Download Microwaves

Microwaves
LBS 267L
Objectives
(1) To learn something about microwaves.
(2) To use microwaves to study various interference phenomena, including Bragg Reflection.
Introduction
The term microwaves is applied to that part of the electromagnetic radiation spectrum with wavelengths of a few centimeters and frequencies of
the order of 10 GHz (Billions of Cycles/sec). Microwaves are produced by oscillating at the appropriate frequency in an electrode. The electrode is
inside a metal wave-guide of rectangular cross-section through which the microwaves are transmitted. To propagate the waves into the air without
reflections and without too much spreading out, a horn is attached to the end of the waveguide.
In this experiment you will study the properties of microwaves. Since, like visible light, they are electromagnetic waves, microwaves should have
properties similar to those for visible light. However, since microwaves have wavelengths of a few centimeters, instead of the 3-6 x 10-5 cm of visible
light, diffraction effects are scaled up to where they can be easily observed with normal sized objects. Compare the ease of observation of interference
in this experiment with that in the Michelson Interferometer.
We indicate below several experiments which you should try, but encourage you to use your own ingenuity to devise additional experiments.
The apparatus is basically straightforward. The receiver is an antenna that detects the electric field in the electromagnetic wave. The signal is
rectified and fed into a meter that reads its intensity. Initially, line up the transmitter and receiver and adjust the meter to a middle reading. For a
freely propagating electromagnetic wave, the electric and magnetic field vectors oscillate in a plane perpendicular to the direction of propagation. Furthermore, the electric and magnetic field vectors are perpendicular to each other. At a particular point in space, and at a particular time, we would
have the picture shown in Fig. 1.
Figure 1
At a fixed time, but at a different point in space we might have the picture shown in Fig. 2. If the electromagnetic wave passes through a grid of
parallel conducting wires, those components of the electric field vector which are parallel to the wires induce a current in the wires. Due to the finite
resistance of the wires, energy is dissipated into heat (Ohmic losses!). Therefore, the parallel components of the electric field vector are strongly
attenuated after the wave has passed through the grid.
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Figure 2
Polarization
(a) Are the transmitter and receiver polarized? Rotate one with respect to the other and see if you can observe any effects from polarization. In
which direction are they polarized. (Can you tell?) Explain exactly what you can and can not determine by doing this.
(b) Place the screen of parallel wires in the beam and observe the variation in receiver intensity when you rotate it between positions where the
wires are vertical and horizontal. See if you can deduce from this if the beam is polarized, and if so, in what direction the electric field vector is
pointing. What exactly can you determine from this procedure?
(c) Hold one polarizing screen at 450 and use the second screen (placed between the first and the receiver) to determine the direction of
polarization of the radiation that has passed through the first. Explain your observations.
(d) Look inside the horns of the transmitter and receiver. What is in there? How does this relate to the microwave's polarization?
Absorption
Place various objects in the path of the microwave and observe the effect. Note: The object to be tested must occupy a substantial portion of the
cross-section between the source and receiver, or the microwaves will simply pass around it. In particular, try a paper towel, first dry and then wet.
Try a metal plate. Make qualitative conclusions.
Measurement of Wavelengths
Standing Waves. When two waves of the same frequency travel in opposite directions they interfere and produce standing waves. At nodes (N),
the electric field is zero, whereas at antinodes the fields vary with time between the two extreme values, as shown below. In our apparatus, most of
the incident radiation is absorbed by the receiver, but some is reflected. This reflected part is free to form standing waves with the incident waves.
Between the transmitter and receiver there is therefore a standing wave component superimposed on a larger traveling wave component. To measure
the wavelength of the standing wave, we need to measure the distance between its nodes (Fig. 3). There are two ways this can be done. First, if you
vary the position of the receiver on its track you will observe maxima and minima /2 apart. Second, if you use a moderate absorber (e.g. plastic
screens supplied) then maxima and minima each /2 apart will be observed as the screen is moved between the transmitter and receiver. Explain why
the maxima and minima are /2 apart.
Figure 3
(a) Observe the change in meter reading as you slowly move the receiver a several centimeters further away from the transmitter. You should see
maxima and minima. Now measure the positions of 5 or more consecutive maxima (or minima). From this determine the wavelength with a brief
error analysis.
(b) Now place a partial absorber between the transmitter and receiver. Observe the changes in intensity at the receiver as you slowly move the
absorber back and forth. Again measure the screen positions for 5 or more consecutive maximum (or minimum) readings on the receiver. Calculate
(with error analysis) the microwaves wave length. When the receiver reads a minimum is the absorber at a minima or maxima in the standing
microwave? Explain.
(c) The transmitter is labeled with its frequency. Use c = f , to find the wavelength of microwaves produced by your transmitter. Do your results
agree with this?
Reflection
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Check to see whether the angle of incidence onto a metal reflector equals the angle of reflection.
Lloyd's Mirror
Two waves arrive at the detector, the direct beam and the beam reflected from a metal plate (Fig. 4). With no phase changes, a path difference of
 would cause constructive interference, and a path difference of 2 destructive interference. By varying H (use a lab jack) a series of maxima and
minima can be observed.
Figure 4
We may understand Lloyd's mirror by assuming light is emitted by the real source S and its mirror image S' as shown in Fig. 5. At the point of
observation P the two waves interfere. The difference in path length is
D(1 + 2H2/D2) - D
= 2H2/D
The reflected wave experiences a phase shift of  =
source). We, therefore, have constructive interference if:
1800.
Figure 5
(This is equivalent to the image source oscillating exactly out of phase with the real
Smax = n + /2 = 2H2/D,
where n is an integer number. Destructive interference occurs if:
Smin = n = 2H2/D
Now if you measure H1 for one minima (maxima) and then measure H2 for the next minima (maxima), you can find the wavelength from:
 = 2(H22 - H12)/D
Bragg Reflection
Information on the crystal structure of real solids is frequently obtained by Bragg reflection of X-rays from the crystal lattice. With the much
larger wavelength of microwaves, we can look at a macroscopic crystal model. The theory is the same.
The phenomenon of Bragg reflection involves reflection from adjacent planes of atoms (Fig. 6). (In our case, the "atoms" are ordinary steel balls
in a foam matrix.) Constructive interference occurs if the path length difference S between the two rays 1 and 2 is an integer multiple of the
wavelength: S = n



Figure 
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On each side, we have: S/2 = d sin or S = 2d sin
We, thus, have constructive interference (i.e. constructive reflection from the different lattice planes) for
nd sin , n = 1,2...
Make measurements every 5˚ for as wide a range of angles as you can. Plot your intensity measurements vs. angle. Do you see any peaks? You
can calculate where the maximum constructive interference should occur from the above equation.
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