Download Lab #10

Physics 144 – Chowdary
How Things Work
Spring 2006
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Lab #10: Polarization and Refraction of Light
Introduction
Light is all around us, as is matter. The interaction of light with matter can be quite complex and result in
tremendously interesting phenomena. We can understand many aspects of the interaction of light with matter by
considering the electromagnetic wave nature of light, how electromagnetic waves are produced, and the fact that
light interacts with matter mainly by the effect of the electric field of the EM wave on the electrons in matter.
In today’s lab, we’ll explore how light interacts with matter by studying polarization and refraction. In
polarization, the electric field part of the EM wave has a particular direction. This affects what directions the EM
wave can travel, and also influences the interaction of the EM wave with matter. In refraction, the speed of the EM
wave changes as it goes from one medium into another. This changes the direction the EM wave travels.
Equipment
In the first part of the lab, you’ll use a regular incandescent lamp with an attachment that collimates
(focuses) the light into a beam. You’ll also use polarizing filters; these filters block out light with a certain
polarization direction, but lets through light with the “correct” polarization direction. You’ll also be shining the
light through a tank filled with a water/creamer mixture (the dissolved creamer scatters/re-directs the light from
its original incident direction); you’ll look at the light scattered out the sides and top of the tank as well as reflected
off a glass plate on which the tank is sitting. You’ll look at a simulation of a charged particle undergoing harmonic
motion and see the pattern of electric fields radiating out from the charge to try to understand the behavior you’ll
observe.
In the second part of the lab, you’ll use a laser box to produce a single bright beam of incident light. You’ll aim this
incident beam at a semi-circular piece of plastic mounted on a protractor, and examine the angles of any reflected
and refracted/transmitted beams. You’ll also use a curved piece of plastic to see how beams can be focused to a
point.
Part I: Polarization
Theory
Waves can be broadly categorized as longitudinal or transverse. In a longitudinal wave, the displacement from
equilibrium is parallel to the direction of propagation of the wave. Examples of longitudinal waves are sound
waves and compression waves on a slinky. In a transverse wave, the displacement from equilibrium is
perpendicular to the propagation direction; examples include water waves and waves on strings. Light, which is
an electromagnetic wave, is transverse.
Consider light propagating parallel to the z-axis, i.e. out of the plane of this page. The associated electric and
magnetic fields are perpendicular to each other and the propagation direction of the light, i.e. they point parallel to plane
of the page. Thus, the electric field is parallel to the x-y plane but it need not have any particular orientation in the
x-y plane. If the electric fields along the light wave are randomly orientated in the x-y plane, the light is called
unpolarized. If, however, the electric field has a fixed orientation, the light is said to be linearly polarized. In this lab
you will investigate the polarization of scattered and reflected light using polarizing filters.
Unpolarized light sources are common but polarized light can be produced in various ways. You will investigate
the production of polarized light by scattering, reflection, and absorption. In particular you will use polarizing filters to
produce polarized light. This lab introduce polarizing filters and has you explore polarization by absorption,
scattering, and reflection. You’ll consider a model of absorption and re-radiation by charged particles to explain
the observations.
Polarization is important for exploring the transverse nature of electromagnetic waves and the interaction of light
with matter. Polarization has many technical applications such as polarizing sunglasses, non-destructive
evaluation techniques and liquid crystal displays such as flat panel monitors. While the electromagnetic and wave
nature of light, along with the idea of re-radiation, is discussed in other parts of class, this lab is your main chance
to explore the nature of the polarization of light.
Polarization by Absorption and Polarizing Filters
1) Turn on the lamp using the power strip. Pick up and examine the slide mounted polarizing filter (polarizer, or
filter). Look at the lamp through the polarizer (look along the beam), holding the polarizer vertically. Rotate
polarizer about an axis through its plane, continuing to look at the lamp through the polarizer. Rotate the filter
through 360o. Do you notice any dimming of light as you rotate the filter? You shouldn’t notice much dimming,
which is evidence that light from the lamp is essentially unpolarized. Write down your observations.
2) Now, also take a second slide mounted polarizer. Hold the first filter in some fixed orientation. Hold the second
filter in front of the first so that you are looking at the lamp through both filters. Rotate just the second filter. What
do you notice? Write down your observations.
3) Even though light from the lamp is unpolarized, passing through one filter just lets through that part of the
unpolarized light that is oriented parallel to the transmission axis of the first filter. The light that emerges from the
first filter is then polarized. The second filter only lets through that part of the light from the first filter that is
parallel to the transmission axis of the second filter. When the transmission axes of the two filters are parallel, all
the light that makes it through the first filter also makes it through the second filter. When the transmission axes of
the two filters are perpendicular, none of the light that makes it through the first filter passes through the second
filter. (Of course, this is for ideal polarizers; in real materials, some of the light can pass through a set of polarizers
with perpendicular transmission axes, and even when the transmission axes are parallel, not all the light can make
it through.)
