shape of the graph of the Light Intensity versus the square of the cosine of the angle?
4) Theoretically, what percentage of incident plane polarized light would be transmitted through
three polarizers which each have their axes rotated 17 degrees from each other? Assume ideal
polarizers and assume that the first polarizer’s axis is 17 degrees from the axis of the second
polarizer.
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