PASCO scientific 080187 Gun Diode Microwave Transmitter User Manual 012 04630G cov p65

PASCO scientific Gun Diode Microwave Transmitter 012 04630G cov p65

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012-04630G

MICROWAVE OPTICS

Instruction Manual and

Experiment Guide for

the PASCO scientific

Model WA-9314B

Includes

Teacher's Notes

and

Typical

Experiment Results

Phone (916) 786-3800  FAX (916) 786-8905  web: www.pasco.com

10101 Foothills Blvd.  Roseville, CA 95678-9011 USA

better

teach science

ways to

012-04630G Microwave Optics

Table of Contents

Section Page

Introduction ...................................................................................................... 1

Equipment......................................................................................................... 1

Initial Setup ...................................................................................................... 3

Accessory Equipment ....................................................................................... 3

Assembling Equipment for Experiments.......................................................... 5

Experiments

Experiment 1: Introduction to the System ............................................ 7

Experiment 2: Reflection ................................................................... 11

Experiment 3: Standing Waves - Measuring Wavelengths ............... 13

Experiment 4: Refraction Through a Prism ....................................... 17

Experiment 5: Polarization ................................................................ 19

Experiment 6: Double-Slit Interference ............................................ 21

Experiment 7: Lloyds Mirror............................................................. 23

Experiment 8: Fabry-Perot Interferometer ........................................ 25

Experiment 9: Michelson Interferometer .......................................... 27

Experiment 10: Fiber Optics.............................................................. 29

Experiment 11: Brewster's Angle ...................................................... 31

Experiment 12: Bragg Diffraction ..................................................... 33

Teacher's Guide .............................................................................................. 35

Appendix ........................................................................................................ 45

Schematic Diagrams ....................................................................................... 46

Replacement Parts List ................................................................................... 47

➤➤

➤

This device complies with Part 15 of the FCC Rules. Operation is subject to the

following two conditions:

1. this device may not cause harmful interference.

2. this device must accept any interference received, including interference that may

cause undesired operation.

Changes or modifications not expressly approved by Pasco Scientific could void the user's author-

ity to operate the equipment.

Microwave Optics 012-04630G

The PASCO scientific 012-04630E Model WA-9314B

Microwave Optics manual is copyrighted and all rights

reserved. However, permission is granted to non-profit

educational institutions for reproduction of any part of the

manual providing the reproductions are used only for their

laboratories and are not sold for profit. Reproduction

under any other circumstances, without the written

consent of PASCO scientific, is prohibited.

Limited Warranty

PASCO scientific warrants the product to be free from

defects in materials and workmanship for a period of one

year from the date of shipment to the customer. PASCO

will repair or replace at its option any part of the product

which is deemed to be defective in material or workman-

ship. The warranty does not cover damage to the product

caused by abuse or improper use. Determination of

whether a product failure is the result of a manufacturing

defect or improper use by the customer shall be made

solely by PASCO scientific. Responsibility for the return

of equipment for warranty repair belongs to the customer.

Equipment must be properly packed to prevent damage

and shipped postage or freight prepaid. (Damage caused

by improper packing of the equipment for return shipment

will not be covered by the warranty.) Shipping costs for

returning the equipment after repair will be paid by

PASCO scientific.

Please—Feel free to duplicate this manual

subject to the copyright restrictions below.

Equipment Return

Should the product have to be returned to PASCO

scientific for any reason, notify PASCO scientific by

letter, phone, or fax BEFORE returning the product. Upon

notification, the return authorization and shipping

instructions will be promptly issued.

➤ ➤

➤ NOTE: NO EQUIPMENT WILL BE

ACCEPTED FOR RETURN WITHOUT AN

AUTHORIZATION FROM PASCO.

When returning equipment for repair, the units must be

packed properly. Carriers will not accept responsibility for

damage caused by improper packing. To be certain the

unit will not be damaged in shipment, observe the follow-

ing rules:

➀The packing carton must be strong enough for the

item shipped.

➁Make certain there are at least two inches of

packing material between any point on the

apparatus and the inside walls of the carton.

➂Make certain that the packing material cannot shift

in the box or become compressed, allowing the

instrument come in contact with the packing

carton.

Address: PASCO scientific

10101 Foothills Blvd.

Roseville, CA 95747-7100

Phone: (916) 786-3800

FAX: (916) 786-3292

email: techsupp@pasco.com

web: www.pasco.com

Credits

This manual edited by: Dave Griffith

Teacher’s guide written by: Eric Ayars

012-04630G Microwave Optics

Microwave Transmitter with Power Supply

Introduction

GUNN DIODE

MICROWAVE

TRANSMITTER

PAS CO scientific

Gunn Diode Transmitter

The Gunn Diode Microwave Transmitter provides 15 mW

of coherent, linearly polarized microwave output at a

wavelength of 2.85 cm. The unit consists of a Gunn di-

ode in a 10.525 GHz resonant cavity, a microwave horn

to direct the output, and an 18 cm stand to help reduce

table top reflections. The Transmitter may be powered

directly from a standard 115 or 220/240 VAC, 50/60 Hz

outlet by using the provided power supply. Other features

include an LED power-indicator light and a rotational

scale that allows easy measurement of the angle of po-

larization.

The Gunn diode acts as a non-linear resistor that oscillates

in the microwave band. The output is linearly polarized

along the axis of the diode and the attached horn radiates

a strong beam of microwave radiation centered along the

axis of the horn.

To Operate the Microwave Transmitter

Simply plug the power supply into the jack on the

Transmitter's bottom panel and plug the power supply into

a standard 115 or 220/240 VAC, 50/60 Hz outlet. The

LED will light indicating the unit is on.

➤➤

➤

CAUTION: The output power of the Microwave

Transmitter is well within standard safety levels.

Nevertheless, one should never look directly into the

microwave horn at close range when the Transmit-

ter is on.

Power Supply Specifications:

9 Volt DC, 500 mA;

Miniature Phone Jack Connector (the tip is positive)

Equipment

There are many advantages to studying optical phenom-

ena at microwave frequencies. Using a 2.85 centimeter

microwave wavelength transforms the scale of the experi-

ment. Microns become centimeters and variables ob-

scured by the small scale of traditional optics experiments

are easily seen and manipulated. The PASCO scientific

Model WA-9314B Basic Microwave Optics System is

designed to take full advantage of these educational ben-

efits. The Basic Microwave Optics System comes with a

2.85 centimeter wavelength microwave transmitter and a

receiver with variable amplification (from 1X to 30X).

All the accessory equipment needed to investigate a vari-

ety of wave phenomena is also included.

This manual describes the operation and maintenance of

the microwave equipment and also gives detailed instruc-

tions for many experiments. These experiments range

from quantitative investigations of reflection and refrac-

tion to microwave models of the Michelson and Fabry-

Perot interferometers. For those who have either the

Complete Microwave Optics System (WA-9316) or the

Microwave Accessory Package (WA-9315), the manual

describes experiments for investigating Bragg diffraction

and Brewster's angle.

012-04630GMicrowave Optics

Microwave Receiver

The Microwave Receiver provides a meter reading that,

for low amplitude signals, is approximately proportional

to the intensity of the incident microwave signal. A mi-

crowave horn identical to that of the Transmitter's collects

the microwave signal and channels it to a Schottky diode

in a 10.525 GHz resonant cavity. The diode responds

only to the component of a microwave signal that is polar-

ized along the diode axis, producing a DC voltage that

varies with the magnitude of the microwave signal.

Special features of the Receiver include four amplification

ranges—from one to thirty—with a variable sensitivity

knob that allows fine tuning of the amplification in each

range. For convenience in class demonstrations, banana

plug connectors provide for an output signal via hookup

to a projection meter (such as PASCO Model ES-9065

Projection Meter or SE-9617 DC Voltmeter). This output

can also be used for close examination of the signal using

an oscilloscope. The receiver is battery powered and has

an LED battery indicator; if the LED lights when you turn

on the Receiver , the battery is working. As with the

Transmitter, an 18 cm high mount minimizes table top

reflections, and a rotational scale allows convenient mea-

surements of polarization angle.

