Investigation Of Electromagnetic Phenomena Through The Use Of
Microwave Frequency Radiation
Ryan Berg
Charlie Watson
April 12, 2010
Abstract
use of the equipment included in the PASCO Microwave Optics System (alongside other equipment
This series of experiments is meant as an investi- that was used to replace specific PASCO compogation of several properties of electromagnetic wave nents, specified in the apparatus section), a variety
propagation, through the observation of phenomena of straightforward optical experiments can be perthat are specific to waves. The wavelength of visible formed, with the results can be easily interpreted,
light is very small, and to be able to see wave ef- due to the relatively large size of the microwave wavefects easily, most objects that interact with the wave length, as compared to that of visible light.
need to be on the order of the wavelength of the wave
We begin with an investigation of simply measur(e.g. polarizer slits of size comparable to the waveing the wavelength emitted by the microwave translength of visible light are not visible to the naked eye).
mitter. When two electromagnetic waves overlap in
Through the use of microwaves, with a wavelength
space, they interfere with one another. When the
of a magnitude measurable with a simple ruler, opspacing between an emitter and receiver is a multitical experiments under consideration can be made
ple of the wavelength λ2 , the waves that are reflected
much larger scale, and wave properties can be obfrom the receiver actually overlap with the incoming
served with much larger apparatus. The phenomena
waves, producing a standing wave pattern. This exunder consideration were polarization effects, and the
periment then investigates this property, by moving
famous double slit experiment.
the microwave emitter in such a way that we may detect the nodes of the waves, thus gaining knowledge
of the maximum amplitudes of the propagated waves,
1 Introduction
allowing us to calculate the wavelength.
The receiver picks up a signal by having the incoming microwaves induce oscillations in a diode within
the cone of the receiver; if the microwaves are aligned
along the axis of the diode to produce a maximum
signal (the incoming waves are polarized such that
the induced current in the receiver’s circuit it s maximum), then at the previously mentioned wavelengths,
we will have set up a standing wave pattern. This
simple experiment is meant to familiarize us with
the equipment, and prepare us for more sophisticated
experiments. Next, we investigate the phenomenon
The small scale of traditional optics experiments
(that is, use of electromagnetic radiation from the
ultraviolet to the infrared wavelength range) can obscure the interaction of electromagnetic waves with
macroscopic objects, as components that deal with
effects such as interference need to be on the same
scale as the wavelength of electromagnetic waves to
observe more exotic effects. Through the use of microwave frequency waves, our experiments become
much larger scaled, and the experimental components
are easily constructed and manipulated. Through the
1
of polarization. The microwave emitter emits radiation that is linearly polarized; that is, the electromagnetic waves (namely the electric field) remains
aligned in a plane as it propagates through space.
As the transmitter emits polarized microwaves, the
detector can only register wave components that are
polarized along a preferred axis. Thus, when either
the transmitter or receiver is rotated, the magnitude
of the electric field detected will vary. Here, we will
also investigate how a polarizer, placed between the
receiver and transmitter, can affect the magnitude of
the electric field that is detected.
Next, we move onto double slit interference. When
an electromagnetic wave passes through an aperture
with two slits, the resulting interference pattern produces a series of maxima and minima in intensity of
the electric field. This simple experiment, when using clean microwaves (electromagnetic radiation of a
microwave frequency and wavelength), as opposed to
dirty (radiation that includes a variety of frequencies)
microwaves, is a classic example of the wave properties of electromagnetic radiation (or waves in general
for that matter).
In this report, we organize each section into its own
miniature form of a larger lab. Each section begins
with the necessary theory for the experiment, then
description of the experiment itself, then data analysis, and finally results for the section. This is done for
three sections; first, we measured the wavelength and
frequency of the microwave radiation. Second, we investigated the effects of polarizers, and thus this is
the second section of the report. Lastly, we investigate double slit interference, and this is the last of
the three main sections. Finally, at the end of the
paper, there is a discussion of the results.
