Download Phy 142L Spr 2016 Lab 5

D U K E
P H Y S I C S
Polarization of Light
L
ight is a transverse electromagnetic wave; that is, the changing electric and magnetic fields that
constitute light are always perpendicular to the direction of propagation. More specifically,
the direction a
 
light wave is traveling at a given point in space is given by the cross product E × B at that point. The
electric field can point in any direction perpendicular to the propagation
direction and the magnetic field

must then be perpendicular to both of them. The direction of E for a particular light ray is called the
polarization of the light. Because the fields are oscillating from positive to negative along the polarization
€
direction, we do not distinguish between polarization in the +eˆ and −eˆ directions. That is, when we say a
light wave is “polarized at 45˚,” we mean that if we are looking along the direction of propagation, the
€
electric field points half the time in the 45˚ direction and half the time in the 225˚ direction.
The figure at right shows an unpolarized light€
beam (containing rays with all different
polarizations) coming from behind the page and
passing through two polarizers. After passing
through the first one, the whole beam is polarized
at 0˚. After passing through the second, which is
oriented at an angle θ with respect to the first, the
beam emerges polarized in the θ direction with its
intensity reduced by a factor of cos2 θ .
€
The red €segments in the figure indicate the
direction and strength€of the electric field. Nothing
€ and forth in space. The
is actually moving back
figure is just supposed to illustrate that the field at
each single point in space is a vector quantity.
In this lab you will measure the intensity of
polarized light (generated by a laser) after it passes
through a polarizer, as a function of the angle at
which the polarizer is set. Then you will measure what happens when the polarizer is set to let no light pass
and a second polarizer is inserted between it and the laser.
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D U K E
P H Y S I C S
P O L A R I Z A T I O N
Experiments
I. Malus’ Law
Your lab station is equipped with a laser and three polarizers. Each polarizer allows the passage
of all light that is polarized in the direction defined by the 0 and 180˚ marks on the polarizer.
Light that is polarized in the 90˚ (or 270˚) direction, however, is absorbed by the Polaroid
material.
When performing your experiments, try to ensure
that your laser is not aimed directly at another
group, as stray laser light can damage the eye.
Your experiment will use a light sensor connected
to the Logger Pro interface. Be aware that the
sensor is affected by ambient light. You should
note what it reads when you are not sending any
light into it from the laser or incandescent source.
Suppose the light from the source passes through a
polarizer set at an angle φ (measured with respect to
a reference direction we choose to call “0”). The electric field of the light passed by the
polarizer is then oscillating in a plane at an angle φ. Now suppose the light passes through a
second polarizer, this one set at an angle θ with respect to the 0 direction. Our light sensor
measures the intensity of the transmitted beam, which we expect to be described by Malus’ Law:
Let’s see if this is right.
I = A E2 = Io cos 2(θ-φ) .
Part A. Effect of a polarizer on the intensity of a plane polarized beam
Set up the laser and two polarizers, aligning the beam so that it enters the center of the sensor. Set the
detector sensitivity to 150,000 Lux using the switch on the side of the small plastic sensor box. [A
Lux is the SI unit of illuminance, a measure of light intensity, and is often used to gauge the
“brightness” or “darkness” of an environment. A moonless clear night sky yields approximately
0.001 Lux; a full moon at night yields approximately 0.25 to 1 Lux. A normal room might be
illuminated from 80 to 200 Lux, and a brightly lit office might be 400 Lux.]
Open the Polarization.cmbl file. With both polarizers set to 0 degrees, click the green “collect” button
to acquire one second of intensity data, then record the observed value. Repeat this for at least 18
settings of the second polarizer between 0 and 360 degrees.
Use Logger Pro to fit your data using an expression of the form of Malus’ Law. You will have to
think about appropriate values for the amplitude and period of the fitting function.
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D U K E
P H Y S I C S
P O L A R I Z A T I O N
Part B. Effect of a third polarizer
What will happen if polarized light (having passed through the first polarizer) passes through a
sequence of two more linear polarizers? How much of the intensity will be transmitted? The answer
depends on the angular settings of the polarizers. Here we will explore one possible arrangement of
settings. (You are welcome to experiment with others.)
Set one polarizer at 0˚ and a second at 90˚ so that the minimum intensity of laser light is transmitted
through the pair. Now insert the third polarizer between the two and set at 45˚. [Take a moment to
appreciate the magic trick you just performed!] Measure the intensity of light transmitted as a
function of the angle of the middle polarizer. How does the transmitted intensity vary?
Write an explanation of the observed effects in terms of what you learned from Part A.
II. Polarization of reflected light
We will now have a look at how the polarization of light can affect the intensity of reflected light
from the surface of a piece of plastic. You will use a laser and polarizer to create a polarized
beam that strikes the surface of a plastic ruler. You will then adjust the position of your sensor to
detect the intensity of the reflected beam. The idea is to see how the reflected intensity depends
on the angle of incidence of the beam on the ruler.
(a) With the polarizer set so that the beam is polarized horizontally (i.e., such that the electric
field at the spot on the ruler lies in the plane of the ruler), measure the reflected intensity for at
least 10 angles of incidence between 30˚ and 80˚. Plot the data.
(b) Now rotate the polarizer 90˚ so that the electric field at the spot on the ruler lies in the
vertical plane containing both the incident and reflected beams. Repeat the same set of
measurements you made for the horizontal polarization case. Plot this data.
Note that the laser light itself is partially polarized in a direction that you don’t know before it
passes through the polarizer, so you cannot compare intensities from the two cases directly.
You can, however, compare the ways in which reflected intensity depends on the angle of
incidence. Discuss your results qualitatively.
How does the effect you observed help explain why polarized sunglasses cut down substantially
on glare?
Your report should include:
§ Part I.A:
o An organized data table
o A graph of intensity vs. relative angle, including the data and the Malus’ Law fit
o A discussion of the fit between your data and Malus’ Law
§ Part I.B:
o An organized data table and a graph of intensity vs. angle of the inserted polarizer
o An explanation of the salient features of the graph
§ Part II:
o An organized data table for each polarizer setting.
o A qualitative description of the observed effects and discussion of their relevance for
understanding how polarized sunglasses work.
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