The female audio connector on the side of the Receiver is

for an optional Microwave Detector Probe ( PASCO

Model WA-9319). The probe works the same as the Re-

ceiver except it has no horn or resonant cavity. The Probe

is particularly convenient for examining wave patterns in

which the horn could get in the way, such as the standing

wave pattern described in Experiment 3 of this manual.

➤➤

➤

NOTE: The detector diodes in the Receiver (and

the Probe) are non-linear devices. This non-linear-

ity will provide no problem in most experiments. It

is important however, to realize that the meter read-

ing is not directly proportional to either the electric

field (E) or the intensity (I) of the incident micro-

wave. Instead, it generally reflects some intermedi-

ate value.

To Operate The Microwave Receiver:

➤➤

➤

NOTE: Before using the Receiver, you will need

to install the two 9-volt transistor batteries—they are

included with the system. See the instructions in the

Maintenance section at the end of this manual.

①Turn the INTENSITY selection switch from OFF to

30X, the lowest amplification level. The battery indi-

cator LED should light, indicating that the battery is

okay. If it does not, replace the battery following the

procedures in the Maintenance section of this manual.

➤➤

➤

NOTE: The INTENSITY selection settings (30X,

10X, 3X, 1X) are the values you must multiply the

meter reading by to normalize your measurements.

30X, for example, means that you must multiply the

meter reading by 30 to get the same value you

would measure for the same signal with the INTEN-

SITY selection set to 1X. Of course, this is true

only if you do not change the position of the VARI-

ABLE SENSITIVITY knob between measurements.

②Point the microwave horn toward the incident micro-

wave signal. Unless polarization effects are under in-

vestigation, adjust the polarization angles of the Trans-

mitter and Receiver to the same orientation (e.g., both

horns vertically, or both horns horizontally).

③Adjust the VARIABLE SENSITIVITY knob to attain

a meter reading near midscale. If no deflection of the

meter occurs, increase the amplification by turning the

INTENSITY selection switch clockwise. Remember,

always multiply your meter reading by the appropriate

INTENSITY selection (30X, 10X, 3X, or 1X) if you

want to make a quantitative comparison of measure-

ments taken at different INTENSITY settings.

012-04630G Microwave Optics

Initial Setup

Attaching the Transmitter and Receiver Stands

Hand Screw

Washers

Fixed Arm Assembly (1)

Goniometer (1)

Accessory equipment for the Basic Microwave Optics

System includes:

Rotating Component Holder (1)

Component Holder (2)

ROTATING TABLE

Rotating Table (1)

Accessory Equipment

To attach the microwave Transmitter and Receiver to their

respective stands prior to performing experiments, pro-

ceed as follows:

①Remove the black hand screw from the back panel of

both the Transmitter and the Receiver.

②Attach both units to the stands as shown below. Ob-

serve the location of the washers.

③To adjust the polarization angle of the Transmitter

or Receiver, loosen the hand screw, rotate the unit,

and tighten the hand screw at the desired orientation.

Notice the rotational scale on the back of each unit for

measuring the angle of polarization. Be aware, how-

ever, that since the Transmitter and Receiver face each

other in most experiments it is important to match their

polarization angle. If you rotate one unit to an angle of

10-degrees, you must rotate the other to -10-degrees

(350-degrees) to achieve the proper polar alignment.

012-04630GMicrowave Optics

Wide Slit Spacer (1)

Narrow Slit Spacer (1)

Slit Extender Arm (1)

Metal Reflector (2)

Partial Reflector (2)

Polarizers (2)

Tubular

Plastic Bags (4)

Ethafoam Prism Mold w/

Styrene Pellets (1)

Polyethylene Panel (1)

Cubic Lattice with 100 metal

spheres—5x5x4 array (1)

The WA-9315 Microwave Accessory Package (which is

part of the Complete Microwave Optics System Model

WA-9316) includes the following:

The following components, compatible with the WA-

9314B Basic Microwave Optics System, are available

from PASCO scientific:

Model WA-9319 Microwave Detector Probe plugs di-

rectly into the Microwave Receiver. The probe is essen-

tial for experiments in which the horn of the Receiver

might otherwise interfere with the wave pattern being

measured.

Model WA-9318 Microwave Modulation Kit includes a

modulator and microphone. With this kit, you can use

your Transmitter and Receiver as a microwave communi-

cations system.

012-04630G Microwave Optics

Assembling Equipment for Experiments

The arms of the Goniometer slide through the holes in the

Component Holders as shown. Make sure the magnetic

strip on the bottom of the arm grips the base of the car-

riage. To adjust the position of the holders, just slide

them along the Goniometer arms. Attach the mounting

stands of the microwave Transmitter and Receiver to the

arms of the Goniometer in the same manner.

For most experiments it is advantageous to attach the

Transmitter to the long arm of the Goniometer and the

Receiver to the shorter, rotatable arm. This maintains a

fixed relationship between the microwave beam and com-

ponents mounted on the long arm (or on the degree plate)

of the Goniometer. In turn the Receiver moves easily to

sample the output.

Reflectors, Partial Reflectors, Polarizers, Slit Spacers, and

the Slit Extender Arm all attach magnetically to the Com-

ponent Holders. The metric scale along the Goniometer

arms and the degree plate at the junction of the arms al-

low easy measurement of component placement. When

rotating the rotatable arm, hold the degree plate firmly to

the table so that it does not move.

➤➤

➤IMPORTANT NOTES:

1. CAUTION—Under some circumstances, microwaves can interfere with elec-

tronic medical devices. If you use a pacemaker, or other electronic medical

device, check with your doctor or the manufacturer to be certain that low power

microwaves at a frequency of 10.525 GHz will not interfere with its operation.

2. Always mount the apparatus on a CLEAN, SMOOTH table. Before setting up

the equipment, brush off any material—particularly metal chips—that might

have adhered to the magnetic strips on the bottom of the Goniometer arms.

Mounting the Component Holder

012-04630GMicrowave Optics

Copy-Ready Experiments

The following Experiments provide a thorough introduction to wave theory using

the microwave system. We expect that the student approaches each experiment

with the appropriate theoretical background, therefore, basic principles are only

briefly discussed in each experiment.

The experiments are written in worksheet format. Feel free to photocopy them for

use in your lab.

012-04630G Microwave Optics

EQUIPMENT NEEDED:

– Transmitter – Goniometer

– Receiver – Reflector (1)

Purpose

This experiment gives a systematic introduction to the Microwave Optics System. This may

prove helpful in learning to use the equipment effectively and in understanding the significance of

measurements made with this equipment. It is however not a prerequisite to the following experi-

ments.

Procedure

①Arrange the Transmitter and Receiver on the Goni-

ometer as shown in Figure 1.1 with the Transmitter

attached to the fixed arm. Be sure to adjust both

Transmitter and Receiver to the same polarity—the

horns should have the same orientation, as shown.

②Plug in the Transmitter and turn the INTENSITY

selection switch on the Receiver from OFF to 10X.

(The LEDs should light up on both units.)

③ Adjust the Transmitter and Receiver so the distance

between the source diode in the

Transmitter and the detector diode

in the Receiver (the distance la-

beled R in Figure 1.1) is 40 cm

(see Figure 1.2 for location of

points of transmission and recep-

tion). The diodes are at the loca-

tions marked "T" and "R" on the

bases. Adjust the INTENSITY and

VARIABLE SENSITIVITY dials

on the Receiver so that the meter

reads 1.0 (full scale).

④Set the distance R to each of the

values shown in Table 1.1. For each

value of R, record the meter reading.

(Do not adjust the Receiver controls

between measurements.) After mak-

ing the measurements, perform the

calculations shown in the table.