Figure 1: Transmitter and Receiver Aligned, reproduced from Ref.[1]
detect microwaves that are polarized along the same
axis, the two cones must share a common axis of polarization, else there will be no microwaves detected.
This is done by adjusting the Meter Multiplier on the
receiver, or the Repeller on the transmitter. As we
move the transmitter along a track (making sure to
keep the transmitter in line with the receiver), the
reading on the transmitter changes.
The effective range of the microwave emitter is not
very large. A distance of over half a metre yields very
little variation in the meter readings, and it became
difficult to determine where nodes are placed. In order to yield better results, the separation distance
was always within a range that produced a sizeable
reading on the microwave receiver.
The cones attached to the transmitter and receiver
are not perfect collectors of microwaves. If the distance between the two cones is not a multiple of λ/2,
the transmitted waves reflect back and forth between
the two cones, causing destructive interference, and
a general lack of maxima. This does not set up a
2 Procedure I: Measurement of standing wave pattern, and we would not be able to
find nodes. As the cones approach these separation
Microwave Wavelength
distances of λ/2, the reflected waves end up constructively interfering and overlapping with one another,
2.1 Theory
and the meter reads a maximum. Thus, lining up the
We began by setting up the experiment such that transmitter and receiver in a line as in Figure 1, we
the horns are as close as possible to get a maximum can slide the receiver along this axis, and find where
reading on the receiver. Since the radiation emitted the readings are maximums.
To calculate our wavelengths, we used the relation
from the receiver is polarized, the receiver can only
2
where ν is the frequency of the radiation (measured
8
nλ
∆d =
.
(1) in Hz) and c = 3 × 10 m/s. We can use Equation (3)
2
to calculate the frequency of the microwave radiation.
Here, n is the number of maxima passed in separating These results are tabulated in Table 2.
the cones , ∆d the separation distance between the
λ (m)
ν (GHz)
cones, and λ the wavelength of the microwave radia0.029
±
0.002
10.45
± 0.71
tion. Rearranging this to solve for our wavelength λ,
0.029
±
0.001
10.38
± 0.36
we have
Table 2: Wavelength λ (m) and Frequency ν (Hz)
2∆d
.
(2)
n
To use this equation, we measured the separation
distance between the cones, after passing a number of
maxima. This is done to reduce error, as doing it over
one maximum was likely to introduce unreasonable
error, and an average smoothed this out.
λ=
2.4
Discussion
The listed value for the frequency of the microwave
frequency for the PASCO Optics Kit is ν = 10.525 ×
109 Hz. Our measured values then line up adequately
within error of the expected outcome, however, the
error is somewhat large compared to the measured
values. This may be due to the fact that the equip2.2 Apparatus
ment is not particularly sensitive in some ways, and
In this experiment, the basic PASCO Microwave that measuring accurately the wavelength with simOptics Kit was used. However, the receiver was ply a ruler is difficult due to the nature of the emitter
damaged, so we used the replacement INSERT RE- and receiver cones. The ambiguity in where the most
PLACEMENT HERE as a receiver instead. The two effective collecting points causes difficulty in measurewere then mounted on the simple included track for ment. In the end, however, we have verified that the
the transmitter and receiver, as seen in Figure 1.
wavelength of the microwave radiation emitted is in
fact approximately 2.85 cm, as claimed in the PASCO
Lab Manual.
2.3 Data Collection
To use the equations to find the wavelength of the microwave radiation, we needed the separation distance
between the cones. We measured the separation distance between the cones, and used Equation (2) to
calculate the wavelength of the microwave radiation.
These results are tabulated in Table 1.
3
3.1
Procedure II: Polarization
Theory
As with the last experiment, we adjust the Meter Multiplier on the receiver, or the Repeller on the
n
∆d (m)
λ (m)
transmitter in order to get a good spread in reading on the transmitter dial. To simplify readings, we
5 0.145 ± 0.005 0.029 ± 0.002
want a nearly full-scale deflection of the transmitter
8 0.215 ± 0.005 0.029 ± 0.001
meter, to more easily detect fluctations in intensity
Table 1: Measured Separation Distance ∆d (m) and of radiation. It should be noted that although the
amount of deflection was optimized, we were unable
Calculated Wavelength λ (m)
to get a full-scale deflection, and were only able to get
We can use this data to calculate simply the fre- approximately half-scale. This may introduce some
quency of the emitted radiation, through the formula extra error in what is calculated. The apparatus was
set up as is seen in Figure 1, similar to the setup in
c = λ ν,
(3) Procedure I.