Briefly explain in your own words how you know that the light from the lamp is unpolarized. Also describe what
happens to unpolarized light when it passes through one polarizing filter or two polarizing filters. Why are they
called filters?
Polarization by Scattering
4) Obtain a glass plate from the front of the room. Also, fill the little plastic tank at your lab station about ¾ full
with a mixture of water and creamer that you can obtain from the front. This cloudy mixture is used because if
light passes through it, some of the light will be scattered off to the side, while some of the light will be transmitted
straight through the cloudy water mixture.
5) Set up your apparatus as shown in Figure 1. Make sure that the
shiny reflective side of the glass plate faces up; please be careful
with the plate as it is made of glass. You can adjust the vertical
height of the lamp as needed to make sure that the light beam goes
through the tank.
6) With the lights dim, you should be able to see the transmitted
light coming out of the tank on the opposite side of the light source,
and the scattered light coming out of the sides and top of the tank.
(You may also see the reflected image in the glass plate; we’ll come
back to this in the next part). Take one of the slide mounted
polarizing filters, and look at the transmitted light, from an angle if
necessary. Make sure you are looking at the transmitted light;
remember that this light is coming out of the tank on the opposite
side from where the light enters. Rotate the filter and see what
happens to the intensity of the light. Is the transmitted light
polarized or unpolarized? If the transmitted light is polarized,
indicate the direction of its polarization by sketching the relative
orientation of your polarizing filter when the transmission axis is
parallel to the polarization direction of the light.
7) Now, look at the light scattered out the side of the tank. This light is perpendicular to the path of the light beam.
Is the light scattered from this side of the tank polarized or unpolarized? If the scattered light is polarized,
indicate the direction of its polarization with respect to your polarizing filter by sketching the relative orientation of
your polarizing filter when its transmission axis is parallel to the polarization direction of the light.
8) Finally, look at the light scattered out the top of the tank. This light is also perpendicular to the path of the light
beam. Answer the same question about any polarization of this light, and indicate the polarization direction.
9) We will apply the ideas of radiation and re-radiation to explain these results by first examining the electric field
lines produced by an accelerated charge. Electromagnetic waves are produced by accelerated charges, and by
looking at a simulation of an accelerated charge, we’ll be able to observe some features of the emitted
electromagnetic waves. You can access the simulation by going to the PHYS141 folder on the desktop, and then
going into the Phys144 folder and double-clicking on “Accelerated Charge Simulation”. Follow the notes on the
web-page; make sure you are in SHO mode and that you have set the speed to around V = 0.3. You should notice
that the disturbance in the field pattern propagates out from the charge, and that the electric field oscillations are
perpendicular to the propagation direction. What do you notice about the pattern of electric fields made by an
oscillating charge? Where is the disturbance smallest? Where is the disturbance biggest? Don’t close the
simulation just yet.
10) The idea of re-radiation involves this directional dependence of the electromagnetic waves created by an
accelerated charge. When light is incident on an atom or molecule, the charges in the atom or molecule (usually the
electrons) are placed in a region of oscillating electric and magnetic fields from the light. Since the electric field is so
much larger than the magnetic field, we can usually just consider the effects of the oscillating electric field, which
causes the electrons to also oscillate. These oscillating electrons then re-radiate, emitting radiation in a preferred
direction depending on their direction of oscillation. Consider the simulation again, and imagine a test electron
placed in the field to the right of the oscillating charge. That electron will also begin to oscillate, and it will emit
radiation preferentially in the plane perpendicular to its oscillation direction, with no radiation in the direction
parallel to its oscillation direction. Explain the polarization behavior of the transmitted and scattered light from
the tank in terms of this re-radiation model.
11) Determine whether the transmission axis of the polarizing filters is parallel to the filter’s long edge or its short
edge. Use the polarizer to determine the polarization of light from a computer screen (if any). Determine the
polarization of light from a calculator screen (if any). At the front of the room are some polarizing sunglasses;
determine the transmission axis of the sunglasses. (Sunglasses which are sold as polarizing sunglasses often are not
actually polarizing, so buyer beware!)
Polarization by Reflection
12) Consider again the set-up shown in Figure 1, where light passes through a tank filled with a scattering mixture
of water and creamer. In the previous part, you considered the polarization of light that was transmitted and light
that was scattered. Now, you will consider the polarization of reflected light. If you look at the glass plate, you will
see a reflected image of the tank. Look at the reflected image of the tank through your polarizing filter. Stand so
that the angle between your viewing direction and horizontal is approximately 30 o (tall people will need to stand
further away and short people will need to stand closer to the tank). Rotate your polarizing filter. What do you
notice about the reflected image? Write down your observations.