⑤Set R to some value between 70 and

90 cm. While watching the meter,

slowly decrease the distance between

the Transmitter and Receiver. Does

the meter deflection increase steadily

as the distance decreases?

Experiment 1: Introduction to the System

Figure 1.1 Equipment Setup

5 cm 5 cm

Transmitter Receiver

Effective Point of Reception of

Transmitter Signal

Effective Point of Emission of

Transmitter Signal

Figure 1.2 Equipment Setup

(cm) Meter Reading (M) M X R

(cm)

M X R

(cm

)

100

1.0 40 1600

Table 1.1

012-04630G

Microwave Optics

⑥Set R to between 50 and 90 cm. Move a Reflector, its plane parallel to the axis of the microwave

beam, toward and away from the beam axis, as shown in Figure 1.3. Observe the meter read-

ings. Can you explain your observations in steps 5 and 6? Don’t worry if you can’t; you will

have a chance to investigate these phenomena more

closely in Experiments 3 and 8, later in this manual. For

now just be aware of the following:

➤➤

➤IMPORTANT: Reflections from nearby objects, in-

cluding the table top, can affect the results of your mi-

crowave experiments. To reduce the effects of extrane-

ous reflections, keep your experiment table clear of all

objects, especially metal objects, other than those com-

ponents required for the current experiment.

⑦Loosen the hand screw on the back of the Receiver and

rotate the Receiver as shown in Figure 1.4. This varies

the polarity of maximum detection. (Look into the

receiver horn and notice the alignment of the detector

diode.) Observe the meter readings through a full 360

degree rotation of the horn. A small mirror may be

helpful to view the meter reading as the receiver is

turned. At what polarity does the Receiver detect no

signal?

Try rotating the Transmitter horn as well. When fin-

ished, reset the Transmitter and Receiver so their polari-

ties match (e.g., both horns are horizontal or both horns

are vertical).

⑧Position the Transmitter so the output surface of the horn

is centered directly over the center of the Degree Plate of

the Goniometer arm (see Figure 1.5). With the Receiver

directly facing the Transmitter and as far back on the

Goniometer arm as possible, adjust the Receiver controls

for a meter reading of 1.0. Then rotate the rotatable arm

of the Goniometer as shown in the figure. Set the angle

of rotation (measured relative to the 180-degree point on

the degree scale) to each of

the values shown in Table

1.2, and record the meter

reading at each setting.

Figure 1.5 Signal Distribution

Figure 1.3 Reflections

Reflector

Figure 1.4 Polarization

Handscrew

Table 1.2

Meter

Reading

Angle of

Receiver

0°

10°

20°

30°

40°

50°

Meter

Reading

Angle of

Receiver

70°

80°

90°

100°

110°

120°

Meter

Reading

Angle of

Receiver

140°

150°

160°

170°

180°

60° 130°

012-04630G Microwave Optics

Questions

①The electric field of an electromagnetic wave is inversely proportional to the distance from

the wave source

(i.e., E = 1/R). Use your data from step 4 of the experiment to determine if the meter read-

ing of the Receiver is directly proportional to the electric field of the wave.

②The intensity of an electromagnetic wave is inversely proportional to the square of the distance

from the wave source (i.e., I = 1/R2). Use your data from step 4 of the experiment to determine

if the meter reading of the Receiver is directly proportional to the intensity of the wave.

③Considering your results in step 7, to what extent can the Transmitter output be considered a

spherical wave? - A plane wave?

012-04630G

Microwave Optics

Notes

012-04630G Microwave Optics

Experiment 2: Reflection

EQUIPMENT NEEDED:

– Transmitter – Goniometer

– Receiver – Metal Reflector

– Rotating Component Holder

Procedure

①Arrange the equipment as shown in figure 2.1

with the Transmitter attached to the fixed arm

of the Goniometer. Be sure to adjust the Trans-

mitter and Receiver to the same polarity; the

horns should have the same orientation as

shown.

②Plug in the Transmitter and turn the Receiver

INTENSITY selection switch to 30X.

③The angle between the incident wave from the

Transmitter and a line normal to the plane of

the Reflector is called the Angle of Incidence

(see Figure 2.2). Adjust the Rotating Compo-

nent Holder so that the Angle of Incidence

equals 45-degrees.

④Without moving the Transmitter or the Reflec-

tor, rotate the movable arm of the Goniometer

until the meter reading is a maximum. The

angle between the axis of the Receiver horn and

a line normal to the plane of the Reflector is

called the Angle of Reflection.

⑤Measure and record the angle of reflection for

each of the angles of incidence shown in Table 2.1.

➤NOTE: At various angle settings the Receiver will

detect both the reflected wave and the wave coming

directly from the Transmitter, thus giving misleading

results. Determine the angles for which this is true

and mark the data collected at these angles with an

asterisk "*".

Figure 2.1 Equipment Setup

Figure 2.2 Angles of Incidence and Reflection

Angle of

Incidence

Angle of

Reflection

Reflector

Angle of

Incidence

20°

30°

40°

50°

60°

Angle of

Reflection

70°

80°

90°

Table 2.1

012-04630G

Microwave Optics

Questions

①What relationship holds between the angle of incidence and the angle of reflection? Does this rela-

tionship hold for all angles of incidence?

②In measuring the angle of reflection, you measured the angle at which a maximum meter reading

was found. Can you explain why some of the wave reflected into different angles? How does this

affect your answer to question 1?

③Ideally you would perform this experiment with a perfect plane wave, so that all the Transmitter

radiation strikes the Reflector at the same angle of incidence. Is the microwave from the Transmitter

a perfect plane wave (see Experiment 1, step 7)? Would you expect different results if it were a

perfect plane wave? Explain.

Questions for Additional Experimentation

①How does reflection affect the intensity of the microwave? Is all the energy of the wave striking the

Reflector reflected? Does the intensity of the reflected signal vary with the angle of incidence?

②Metal is a good reflector of microwaves. Investigate the reflective properties of other materials.

How well do they reflect? Does some of the energy pass through the material? Does the material

absorb some of it? Compare the reflective properties of conductive and non-conductive materials.

012-04630G Microwave Optics

Experiment 3: Standing Waves - Measuring Wavelengths

➤➤

➤ NOTE: This experiment is best performed using the PASCO Microwave Detector Probe

(Model ME-9319), as described in Method A below. However, for those without a

probe, Method B may be used, although in this Method λ can not be measured directly

from the standing wave pattern.

EQUIPMENT NEEDED:

– Transmitter – Goniometer

– Receiver – Reflector (1)

– Component Holder (2) – Microwave Detector Probe (ME-9319 )

Introduction

When two electromagnetic waves meet in space, they superpose. Therefore, the total electric

field at any point is the sum of the electric fields created by both waves at that point. If the

two waves travel at the same frequency but in opposite direction they form a standing wave.

Nodes appear where the fields of the two waves cancel and antinodes where the superposed

field oscillates between a maximum and a minimum. The distance between nodes in the

standing wave pattern is just 1/2 the wavelength (λ) of the two waves.

Procedure

Method A

In this experiment, you will reflect the wave

from the Transmitter back upon itself, creating

a standing wave pattern. By measuring the

distance between nodes in the pattern and mul-

tiplying by two, you can determine the wave-

length of the microwave radiation.

①Arrange the equipment as shown in Figure 3.1.

②Plug the Detector Probe into the side connector

on the Receiver. Face the Receiver horn di-

rectly away from the Transmitter so that none

of the microwave signal enters the horn. Adjust

the Receiver controls as needed to get a strong

meter reading.

③Slide the Probe along the Goniometer arm (no more than a centimeter or two) until the meter

shows a maximum reading. Then slide the Reflector (again, no more than a centimeter or

two) to find a maximum meter reading. Continue making slight adjustments to the Probe

and Reflector positions until the meter reading is as high as possible.

④Now find a node of the standing wave pattern by adjusting the Probe until the meter reading

is a minimum. Record the Probe Position along the metric scale on the Goniometer arm.