3
The microwave radiation induces a current in a polarization axis, at intervals of 10◦ . At each interval,
diode in the receiver, and this current is what the re- we record the meter reading on the receiver. The
ceiver picks up and displays. However, since the elec- results of this are tabulated in Table 3.
tric field that propagates only oscillates in a plane,
only the component of the electric field alligned with
Angle of
Meter
Angle of
Meter
the diode contributes to this induced current. Figure
Receiver Reading (mA) Receiver Reading (mA)
2 shows how this is seen in practice. When a polarizer
0◦
0.50
100◦
0.04
is inserted between the transmitter and the emitter,
◦
◦
10
0.48
110
0.12
the polarizer essentially acts as a new source of radi◦
◦
20
0.44
120
0.16
ation, simply with a reduced intensity and with ra◦
◦
30
0.43
130
0.26
diation polarized along the direction of the slit. This
◦
◦
40
0.39
140
0.30
intensity drop should fall off like
50◦
0.32
150◦
0.35
60◦
0.20
160◦
0.44
M eterReading = M0 cos θ,
(4)
70◦
0.10
170◦
0.48
80◦
0.06
180◦
0.50
where M0 is the reading of the receiver when the
90◦
0.00
receiver and emitter are aligned, and θ is the angle
that either the emitter is rotated by or the polarizer
Table 3: Amperage Detected At Various
is rotated by with respect to the vertical polarization.
Polarization Angles
To see the effects of this polarization and how we
Next, to observe the effect from a different percan detect it in practice, we can simply rotate either
the transmitter or the receiver. As we rotate either of spective, we can introduce a polarizer between the
the two away from the common axis of polarization, transmitter and the detector, while the transmitter
the meter on the receiver should detect less and less and receiver are aligned as such to receive a maxmicrowave radiation (in the form of less induced cur- imum signal. In this fashion, even though if there
rent). To enable this, we have a screw at the back of were nothing between the transmitter and the detecthe receiver, and allow it to rotate at even intervals, tor we would read a maximum, the introduction of a
and record the meter reading as the receiver rotates. polarizer changes what intensity we detect.
The change we detect is related to the angle that
the slits make with the horizontal. As the emitter ra3.2 Apparatus
diates horizontally polarized microwaves, slits aligned
In this experiment, the basic PASCO Microwave horizontally don’t impede the wave motion at all.
Optics Kit was used, as was with the previous sec- However, as the slits are tilted up from a horizontion. Again, however, the receiver was damaged, so tal position, the meter reads less and less current.
we used the replacement INSERT REPLACEMENT Cataloging the meter readings at several angles. We
HERE as a receiver instead. The two were then collect this data in Table 4.
mounted on the simple included track for the transAngle of
Meter
mitter and receiver as was done in Procedure I. We
Polarizer Reading (mA)
also used a simple stand with a clamp in order to
0◦
5.2
suspend the receiver off of the table, and so that we
22.5◦
4.8
could rotate it to observe our polarization effects.
45◦
4.2
67.5◦
2.2
3.3 Data Collection
90◦
0
Table 4: Meter Reading For Various Polarizer
Angles
First, we set up the apparatus across one another,
and let the receiver rotate away from the common
4
Here, M0 is the magnitude of the meter reading
when the polarization angle is 0◦ , and θ is the angle at which the receiver is rotated away from the
axis with respect to the transmitter. If we plot the
above function and the meter readings we got from
the receiver on the same plot, we obtain Figure 3.