13) Now, standing in the same location as before, make sure that you can view both the scattered beam out the side
of the tank along with the reflected image of the tank in the glass plate. You know from your previous experience
that there is an orientation of the polarizing filter that blocks the scattered light. When you hold the filter in this
orientation, what do you notice about the reflected light? When you rotate the filter to allow transmission of the
scattered light, what do you notice about the reflected light? Write down your observations.
14) Explain this special polarization dependent phenomenon in terms of the re-radiation model. Consider that the
light being reflected from the surface is actually being re-radiated by atoms at the surface.
Part II: Refraction
Theory
When light interacts with matter it can be absorbed, reflected and/or transmitted (pass through). What will
happen depends both on the material and on the frequency of the light. For example, water is transparent for
visible light. Microwave radiation, on the other hand, is strongly absorbed by water (this is the principle behind
microwave ovens). Wood and paper, by contrast, absorb or reflect visible light, but allow radio waves to pass. In
this lab, you will investigate one of the effects of light interacting with matter. This lab deals with the refraction
(bending) of light when it passes from one material into another. This principle forms the basis for much of what is
referred to as Classical Optics, a field with many applications in all the fields of science and engineering, as well as
medicine.
We will explore the ideas of refraction in class, but your main experience with it will be in this lab. In this lab you
will explore and verify a quantitative relationship that describes the path of light in different media. You’ll also
learn how the ideas of refraction connect to fiber optics and bending light along a curving path. Finally, you’ll see
how refraction causes a lens to bend and focus light. You will return to the idea of using lenses to bend light and
form images as well as constructing simple optical instruments such as telescopes and microscopes later in the
semester.
When light travels through the vacuum of space, it propagates at a speed c = 3.0 x 108 m/s relative to any observer.
On the other hand, light slows down when it passes through matter. The speed at which light passes through a
material is characterized by n, the index of refraction of the material, defined as the ratio of the speed of light c in
vacuum to the propagation speed v in the material (the medium)
speed of light in vacuum
n = speed of light in medium =
The index of refraction depends critically on the properties of the
material (chemical composition, density, temperature, pressure), as
well as the wavelength of the light passing through. Air has an index
of refraction that is almost exactly one, i.e., light travels almost as fast in
air as in a vacuum. For everything else, n is greater than 1, since light
going from vacuum to another medium can only slow down, and not
speed up.
c
.
v
(1)
1
1'
n1
n2
2
When a beam of light hits the interface between two different materials,
part of the light is reflected and part is transmitted into the second
medium. Because of the difference in propagation speeds, the
transmitted light bends with respect to the incident beam. This process
is shown in Figure 2.
Figure 2: An incident light beam could
both reflect and transmit/refract when
going from one medium to another.
Note: all the angles must be measured from the normal,
i.e., from a line that is perpendicular to the interface.
Simple (but slightly tedious) geometrical arguments can show that the angle  1 ' of the reflected beam is the same
as the incident angle  1 , known as the Law of Reflection. The transmitted beam is bent, relative to the incident
beam. The relation describing this bending is referred to as Snell's Law, or the Law of Refraction:
n1 sin 1  n2 sin  2
(2)
where  1 and  2 are the propagation angles (relative to a line perpendicular to the interface) for the light in
media with indices of refraction n 1 and n 2 , respectively. It is important to emphasize again that the angles here
are measured with respect to the normal to the interface.
Refraction (Low Index into High Index)
The apparatus for this (and the next) part of the lab is a
simple table that consists of a laser and a small rotating platform
with a protractor. You will also use a semicircular plastic container.
See Figure 3.
semicircular
container
refracted
beam
The laser is aimed such that the beam always points directly toward
the center of the semi circle, regardless of its orientation. The laser
beam may be bent at the flat side of the semicircle due to refraction.
However, the beam is undeflected at the curved side, since the angle
of incidence is always 0 at this interface. Make sure you
understand this point -- it is key geometrical feature in this
experiment.
15) Use the hemispherical piece of solid plastic. Orient the flat side
of the piece of plastic along the 90 - 270 line. Make sure that the
laser is aimed directly at the center of the semicircle. By rotating the
stage, adjust the angle of incidence to be 0. Measure the angle of
refraction (note that the refracted beam will likely be a little bit
spread out). Is this result consistent with Snell's Law?
16)
Repeat step 15 with angles of
incidence of 20, 40, 60, and 80. For
each case, measure the angle of
incidence, measure the angle of
refraction. Be careful: what are you
measuring these angles with respect to?