Initial Probe Position = _____________________.

Figure 3.1 Equipment Setup

Receiver

Reflector

Detector Probe

012-04630G

Microwave Optics

⑤While watching the meter, slide the Probe along the Goniometer arm until the Probe

has passed through at least 10 antinodes and returned to a node. Record the new

position of the Probe and the number of antinodes that were traversed.

Antinodes Traversed= __________________________.

Final Probe Position = _________________________.

⑥Use your data to calculate λ, the wavelength of the microwave radiation.

λ =_________________________.

⑦Repeat your measurements and recalculate λ.

Initial Probe Position =_________________________.

Antinodes Traversed =_________________________.

Final Probe Position =_________________________.

λ =_________________________.

Questions

①Use the relationship velocity = λν to calculate the frequency of the microwave signal

(assuming velocity of propagation in air is 3x108 m/sec).

(ν = the expected frequency of the microwave radiation -10.525 GHz).

Method B

①Set up the equipment as shown in Figure 3.2. Adjust the Receiver controls to get a

full-scale meter reading with the Transmitter and Receiver as close together as pos-

sible. Slowly move the Receiver along the Goniometer arm, away from the Trans-

mitter. How does this motion effect the meter reading?

The microwave horns are not perfect collectors of microwave radiation. Instead, they

act as partial reflectors, so that the radiation from the Transmitter reflects back and

forth between the Transmitter and Reflector horns, diminishing in amplitude at each

pass. However, if the distance between the Transmitter and Receiver diodes is equal

to nλλ

λλ

λ/2, (where n is an integer and λ is the wavelength of the radiation) then all the

multiply-reflected waves entering the Receiver horn will be in phase with the primary

transmitted wave. When this occurs, the meter reading will be a maximum. (The

distance between adjacent positions in order to see a maximum is therefore λλ

λλ

λ/2.)

②Slide the Receiver one or two centime-

ters along the Goniometer arm to ob-

tain a maximum meter reading.

Record the Receiver position along the

metric scale of the Goniometer arm.

Initial Position of Receiver =

_________________________.

Figure 3.2 Equipment Setup

012-04630G Microwave Optics

③While watching the meter, slide the Receiver away from the Transmitter. Do not stop

until the Receiver passed through at least 10 positions at which you see a minimum meter

reading and it returned to a position where the reading is a maximum. Record the new

position of the Receiver and the number of minima that were traversed.

Minima Traversed= _________________________.

Final Receiver Position = _________________________.

④Use the data you have collected to calculate the wavelength of the microwave radiation.

λ = _________________________.

⑤Repeat your measurements and recalculate λ.

Initial Position of Receiver = _________________________.

Minima Traversed = _________________________.

Final Receiver Position = _________________________.

λ = _________________________.

Questions

①Use the relationship velocity = λν to calculate the frequency of the microwave signal

(assuming velocity of propagation in air is 3x108 m/sec).

(ν = the expected frequency of the microwave radiation -10.525 GHz).

012-04630G

Microwave Optics

Notes

012-04630G Microwave Optics

Experiment 4: Refraction Through a Prism

EQUIPMENT NEEDED:

– Transmitter

– Goniometer

– Receiver

– Rotating Table

– Ethafoam Prism mold with styrene pellets

– Protractor

Introduction

An electromagnetic wave usually travels in a

straight line. As it crosses a boundary between

two different media, however, the direction of

propagation of the wave changes. This change

in direction is called Refraction, and it is sum-

marized by a mathematical relationship known

as the Law of Refraction (otherwise known as

Snell’s Law):

n1sinθθ

θθ

θ1 = n2sinθθ

θθ

θ2;

where θθ

θθ

θ1 is the angle between the direction of propagation of the incident wave and the

normal to the boundary between the two media, and θ2 is the corresponding angle for the

refracted wave (see Figure 4.1). Every material can be described by a number n, called

its Index of Refraction. This number indicates the ratio between the speed of

electromegnetic waves in vacuum and the speed of electromagnetic waves in the material,

also called the medium. In general, the media on either side of a boundary will have dif-

ferent indeces of refraction. Here they are labeled n1 and n2. It is the difference between

indeces of refraction (and the difference between wave velocities this implies) which

causes “bending”, or refraction of a wave as it crosses the boundary between two distinct

media.

In this experiment, you will use the law of refraction to measure the index of refrac-

tion for styrene pellets.

Procedure

①Arrange the equipment as shown in Figure 4.2. Rotate the empty prism mold and see

how it effects the incident wave. Does it

reflect, refract, or absorb the wave?

②Fill the prism mold with the styrene pellets.

To simplify the calculations, align the face of

the prism that is nearest to the Transmitter

perpendicular to the incident microwave

beam.

③Rotate the movable arm of the Goniometer

and locate the angle θ at which the refracted

signal is a maximum.

n1 n2

Boundary between

media

Refracted

Wave

Incident

Wave

θ1

θ2

Figure 4.1 Angles of Incidence and Refraction

Ethafoam Prism

Rotating Table

Figure 4.2 Equipment Setup

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Refracted

Beam

Normal to

Boundary of

Refraction

θ2

θ1

Figure 4.3 Geometry of Prism Refraction

Incident

Beam

➤ NOTE: θ is just the angle that you read directly

from the Degree Scale of the Goniometer.

θ = _________________________.

④Using the diagram shown in Figure 4.3, determine θ1

and use your value of θ to determine θ2. (You will

need to use a protractor to measure the Prism angles.)

θ1 = _________________________.

θ2 = _________________________.

⑤Plug these values into the Law of Refraction to

determine the value of n1/n2.

n1/n2 = _________________________.

⑥The index of refraction for air is equal to 1.00. Use this fact to determine n1, the index of

refraction for the styrene pellets.

Questions

①In the diagram of Figure 4.3, the assumption is made that the wave is unrefracted when it

strikes the first side of the prism (at an angle of incidence of 0°). Is this a valid assumption?

②Using this apparatus, how might you verify that the index of refraction for air is equal to one.

③Would you expect the refraction index of the styrene pellets in the prism mold to be the same as

for a solid styrene prism?

012-04630G Microwave Optics

Experiment 5: Polarization

EQUIPMENT NEEDED:

-Transmitter -Receiver

-Goniometer -Component Holder (1)

-Polarizer (1).

Introduction

The microwave radiation from the Transmitter is linearly

polarized along the Transmitter diode axis (i.e., as the

radiation propagates through space, its electric field re-

mains aligned with the axis of the diode). If the Trans-

mitter diode were aligned vertically, the electric field of

the transmitted wave would be vertically polarized, as

shown in Figure 5.1. If the detector diode were at an

angle θ to the Transmitter diode, as shown in Figure 5.2,

it would only detect the component of the incident elec-

tric field that was aligned along its axis. In this experi-

ment you will investigate the phenomenon of polariza-

tion and discover how a polarizer can be used to alter the

polarization of microwave radiation.

Procedure

①Arrange the equipment as shown in Figure 5.3 and

adjust the Receiver controls for nearly full-scale

meter deflection.

②Loosen the hand screw on the back of the Receiver

and rotate the Receiver in increments of ten de-

grees. At each rotational position, record the meter

reading in Table 5.1.

③What happens to the meter readings if you continue

to rotate the Receiver beyond 180-degrees?

Figure 5.2 Detecting Polarized Radiation

Component

Detected

Vertically

Polarized

Microwave

Detector

Diode

Figure 5.1 Vertical Polarization

Transmitter

Diode

Vertically

Polarized

Microwaves

(E field)

Figure 5.3 Equipment Setup

Meter

Reading

Angle of

Receiver

0°

10°

20°

30°

40°

50°

Meter

Reading

Angle of

Receiver

70°

80°

90°

100°

110°

120°

Meter

Reading

Angle of

Receiver

140°

150°

160°

170°

180°

60° 130°

Table 5.1

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④Set up the equipment as shown in Figure 5.4. Reset

the Receivers angle to 0-degrees (the horns should

be oriented as shown with the longer side horizon-

tal).

