Name: _________________________________ Lab Section: _________ Group Number: __________
Lab Partners: _______________________________________________ Grade: ____________
Physics 202
Lab 4
Ray Optics and Polarization
Pre-Lab
1)
In question 3 in the lab, what will you plot as y and x?
Write down how you will obtain the error bars in your y-values. If you will propagate error, write down
the specific error propagation equation here.
2)
Fill a glass with water. Look down through the water,
and then through the glass to your hand on the outside. Can you see it? Tip the glass towards you and
watch your hand disappear. Why? Do you know what physical phenomena this observation is related to
in this lab?
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3)
Draw a picture of a polarized and unpolarized E-field
(go ahead and just do it at one point in space using an arrow(s)). Polarized means that the E-field
oscillates perpendicularly at a fixed orientation relative to the direction of propagation. See the book (or
notes) for help.
4)
Predict an answer to question 8. For your prediction, a
picture or math will do. For the lab you hand in, you will need to do both.
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Name: _________________________________ Lab Section: _________ Group Number: __________
Lab Partners: _______________________________________________ Grade: ____________
Physics 202
Lab 4
Ray Optics and Polarization
Introduction
Light is the visible part of the electromagnetic spectrum, and like all electromagnetic (EM) waves, originates
from accelerating charge. A simple model of EM wave generation that goes quite far is an analogy to an
oscillating mass on a spring. The mass in this case is an electron or charged part of a molecule, and the
spring is the bond to the nucleus to which the charge is attached. Simple harmonic motion of a charge
generates a sinusoidal EM wave. If the wavelength is between 400 nm and 700 nm we observe it as light.
Figure 1 is a typical schematic used to represent a wave. Imagine you are looking at ripples on a pond (an
aerial view). This could be represented by Fig. 1. The lines denote the crests of the wave. The center between
two lines represents a valley, and you have to use your imagination to see every height in between a crest and
a valley. The distance between two crests or two valleys is a wavelength, . The wave in Fig. 1 is a special
kind of wave called a plane wave. We like simple pictures and so we will just leave the arrow to denote a
plane wave.
crest
ni
Incident angle
reflected angle
i   r
valley
nt
i
r
Normal
t
Refracted angle
ni sin i  nt sin t

Figure 1: Schmatic of a plane wave
Figure 2: Reflection and Refraction at a
dielectric interface.
Figure 2 is the ray-optics schematic for reflection and refraction at the interface of a dielectric (non2
conducting material). The line drawn perpendicular (or 90º) to the interface is called the normal. All angles
are calculated from the normal line. The law of reflection states “the angle of incidence equals the angle of
reflection.”
(1)
i   r
Snell’s Law which relates the incident ray to the refracted ray is:
ni sin i  nt sin t
(2)
where nt is the index of refraction of the material of transmission (the material the light is entering), and ni
the index of refraction of the incident material (the material from which the ray is coming) . The index is the
factor by which the speed of light, c, is slower in materials than in a vacuum, n  c v ( c  3x108 m s ). The
index of air is approximately 1.0. The index for vacuum is exactly 1.0. Note that the power of the sum of the
power transmitted and reflected is equal to the power incident.
If the incident ray of light is going from a material of larger index (slower) to one of smaller index (faster),
there is a critical angle for which all of the light is reflected back into the incident medium.
sin  c
nt
ni
(3)
This phenomenon is referred to as total internal reflection is the reason light can be guided inside the small
higher index core of glass optical fiber.
Finally, another important aspect of electromagnetic waves you will be exploring in the following
experiments is polarization. Figure 3 shows an example of a sinusoidal electric field. An oscillating magnetic
field always accompanies an oscillating electric field (you can’t have E without the M in an EM wave).
However, in Figure 3, the magnetic field has been omitted for clarity.
nucleus
k
m
Fbinding  kx
Electron, -q
Figure 3: Schematic of a polarized EM wave and the effect it has on
The arrows in Fig. 3 represent the strength of the electric field at a given point in space. As the traveling
wave hits the charge, the charge will move in the direction of the arrow. If the arrow is big, the charge is
displaced a lot. If the arrow is small, the charge is displaced a little (convention says arrow denotes the
direction a positive charge would move so technically the charge moves opposite the direction of the arrow).
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How quickly the charge responds to the incident wave is what is responsible for the index of refraction in a
material. This is how light can be slowed to 20 mi/hr. When the mass shakes up and down at a resonance
frequency, this corresponds to energy given up to the material in the form of heat (absorption).
Note how the E-field has a direction and the charge cares about it. For example, if you rotated the massspring system 90 degrees (coming out of the page at you), the charge wouldn’t move up and down since the
arrows don’t line up with the spring. The E-field would have no effect on the charge. Likewise, we could
make a device that burned up the part of the energy of the E-field in one direction so that we could polarize it
in the direction we wanted.
By passing light through a polarizer, a light beam with known electric field direction, or polarization state,
can be prepared. If a beam of polarized light is incident upon a polarization analyzer the transmitted
intensity obeys Malus’ Law:
I  I 0 cos 2 
(4)
where I0 is the maximum transmitted intensity, and  is the angle between the incident light’s polarization
direction and the axis of the analyzer. One useful special case is that the intensity drops ( I  (1 / 2) I 0 ) when
unpolarized light (E-field in every direction, not just one) passes through a polarizer.