Fill out the information in the table. (If
you look carefully, you may also see the
reflected beam (hint: look on the side of
the laser facing the flat side of the
container. Remember that the reflected
beam is on the same side of the interface
as the incident beam.))
medium:
air
laser
Figure 3: Refraction Set-up
angle of incidence
 air
0o
20o
40o
60o
80o
rotating platform
with protractor
incident
beam
medium:
plastic
angle of refraction
/transmission  plastic
17) For each case use these angles and Snell's law to determine the index of refraction for the plastic. You should
obtain 4 values of n plastic (why don’t you get 5 values)? How should you combine these 4 values to come up with
your best estimate for the index of refraction of plastic, n plastic ? Write down your best estimate for n plastic .
Refraction (High Index into Low Index)
In the previous part, you looked at
refraction when the incident beam was in medium
with lower index of refraction than the refracted
beam. You should have seen in this case that the
angle of refraction was always less than the angle
of incidence. This result should make sense to you
considering Snell’s Law. What happens when the
beam goes from a region of higher index of
refraction into a region of lower index? An
interesting result can occur that has tremendous
practical applications (specifically, the entire fiber
optics industry). In this section you will explore
this result for yourself.
18) Using your experimental result for the index
of refraction of plastic, use Snell’s law to predict
the angle of refraction for a light beam that goes
from water into air for the following angles of
incidence: 10o, 20, and 30. Fill in your predicted
values in the table.
 plastic
 air
 air
(predicted)
(measured)
comments
10o
20o
30o
60o
70o
80o
19) Now, try to calculate the angle of refraction for angles of incidence 60, 70o, and 80. You will run into some
difficulties. What did you notice?
20) Let’s explore the physical results of your predictions from the previous part.
Place the plastic hemisphere back on the rotating stage. Rotate the stage such that
the laser beam enters the semicircle from the curved side and exits out the flat
side. Note that this is the opposite of the previous part of the lab; see Figure 4.
Orient the flat side of the container along the 90 - 270 line. We are still interested
in what happens to the beam when it hits the flat interface of the semicircle. You
should see that at the flat interface of the semicircle, the incident beam is in plastic,
while the refracted beam (on the other side of the interface) would be in air.
Rotate the stage to get angles of incidence of 10, 20, and 30, with the beam
incident from the plastic side. For each case, measure the angle of refraction for
the beam leaving the hemispherical cell and write down your measured values in
the table above. Compare the experimental results with that predicted from
Snell's Law. Be a little careful here; remember that the refracted beam should be on
the opposite side of the interface from the incident beam. There will likely be other
beams here since there will also be reflections from the interface.
refracted
beam?
incident
beam
laser
Figure 4: Refraction.
21) Now, explore what happens when the angle of incidence is 60, 70o, and 80. What happens to the refracted
beam? Clearly something is happening differently at lower angles than at higher angles. Go back to a low incident
angle, then slowly increase the incident angle; observe the refracted beam. At some critical angle of the incident
beam, something interesting happens to the refracted beam. Describe what you observe, and write down the value
for this critical angle of incidence.
22) Based on what you have observed, give a definition (in your own words) of total internal reflection. What is the
angle of the refracted beam just at the point at where you first observe total internal reflection? Use Snell's Law to
determine a formula for the critical angle of incidence c for total internal reflection as a function of the indices of
refraction of the two media.
23) Fiber optics depend critically on the principle of total internal reflection. At the front table are some fiber optics
demos for you to examine. Play with these demos for a few minutes, and ask whatever questions you need to be
sure that you understand the principle behind fiber optics.
Parallel vs. Non-Parallel Interfaces
The rotating protractor stage can be removed from the laser table assembly; do so and place the clear
plastic surface on the laser table assembly (this gives you a smooth surface to draw on at the right height for the
laser).
24) Flip over to the back of this page. You’ll see an outline of where to place the rectangular piece of plastic. You’ll
also see lines indicating how to orient the incident laser beam. Orient the paper, prism and laser beam as indicated,
and carefully draw (use a ruler!) the path of the beam leaving the prism. You should be able just to slide the plastic
surface over to orient with the next laser beam. Repeat until you have traced all four exiting beams.
25) Repeat with the second orientation of the rectangular prism.
26) What do you conclude about the incident and exiting beams when the interfaces are parallel, as they are with
the rectangular prism?
27) A lens takes advantage of the fact that light is deflected when it passes through a material with non-parallel
interfaces. A lens can be thought of as many prisms with all of the “bent” exit beams going through a common
point called the focal point. As in steps 24) and 25) above, orient the lens shaped piece of plastic and carefully trace
the exit beams. Do all of the exit beams pass through the same point? We would call this point where parallel
incoming beams converge on the other side of the lens the focal point. What would happen to the focal point if the
lens were more curved? What would happen to the focal point if the lens were flatter? You’ll see more about
lenses soon.