⑤Record the meter reading when the Polarizer is aligned

at 0, 22.5, 45, 67.5 and 90-degrees with respect to the

horizontal.

⑥Remove the Polarizer slits. Rotate the Receiver so the

axis of its horn is at right angles to that of the Transmit-

ter. Record the meter reading. Then replace the Polar-

izer slits and record the meter readings with the Polarizer slits horizontal, vertical, and at 45-

Figure 5.4 Equipment Setup

Angle of

Slits

Horizontal

Vertical

45°

Meter Reading

Angle of

Polarizer

0° (Horiz.)

22.5°

45°

67.5°

90° (Vert.)

Meter Reading

degrees.

Questions

①If the Receiver meter reading (M) were directly proportional to the electric field component

(E) along its axis, the meter would read the relationship M = Mocosθθ

θθ

θ (where θθ

θθ

θ is the angle

between the detector and Transmitter diodes and Mo is the meter reading when θθ

θθ

θ = 0). (See

Figure 5.2). Graph your data from step 2 of the experiment. On the same graph, plot the

relationship Mo cosθθ

θθ

θ. Compare the two graphs.

②The intensity of a linearly polarized electromagnetic wave is directly proportional to the square of

the electric field (e.g., I = kE2 ). If the Receiver’s meter reading was directly proportional to the

incident microwave’s intensity, the meter would read the relationship M = Mocos2θθ

θθ

θ. Plot this rela-

tionship on your graph from question 1. Based on your graphs, discuss the relationship between the

meter reading of the Receiver and the polarization and magnitude of the incident microwave.

③Based on your data from step 5, how does the Polarizer affect the incident microwave?

④Can you explain the results of step 6 of the experiment. How can the insertion of an additional po-

larizer increase the signal level at the detector? ( HINT: Construct a diagram like that shown in

Figure 5.2 showing (1) the wave from the Transmitter; (2) the wave after it passes through the Polar-

izer; and (3) the component detected at the detector diode.)

012-04630G Microwave Optics

Experiment 6: Double-Slit Interference

EQUIPMENT NEEDED:

- Transmitter, Receiver - Goniometer, Rotating

- Component Holder - Metal Reflectors (2)

- Slit Extender Arm - Narrow Slit Spacer

- Wide Slit Spacer

Introduction

In Experiment 3, you saw how two waves moving in

opposite directions can superpose to create a standing

wave pattern. A somewhat similar phenomenon

occurs when an electromagnetic wave passes through

a two-slit aperture. The wave diffracts into two

waves which superpose in the space beyond the aper-

tures. Similar to the standing wave pattern, there are

points in space where maxima are formed and others

where minima are formed.

With a double slit aperture, the intensity of the wave

beyond the aperture will vary depending on the angle

of detection. For two thin slits separated by a dis-

tance d, maxima will be found at angles such that

d sinθθ

θθ

θ = nλλ

λλ

λ. (Where θθ

θθ

θ = the angle of detection, λλ

λλ

λ = the wavelength of the incident radiation,

and n is any integer) (See Figure 6.1). Refer to a textbook for more information about the nature

of the double-slit diffraction pattern.

Procedure

①Arrange the equipment as shown in Figure 6.2. Use

the Slit Extender Arm, two Reflectors, and the Nar-

row Slit Spacer to construct the double slit. (We

recommend a slit width of about 1.5 cm.) Be precise

with the alignment of the slit and make the setup as

symmetrical as possible.

②Adjust the Transmitter and Receiver for vertical po-

larization (0°) and adjust the Receiver controls to give

a full-scale reading at the lowest possible amplifica-

tion.

③Rotate the rotatable Goniometer arm (on which the

Receiver rests) slowly about its axis. Observe the meter readings.

④Reset the Goniometer arm so the Receiver directly faces the Transmitter. Adjust the Receiver

controls to obtain a meter reading of 1.0. Now set the angle θθ

θθ

θ to each of the values shown in

Table 6.1. At each setting record the meter reading in the table. (In places where the meter read-

ing changes significantly between angle settings, you may find it useful to investigate the signal

level at intermediate angles.)

Figure 6.1 Double-Slit Interference

Figure 6.2 Equipment Setup

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⑤Keep the slit widths the same, but change

the distance between the slits by using the

Wide Slit Spacer instead of the Narrow

Slit Spacer. Because the Wide Slit Space

is 50% wider than the Narrow Slit Spacer

(90mm vs 60mm) move the Transmitter

back 50% so that the microwave radiation

at the slits will have the same relative

intensity. Repeat the measurements.

(You may want to try other slit spacings as

well.)

Questions

①From your data, plot a graph of meter

reading versus θθ

θθ

θ. Identify the angles at

which the maxima and minima of the

interference pattern occur.

②Calculate the angles at which you would expect the maxima and minima to occur in a standard two-

slit diffraction pattern—maxima occur wherever d sinθθ

θθ

θ = nλλ

λλ

λ, minima occur wherever

d sinθθ

θθ

θ = nλλ

λλ

λ/2. (Check your textbook for the derivation of these equations, and use the wavelength

measured in experiment 3.) How does this compare with the locations of your observed maxima and

minima? Can you explain any discrepancies? (What assumptions are made in the derivations of the

formulas and to what extent are they met in this experiment?)

③Can you explain the relative drop in intensity for higher order maxima? Consider the single-slit dif-

fraction pattern created by each slit. How do these single slit patterns affect the overall interference

pattern?

➤➤

➤NOTE:

① Wavelength at 10.525 GHz = 2.85 cm.

② The experimenter’s body position may affect the results.

Angle Meter Reading

45°

50°

55°

60°

65°

Angle Meter Reading

0°

5°

10°

15°

20°

25°

30°

35°

40°

70°

75°

80°

85°

Table 6.1

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Experiment 7: Lloyd's Mirror

EQUIPMENT NEEDED:

- Transmitter - Receiver

- Goniometer - Fixed Arm Assembly

- Component Holder - Reflector (1)

- Meter Stick

Introduction

In earlier experiments, such as 3 and 6, you observed

how a single electromagnetic wave can be diffracted

into two waves and, when the two components join

back together, they form an interference pattern.

Lloyd’s Mirror is another example of this phenom-

enon. Just as with the other interference patterns you

have seen, this interference pattern provides a conve-

nient method for measuring the wavelength of the

radiation.

Figure 7.1 is a diagram for Lloyd’s mirror. An elec-

tromagnetic wave from point source A is detected at

point C. Some of the electromagnetic wave, of

course, propagates directly between point A and C,

but some reaches C after being reflected at point B. A maximum signal will be detected when

the two waves reach the detector in phase. Assuming that the diagram shows a setup for a maxi-

mum signal, another maximum will be found when the Reflector is moved back so the path

length of the reflected beam is AB + BC + λ λ

λ λ

λ.

Procedure

①Arrange the equipment as shown in Figure 7.2. For best results, the Transmitter and Receiver

should be as far apart as possible. Be sure the Receiver and Transmitter are equidistant (d1) from

the center of the Goniometer degree plate and that the horns are directly facing each other. (See

Figure 7.3 for location of effective points of transmission and reception). Also be sure that the

surface of the Reflector is parallel to the axis of the

Transmitter and Receiver horns.

②While watching the meter on the Receiver, slowly slide

the Reflector away from the Degree Plate. Notice how

the meter reading passes through a series of minima

and maxima.

③Find the Reflector position closest to the degree plate

which produces a minimum meter reading.

④Measure and record h1, the distance between the center

of the degree plate and the surface of the Reflector.

h1 = _________________________.