The goal for today’s lab is to experimentally verify each formula. You will develop your method for proving
each formula and demonstrate the validity of these equations with graphs.
Part I: Reflection and Refraction
Mount the ray table and the light source on the optics bench as shown in Figure . Power the light source.
The light source should be oriented so that the multiple slits are facing the ray table. Adjust the slit mask on
the front of the light source so the light source projects one ray of light across the middle of the top surface
of the ray table. Locate the ray table so that its edge is roughly 2 cm from the light source. Adjust the light
source position such that the single ray of light emanating from the source passes straight along the diameter
of the table.
Figure 4: Apparatus for the study of reflection and refraction of light .
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Place the cylindrical lens on the ray table so that its straight edge lies along the diametrical line that joins the
two 90° marks, as in Figure 5.
Figure 5: Incident, reflected, and transmitted rays.
Hold the lens only at the edges. With the aid of the millimeter scale markings on the table, center the
cylindrical lens upon the line that joins the two 0° marks.
Fine tune the positioning of the lens on the table using the following procedure: Set the ray table for i
= 0°. Verify that t = 0°. If it does not, carefully center the lens to achieve the desired condition. Rotate the
ray table clockwise to i = 80°. Verify that r = 80°. If it does not, carefully rotate the lens to achieve the
desired condition. Rotate the ray table counter-clockwise to i = 80°. Verify that r = 80°. If it does not,
carefully rotate the lens to achieve the desired condition. Iterate these steps until all conditions
simultaneously hold true.
1. Explain why a lens of this particular shape is used to study the refraction of light on the ray table.
Why does the refracted ray not undergo additional refraction upon exiting the lens?
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2. To verify the law of reflection, plot r vs i. You should get a slope of 1.0. Be sure to include error
bars and an error in your slope. How well do you know your experimental setup (i.e. does your value
of slope  your error in slope include the value 1.0? Write down your results here as well as in your
spreadsheet.
3. Verify the law of refraction by making some kind of plot whose slope is the index of refraction of the
plastic. Assume the index of air is 1.0. Just include error bars in the y-dimension. Careful: You will
need to propagate the error of a trig function. When you insert an angle into a trig function, you can use
radians or degrees. In any other case (outside of a trig function) you need to use radians!
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Part II: Internal Reflection
Fine tune the lens position using the procedure found in Part I. Then rotate the ray table to establish an incident
angle of 0°, but with the curved surface of the lens facing the light source. In this orientation the incident ray is
in the acrylic side, instead of in the air side.
Rotate the lens slowly from 0° to 90° (either direction), and observe how the light ray interacts with the planar
interface.
4. What do you observe about the light ray as you rotate the lens? Does the behavior of the light ray
change?
5. Measure the critical angle given by equation (3). Use it to calculate the index of the glass and
compare to your answer in number 3. Write your results here. As always, include error. Propagation
will do in this case.
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Part III: Polarization
Mount the diode laser, polarizer, analyzer, and light sensor with aperture disk on the optics bench as shown in
Figure .
Figure 6: Apparatus for the analysis of polarized light.
A polarized beam of light is formed by passing the light from the diode laser, which we assume is unpolarized,
through the first polarizer. The polarization state of the light is studied by means of a second identical polarizer
referred to as a polarization analyzer. The polarization analyzer is manually rotated just like the first polarizer.
There is an angular measure along the outer edge of each polarizer. The light intensity transmitted through the
analyzer is measured using the light sensor. An aperture slit is used to shield against stray room light and to
keep the light level presented to the sensor within its measurement limit. Approximate location of the
components (as measured by the position indicators on each mount) of the apparatus is as follows:
ITEM
POSITION RELATIVE TO
LIGHT SOURCE (cm)
Polarizer
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Analyzer
Light Sensor
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Plug the light sensor into Analog Channel A on the Interface box. Set the gain switch on the light sensor to 1.
Rotate the aperture disk so that slit #6 is in front of the sensor. Plug in and turn on the diode laser. Power the
interface.
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6. Before using the polarization analyzer, check whether the diode laser is polarized. Describe how you do
so and briefly state your results.
7. Cross the polarizer and analyzer (this means orient them at 90º). You should get no light through. What
do you observe experimentally? What happens when they are oriented at the same angle?
8. Borrow a third analyzer from another group and place it in between two crossed polarizers. Rotate this
middle polarizer and observe what happens. Do you get light through? If so, for what orientation of the
polarizer do you get maximum signal. If not, why? Explain this in words and pictures and then
mathematically using equation 4. For full credit, give an intuitive answer using words and pictures in
addition to the math. Math is a crutch for weak physicists.
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Post-lab Questions:
1) What was the objective of this lab? Do you feel the objective was appropriately achieved? Why or why
not?
2) Name the two most significant sources of error in this experiment (Be specific – do NOT say, for
example, “human error” or “equipment limitations”). Are these errors likely to be random or systematic?
Explain.
3) Describe some ways that the error in this lab could be reduced, including the possible purchase of
additional equipment.
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4) What were the results of this experiment? Was there a physical law you were trying to verify, if so, state
that law. Were you trying to determine the value of some quantity or quantities? If so, what was (were) the
value(s)? Do the error(s) in the value(s) make sense? If not, please explain why.
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