Figure 2:
Ref.[2]
Polarization Angles, reproduced from
To conclude the procedure for investigating polarization, we can investigate one of the most interesting
effects that polarizers have. We begin by having the
transmitter completely unaligned with the detector
(such that they are 90◦ to one another, so that the Figure 3: Relationship Between Equation and Meter
receiver detects no microwave radiation). We then Readings, reproduced from Ref.[2]
place a polarizer in between the two cones, and tabulate the effect in Table 5.
Angle of
Slits
Horizontal
Vertical
45◦
3.4
Meter
Reading (mA)
0
0
4.4
Discussion
This equation seems to describe the general scheme of
what we observed, however the error in taking the receiver readings makes things unclear. Several factors
in the difficulty of measuring the intensity proved difficult to overcome. The rotation of the receiver made
Table 5: Meter Reading Upon Insertion of Polarizer
the distance from the receiver change slightly, and the
Thus, the insertion of a polarizer at an angle not meter readings were very sensitive to cone separation
aligned along either the axis of the emitter or the distance and orientation.
receiver, we manage to detect microwave radiation,
even though without the polarizer we didn’t detect
Procedure III: Double Slit
any. The polarizer changes the polarization of the mi- 4
crowaves that are emitted, and are thus able to have
Interference
a component of the electric field partially along the
axis of the transmitter, which allows some microwave 4.1 Theory
radiation to be detected, where this was previously
When setting up the emitter and the receiver, the
not observable. If the receiver meter reading were
directly proportional to the electric field component microwaves can only interfere with one another in
along its axis, the meter would read the relationhsip the plane along which they are aligned. That is, if
we set up a standing wave pattern, we only have a
M eterReading = M0 cos θ.
(5) constructive interference pattern, reinforcing maxima
5
4.3
and minima. However, when we introduce a diffraction grating in between the transmitter and the receiver (in our case, this is a metal sheet with two
wide slits cut vertically in it) the waves, upon travelling through the two slits, interfere in a more complicated pattern. The nodes where we detect maximum
intensity spread out over a constant radius away from
the center of the double slit polarizer, and one way
they can be detected is by sliding the detector around
an angle at a constant radius, as seen in Figure 4.
Data Collection
From here, we investigate the purely wave property
of interference, in the form of the double slit experiment. In between the transmitter and receiver, we
set up a piece of metal with two slits in it (of width
2.20 cm), with a distance 7.25 cm between the centers
of the two slits. This mimics the setup of Figure 5.
Figure 5: The Double Slit Setup, reproduced from
Ref.[3]
To detect points of maximum intensity, we simply
scan the receiver around the double slit diffraction
grating, and look for points where we obtain maximum readings on the receiver. We catalog this action
in Table 6.
Figure 4: Scanning The Receiver To Detect Maximum Intensities, reproduced from Ref.[3]
Angle
4.2
Apparatus
0◦
5◦
10◦
15◦
17.5◦
20◦
22.5◦
25◦
27.5◦
30◦
32.5◦
35◦
37.5◦
For the final experiment, the basic PASCO Microwave Optics Kit was used once again, as before. Again, however, the receiver was damaged, so
we again used the replacement INSERT REPLACEMENT HERE as a receiver instead. The two were
then mounted on the included miniature optics table, with a disk with angles written on it, which was
part of the PASCO Microwave Optics Kit. This disk
attaches to the tracks used earlier, and allows the
tracks to be rotated through an angle, while keeping
the receiver a constant distance from the diffraction
grating.
6
Meter
Reading (mA)
0.47
0.45
0.04
0.08
0.43
0.45
0.46
0.44
0.45
0.415
0.18
0.1
0.27
Angle
40◦
42.5◦
45◦
47.5◦
50◦
52.5◦
55◦
60◦
65◦
70◦
75◦
80◦
85◦
Meter
Reading(mA)
0.40
0.45
0.46
0.45
0.44
0.40
0.09
0.17
0.32
0.14
0.03
0.03
0.03
Table 6: Meter Reading For Various Angles of the
Receiver
We can calculate where we expect our maxima to
appear, by using the diffraction grating formula (see
Ref.[4]),
d sin θ = nλ.