Figure 7.1 Lloyd's Mirror

Figure 7.2 Equipment Setup

1.0 meter or more

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⑤Slowly slide the Reflector away from the degree plate until the meter reading passes through a maxi-

mum and returns to a new minimum. Measure and record h2, the new distance between the center

of the degree plate and the surface of the Reflector.

h2 = _________________________.

⑥Measure d1 the distance between the center of the degree scale and the Transmitter diode.

d1 = _________________________.

⑦Use your collected data to calculate λλ

λλ

λ, the wavelength of the microwave radiation.

λ = _________________________.

⑧Change the distance between the Transmitter and Receiver and repeat your measurements.

h1 = _________________________.

h2 = _________________________.

d1 = _________________________.

λ = _________________________.

Questions

①What is the advantage in having the effective transmission and reception points equidistant from the

center of the degree plate in this experiment?

➤➤

➤ NOTE: Don’t stand in front of the apparatus while conducting the experiment. Your body acts as

a reflector. Therefore, try to stand to one side behind the plane of the antenna horn.

5 cm 5 cm

Figure 7.3 Transmission and Reception Points

Receiver

Transmitter

Effective Point of Emission of

Transmitter Signal Receiver

Effective Point of Reception of

Transmitter Signal

012-04630G Microwave Optics

Experiment 8: Fabry-Perot Interferometer

EQUIPMENT NEEDED:

- Transmitter - Receiver

- Goniometer - Component Holders (2)

- Partial Reflectors (2)

Introduction

When an electromagnetic wave encounters a partial reflector, part of the wave reflects and part of

the wave transmits through the partial reflector. A Fabry-Perot Interferometer consists of two

parallel partial reflectors positioned between a wave source and a detector (see Figure 8.1).

The wave from the source reflects back and forth between the two partial reflectors. However,

with each pass, some of the radiation passes through to the detector. If the distance between the

partial reflectors is equal to nλλ

λλ

λ/2, where λλ

λλ

λ is the wavelength of the radiation and n is an integer,

then all the waves passing through to the detector at any instant will be in phase. In this case, a

maximum signal will be detected by the Receiver. If the distance between the partial reflectors is

not a multiple of λλ

λλ

λ/2, then some degree of destructive interference will occur, and the signal will

not be a maximum.

Procedure

①Arrange the equipment as shown in Figure 8.1. Plug in

the Transmitter and adjust the Receiver controls for an

easily readable signal.

②Adjust the distance between the Partial Reflectors and

observe the relative minima and maxima.

③Adjust the distance between the Partial Reflectors to

obtain a maximum meter reading. Record, d1, the

distance between the reflectors.

d1 = _________________________.

④While watching the meter, slowly move one Reflector away from the other. Move the Reflector

until the meter reading has passed through at least 10 minima and returned to a maximum.

Record the number of minima that were traversed. Also record d2, the new distance between the

Reflectors.

Minima traversed = _________________________.

d2 = _________________________.

⑤Use your data to calculate λλ

λλ

λ, the wavelength of the microwave radiation.

λ = _________________________.

⑥Repeat your measurements, beginning with a different distance between the Partial Reflectors.

d1 = _________________________. Minima traversed = _________________________.

d2 = _________________________. λ = _________________________.

Figure 8.1 Fabry-Perot Interferometer

Partial Reflectors

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Questions

①What spacing between the two Partial Reflectors should cause a minimum signal to be delivered

to the Receiver?

②In an optical Fabry-Perot interferometer the interference pattern usually appears as a series

of concentric rings. Do you expect such a pattern to occur here? Why? Check to see if

there is one.

012-04630G Microwave Optics

Experiment 9: Michelson Interferometer

EQUIPMENT NEEDED:

- Transmitter, - Receiver

- Goniometer, - Fixed Arm Assembly

- Component Holders (2) - Rotating Table, Reflectors (2)

- Partial Reflector (1)

Introduction

Like the Fabry-Perot interferometer, the Michelson

interferometer splits a single wave, then brings the

constituent waves back together so that they superpose,

forming an interference pattern. Figure 9.1 shows the

setup for the Michelson interferometer. A and B are

Reflectors and C is a Partial Reflector. Microwaves

travel from the Transmitter to the Receiver over two

different paths. In one path, the wave passes directly

through C, reflects back to C from A, and then is re-

flected from C into the Receiver. In the other path, the

wave reflects from C into B, and then back through C

into the Receiver.

If the two waves are in phase when they reach the

Receiver, a maximum signal is detected. By moving

one of the Reflectors, the path length of one wave

changes, thereby changing its phase at the Receiver so

a maxium is no longer detected. Since each wave

passes twice between a Reflector and the Partial Re-

flector, moving a Reflector a distance λλ

λλ

λ/2 will cause a

complete 360-degree change in the phase of one wave at the Receiver. This causes the meter

reading to pass through a minimum and return to a maximum.

Procedure

①Arrange the equipment as shown in Figure 9.1. Plug in the Transmitter and adjust the Receiver

for an easily readable signal.

②Slide Reflector A along the Goniometer arm and observe the relative maxima and minima of the

meter deflections.

③Set Reflector A to a position which produces a maximum meter reading. Record, x1, the posi-

tion of the Reflector on the Goniometer arm.

x1 = _________________________.

④While watching the meter, slowly move Reflector A away from the Partial Reflector. Move the

Reflector until the meter reading has passed through at least 10 minima and returned to a maxi-

mum. Record the number of minima that were traversed. Also record x2, the new position of

Reflector A on the Goniometer arm.

Minima traversed = _________________________.

x2 = _________________________.

Figure 9.1 Michelson Interferometer

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⑤Use your data to calculate λλ

λλ

λ, the wavelength of the microwave radiation.

λ = _________________________.

⑥Repeat your measurements, beginning with a different position for Reflector A.

x1 = _________________________.

Minima traversed = _________________________.

x2 = _________________________.

λ = _________________________.

Questions

①You have used the interferometer to measure the wavelength of the microwave radiation. If you

already knew the wavelength, you could use the interferometer to measure the distance over which

the Reflector moved. Why would an optical interferometer (an interferometer using visible light

rather than microwaves) provide better resolution when measuring distance than a microwave inter-

ferometer?

An Idea for Further Investigation

Place a cardboard box between the Partial Reflector and Reflector A. Move one of the reflectors

until the meter deflection is a maximum. Slowly fill the box with styrene pellets while observing the

meter deflections. On the basis of these observations, adjust the position of Reflector A to restore the

original maximum. Measure the distance over which you adjusted the reflector. Also measure the

distance traversed by the beam through the pellets. From this data, can you determine the styrene

pellets’ index of refraction at microwave frequencies? (The wavelength of electromagnetic radiation

in a material is given by the relationship λλ

λλ

λ = λλ

λλ

λ0/n; where λλ

λλ

λ is the wavelength, λλ

λλ

λ0 is the wavelength

in a vacuum, and n is the index of refraction of the material.) Try boxes of various widths. You

might also try filling them with a different material.

012-04630G Microwave Optics

Experiment 10: Fiber Optics

EQUIPMENT NEEDED:

- Transmitter - Receiver

- Goniometer - Tubular Plastic Bags

- Styrene Pellets

Introduction

Light can propagate through empty space, but it can also propagate well through certain materi-

als, such as glass. In fiber optics, a thin, flexible glass tube functions as a transmission line for

light from a laser, much as a copper wire can function as a transmission line for electrical im-

pulses. In the same way that variation of the electrical impulses can carry information through

the copper wire (for example as a phone message), variation in the intensity of the laser light can

carry information through the glass tube.

Procedure

①Align the Transmitter and Receiver directly across from each other on the Goniometer, and adjust

the Receiver controls for a readable signal.

②Fill a tubular plastic bag with styrene pellets (tie the end or use a rubber band). Place one end of

the bag in the Transmitter horn. What happens to the meter reading? Now place the other end in

the Receiver horn. How does the intensity of the detected signal compare to the intensity when

the bag is not used?

③Remove the plastic bag and turn the Rotatable Goniometer arm until no meter deflection appears.

Place one end of the bag in the Transmitter horn, the other in the Receiver horn. Note the meter

reading.

④Vary the radius of curvature of the plastic bag. How does this effect the signal strength? Does

the signal vary gradually or suddenly as the radial curvature of the plastic bag changes? Find the

radius of curvature at which the signal begins to drop significantly.

Questions

①Check your textbook for information on Total Internal Reflection. Based on the radial curvature

when the signal begins to show attenuation as it passes through the plastic bag, determine the

angle of total internal reflection for the styrene pellets. Can you use this value to determine the

index of refraction of the styrene pellets?

②Would you expect the plastic bag filled with styrene pellets to work the same with radiation at

optical frequencies? Why?

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Notes

012-04630G Microwave Optics

Experiment 11: Brewster's Angle

EQUIPMENT NEEDED:

- Transmitter - Receiver

- Goniometer - Rotating Table

- Polyethylene Panel

Introduction

When electromagnetic radiation passes from one media into another, some of the radia-

tion usually reflects from the surface of the new medium. In this experiment, you will

find that the magnitude of the reflected signal depends on the polarization of the radiation.

In fact, at a certain angle of incidence—known as Brewster’s Angle—there is an angle of

polarization for which no radiation will be reflected. (Check your textbook for more infor-

mation on Brewster’s Angle.)

Procedure

①Arrange the equipment as shown in Figure 11.1, setting

both the Transmitter and the Receiver for horizontal

polarization (90°).

②Adjust the Panel so the angle of incidence of the micro-

wave from the Transmitter is 20°. Rotate the Goniom-

eter arm until the Receiver is positioned where it can

detect the maximum signal reflected from the Panel.

Adjust the Receiver controls for a mid-scale reading,

and record the meter reading in Table 11.1.

Angle Meter Reading

(Horizontal Polarization)

Meter Reading

(Vertical Polarization)

20°

25°

30°

35°

40°

45°

50°

55°

60°

65°

70°

75°

Table 11.1

Figure 11.1 Equipment Setup

Polyethylene

Panel

Rotating

Table

Angle of

Incidence

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③Without changing the angles between the transmitted beam, the Polyethylene Panel, and the Re-

ceiver, rotate both the Transmitter and the Receiver horns so they align for vertical polarization (0°).

Record the new meter reading in the table.

④Repeat steps 2 and 3, setting the angle of incidence to each of the values shown in the table below.

At each point set the Transmitter and Receiver for horizontal polarization and record the meter read-

ing; then set them for vertical polarization and record that reading as well.

⑤Plot a graph of “Meter Reading” versus “Angle of Incidence”. Plot both the vertical and horizontal

polarizations on the same graph. Label Brewster’s Angle—the angle at which the horizontally polar-

ized wave does not reflect.

Questions

①Explain how Polaroid sun-glasses can be used to reduce the glare caused by the sun setting over a

lake or the ocean. Should the glasses be designed to block vertically or horizontally polarized light?

②Could you use the microwave apparatus to locate Brewster’s Angle by examining the transmitted

wave rather than the reflected wave? How?

012-04630G Microwave Optics

Experiment 12: Bragg Diffraction

EQUIPMENT NEEDED:

- Transmitter - Receiver

- Goniometer - Rotating Table

- Cubic Lattice

Introduction

Bragg’s Law provides a powerful tool for investigating crystal structure by relating the

interplanar spacings in the crystal to the scattering angles of incident x-rays. In this experiment,

Bragg’s Law is demonstrated on a macroscopic scale using a cubic “crystal” consisting of 10-mm

metal spheres embedded in an ethafoam cube.

Before performing this experiment, you should understand the theory behind Bragg Diffraction.

In particular, you should understand the two criteria that must be met for a wave to be diffracted

from a crystal into a particular angle. Namely, there is a plane of atoms in the crystal oriented

with respect to the incident wave, such that:

①The angle of incidence equals the angle of reflection, and

②Bragg's equation, 2dsinθ = nλλ

λλ

λ, is satisified; where d is the spacing between the diffracting

planes, θ is the grazing angle of the incident wave, n is an integer, and λλ

λλ

λ is the wavelength of the

radiation.

Procedure

①Arrange the equipment as shown in Figure 12.1.

②Notice the three families of planes indicated in Figure

12.2. (The designations (100), (110), and (210) are

the Miller indices for these sets of planes.) Adjust the

Transmitter and Receiver so that they directly face

each other. Align the crystal so that the (100) planes

are parallel to the incident microwave beam. Adjust

the Receiver controls to provide a readable signal.

Record the meter reading.

Figure 12.1 Equipment Setup

Rotating Table

Cubic Lattice (210) (110)

(100)

Figure 12.2 "Atomic" Planes of the

Bragg Crystal

Figure 12.3 Grazing Angle

Grazing Angle

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③Rotate the crystal (with the rotating table) one degree clockwise and the Rotatable Goniometer arm

two degrees clockwise. Record the grazing angle of the incident beam and the meter reading. (The

grazing angle is the complement of the angle of incidence. It is measured with respect to the plane

under investigation, NOT the face of the cube; see Figure 12.3.)

④Continue in this manner, rotating the Goniometer arm two degrees for every one degree rotation of

the crystal. Record the angle and meter reading at each position. (If you need to adjust the

INTENSITY setting on the Receiver, be sure to indicate that in your data.)

⑤Graph the relative intensity of the diffracted signal as a function of the grazing angle of the incident

beam. At what angles do definite peaks for the diffracted intensity occur?

Use your data, the known wavelength of the microwave radiation (2.85 cm), and Bragg’s Law to

determine the spacing between the (100) planes of the Bragg Crystal. Measure the spacing between

the planes directly, and compare with your experimental determination.

⑥If you have time, repeat the experiment for the (110) and (210) families of planes.

Questions

①What other families of planes might you expect to show diffraction in a cubic crystal? Would you

expect the diffraction to be observable with this apparatus? Why?

②Suppose you did not know beforehand the orientation of the “inter-atomic planes” in the crystal.

How would this affect the complexity of the experiment? How would you go about locating the

planes?

The Bragg Diffraction Experiment was developed by Dr. Harry Meiners of Rensselaer Poly-

technic Institute.

012-04630G Microwave Optics

Teacher's Guide

Exp 1 – Introduction to the System

Notes – on Procedure

④ The meter reading does not vary with distance in an

entirely predictable way, since the microwaves form

standing waves between the transmitter and receiver at

certain distances. In addition, the meter is not directly

related to either the electric field or the intensity of the

incident beam. The meter is useful for measuring rela-

tive intensity at a constant distance, polarization, and

so on.

⑤The meter reading oscillates as the distance is de-

creased. (See experiment 3, method B)

⑥The presence of a reflector increases the meter reading.

⑦The receiver detects no signal when the transmitter

and receiver are at 90° to each other.

⑧The transmitter has a roughly gaussian output distribu-

tion, with the 1/e points at about ±20°.

There is no significant difference between the output

distributions in the horizontal and vertical orientations

Answers – to Questions

①/② The meter reading is not proportional to either the

electric field or the intensity.

③ The transmitter output is more plane wave than

spherical wave, but it has characteristics of both.

012-04630G

Microwave Optics

Notes – on Procedure

⑤

Angle of Incidence Angle of Reflection

20° 23°

30° 31°

40° 41°

50° 54°

60° 63°

70° 85°*

80° 78°*

90° 70°*

The last three points are suspect, due to the spread in the

output pattern of the transmitter. See experiment 1, part 8.

Answers – to Questions

①The angle of incidence equals the angle of reflection.

This does hold for all angles, although it is not clear in

this experiment due to the spread in the output pattern.

②Some of the wave appeared to reflect into different

angles; particularly when the angle of incidence was

70° or 90°. This is actually a diffraction effect, not re-

flection.

③The transmitter does not produce a perfect plane wave,

and this does affect the results.