(6)
Here, d is the spacing between the slits (here,
d=7.25 cm), θ is the angle at which we expect a maximum intensity, λ is the wavelength of the microwave
radiation (here we take λ=2.85 cm), and n counts
the peak number (ie. the numbering of the maxima,
counting away from the centre line). Isolating the
above equation for the angle θ, and we obtain the
equation
nλ
(7)
θ = arcsin
d
Figure 6: Plot of Obtained Data For Double Slit
Diffraction, see Ref.[3]
To find the angle at which we have a maximum
would be difficult, given the inaccurate spread of
data. The apparatus is not particularly accurate with
its meter readings, so it was difficult to obtain accuHere, λ and d are fixed; this leaves n to jump valrate data. Thus, to obtain an approximation of the
ues, from the set n = 1, 2, 3, .... However, for n greater
maximum values, I’ll take the average of the angles
than a certain value, we’ll have the term nλ
d lying that gave a very high meter reading between drops,
outside the domain of arcsin(x). This leaves a finite
and consider the average to be the angle of maximum
number of maxima, and these maxima correspond to
intensity. Doing this, we find that
values of n which keep the factor nλ
d within the domain of arcsin(x). Calculating these angles, we find
n=1:
θ1,average = 22.44◦
(12)
that we only obtain maxima for n=1 and n=2, so
λ
n=1:
θ1 = arcsin
,
(8)
n=2:
θ2,average = 47.50◦
(13)
d
Both of these lie a bit short of the predicted values.
2λ
n=2:
θ2 = arcsin
.
(9) Although the data collection is not exactly precise,
d
which leads to imprecise observed maximum intensity
We can substitute our values for d and λ, and we angles, we can get a feel for where the error is coming
obtain our values for θ,
from. First, the diffraction grating that we used was
circular, and when the edges of the circle were covered
n=1:
θ1 = 23.148◦
(10) up (thereby enlarging the diffraction grating where
the microwaves could not pass through), the intensity
n=2:
θ2 = 51.832◦
(11) of the radiation detected decreased. This means that
the edges were also acting as a diffraction grating,
Making a graph of the data that we obtained, we or, in other words, acting as another slit, creating
plotted of the angle of deflection versus the meter a more complicated diffraction pattern. This skews
reading; this is displayed in Figure 6
the results, and the result is maxima either occuring
where they shouldn’t (like the tail end of the plot)
and the positions and intensities of the maximums.
7
5
Discussion
Through a variety of optics experiments, we’ve seen
many effects that lie solely in the realm of electromagnetic waves, that often have no everyday parallel. The double slit experiment is a particularly interesting example; the nature of the experiment denies the particle nature of light, simply due to the
fact that since there is no center slit, there should be
no observed electric field intensity there. However,
as we observed, we get the most intensity in exactly
the regions where the slits are not, contradicting any
sense of the particulate nature of light. The large
wavelength allowed for these phenomena to be easily observed. The diffraction grating and polarizers
used had slits that had thickness measurable with a
ruler, which is not often the case in optics experiments. The downside to this is the inaccuracy of the
microwave receiver. The receiver is not very accurate;
there are several factors that interfere with the meter
readings. Smaller factors, such as the position of the
experimenters (us!) or the proximity to the the table
on which the apparatus was sitting, contributed to
unstable and/or inaccurate meter readings. The receiver was also highly sensitive to changes in distance
between the cones, and the alignment of the polarization axis. However, we managed to obtain some
decent data, and get a general feel for some optical
effects.
6
References
All diagrams and lab procedures come from the
PASCO - Microwave Optics Lab Manual.
[1] PASCO Lab Manual, ”Standing Waves”, pp.1316.
[2] PASCO Lab Manual, ”Polarization”, pp.19-20.
[3] PASCO Lab Manual, ”Double-Slit Interference”, 21-22.
[4] Eugene Hecht, Optics, 4th ed. (Addison Wesley,
San Francisco, CA, 2002), pp. 450-451.
8