Answers – to Questions for Additional

Experimentation

①Intensity of the reflection does vary with the angle of

incidence; from this we can deduce that the reflector is

not 100% efficient.

②In general, conductors will reflect the microwaves

much better than non-conductors.

Exp 3– Standing Waves - Measuring Wavelengths

Notes – on Procedure

➤ NOTE: There are two different methods

described in this lab. The first method, using the

Microwave Detector Probe, is the easier of the

two; but either will work.

Method A

# of antinode Distance Wavelength

5 7.1 2.84

10 14.1 2.82

15 20.0 2.67

19 27.5 2.89

Average: 2.81

Frequency: 1.07E+10

Method B

# of antinode Distance Wavelength

10 13.3 2.66

15 20.5 2.73

Average: 2.70

Frequency: 1.11E+10

(Fewer points were taken due to the limited resolution

of this method.)

Answers – to Questions

The value obtained by the first method was 1.5% off,

and the second was 5.6% off. If it is possible to take

more data points on the second method, you may get

better results.

Exp 2 – Reflection

012-04630G Microwave Optics

Exp 4– Refraction Through a Prism

Notes – on Procedure

①The empty foam prism absorbs the radiation by a very

slight amount.

③θ = 7° (± 1°)

④θ1 = 22°

θ2 = 29°

⑤/⑥ Our experimental value was: n1 = 1.3 ± 0.05

Answers – to Questions

①This assumption is valid. According to Snell’s law, if

the angle of incidence is zero, the angle of refraction is

zero also.

③The index for a solid styrene prism would be higher,

due to the greater “optical” density of the solid mate-

rial.

General Notes

①The prism mold may be filled with other materials as

well. We used water for one such test. The water ab-

sorbs most of the microwave energy (this is how a mi-

crowave oven works) but enough gets through that it

may be measured on the most sensitive scale of the

receiver. We found that n = 1.4 ± 0.05.

②The jar that the styrene pellets are shipped in has been

used as a cylindrical lens, with limited success.

012-04630G

Microwave Optics

Exp 5– Polarization

Notes – on Procedure

②

➤➤

➤NOTE: There is a consistent “glitch” in the

data at a polarization angle of about 40 and 140

degrees which is not entirely explained by the

non-linearity of the receiver. (This glitch is also

present when the polarizer slits are used in part 5

of this lab.) If you have an explanation of why

this occurs, please let us know.

③Continued rotation of the receiver results in duplica-

tion of the pattern above.

⑤

⑥The meter reading is zero when the polarizer slits are

oriented vertically or horizontally. When the slits are

at 45°, the meter reads about 30% of its maximum

value for that distance.

Answers – to Questions

①/ ② The meter reading more closely matches the inten

sity than it does the electric field.

③The polarizer transmits only the component of the

wave parallel to the polarizer.

④When the transmitter and polarizer are at 90°, the

wave is completely blocked. Placing a polarizer at 45°,

however, introduces a component of the wave parallel

to the receiver so that some of the wave is then picked

up.

012-04630G Microwave Optics

Exp 6– Double-Slit Interference

Answers – to Questions

①/② For the 7.6 cm spacing, the maxima should occur at

22° and 48°.

For the 10.6 cm spacing, the maxima should be at 15°,

33°, and 54°.

These theoretical values are closely matched by the

experimental data. The theory assumes that the dis-

tance between slit plates and receiver are large com-

pared to the slit spacing and wavelength. This require-

ment is barely met in the experimental setup used, and

could cause trouble in some situations.

③The single-slit pattern (see experiment 7) acts as an

upper limit to the multiple-slit pattern from this experi-

ment.

General Notes

①The position of the experimenter has a definite effect

on the measurements in this experiment. Experiment

to find just how much effect there is with your particu-

lar setup, and then take your data accordingly.

②Single-slit diffraction may also be attempted on this

apparatus, though we don’t recommend it. The dis-

tances are too short, relative to the wavelength; so the

analysis requires the Fresnel/Kirchoff approach instead

of the Fraunhoffer approximation. Even with the

Fresnel approach, the “fringes” are too small to be

seen adequately.

Basically, it doesn’t work well at all.

012-04630G

Microwave Optics

Notes – on Procedure

③-⑧

Fringe# h (mm) path length (mm) lambda

1 85 720

2 138 752 32.10

3 171 779 26.63

4 200 806 27.15

5 227 834 28.11

6 251 861 27.06

7 275 890 28.83

8 298 919 29.13

9 317 944 25.08

10 338 973 28.69

average: 27.59

stdev: 1.37

An alternate method is to graph path length versus fringe

number and take the slope of the graph. This slope will be

the wavelength.

From this, λ = 2.79 cm.

Answers – to Questions

①It simplifies the calculations.

Exp 7– Lloyd’s Mirror

012-04630G Microwave Optics

Exp 8– Fabry-Perot Interferometer

Notes – on Procedure

①-④ For best results, do not move the reflector closest

to the transmitter. There are actually two standing

wave patterns that may form: one between the trans-

mitter and first reflector, and one between the two re-

flectors. (There may also be others, such as between

the second reflector and the receiver or the second re-

flector and the transmitter; but these will be negli-

gible.) Moving the first reflector will change the am-

plitude of the wave coming into the region between

the reflectors, and thus give erroneous results.

⑤/⑥ = 2.85 cm

‰ NOTE: An alternate method of analysis is to

make a graph of distance versus fringe number and

take the slope of the line to find the wavelength.

λ = 2.84 cm

Answers – to Questions

First Plate: 75.2

nsecond plate distance Ð

1 54.9 20.3

2 53.6 21.6 1.3

3 52.2 23.0 1.4

4 50.9 24.3 1.3

5 49.4 25.8 1.5

6 47.9 27.3 1.5

7 46.5 28.7 1.4

8 45.0 30.2 1.5

9 43.6 31.6 1.4

10 42.1 33.1 1.5

11 40.8 34.4 1.3

12 39.4 35.8 1.4

13 38.0 37.2 1.4

14 36.6 38.6 1.4

15 35.1 40.1 1.5

16 33.8 41.4 1.3

17 32.3 42.9 1.5

18 30.9 44.3 1.4

19 29.4 45.8 1.5

20 27.9 47.3 1.5

21 26.5 48.7 1.4

22 25.0 50.2 1.5

average: 1.42

①Minima will occur when the spacing is nλ/4, where n

is an odd integer.

② We would normally expect just such a pattern; in this

case, however, the reflectors are too small in relation

to the wavelength used; so the next “ring” is located

beyond the edge of the reflectors and may not be seen.

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Microwave Optics

Exp 9– Michelson Interferometer

Notes – on Procedure

①-④ Best results are obtained when the mirrors are both

a significant distance from the central beamsplitter. If

either mirror is too close to the center, the maxima

splits into two peaks due to secondary interference ef-

fects.

nRefl. Pos. _

1 75.0

2 76.4 1.4

3 77.9 1.5

4 79.4 1.5

5 80.8 1.4

6 82.2 1.4

7 83.7 1.5

8 85.1 1.4

9 86.6 1.5

10 88.0 1.4

11 89.4 1.4

12 90.9 1.5

13 92.3 1.4

14 93.8 1.5

15 95.2 1.4

16 96.6 1.4

17 98.1 1.5

18 99.5 1.4

19 101.0 1.5

20 102.4 1.4

21 104.0 1.6

average: 1.45

From this we can calculate the wavelength as being

2.90 cm.

➤➤

➤ NOTE: An alternate method of analysis is to

plot the reflector position versus fringe number.

The slope of this line will be half the wavelength.

By this method, we calculate the wavelength as

2.89 cm.

Answers – to Questions

①The limit of resolution for distance measurements with

a Michelson interferometer is roughly 1/4 the wave-

length of the light used. Thus with these microwaves,

we can measure distance changes of about 7 mm.

With a visible-light interferometer and a wavelength of

633 nm (HeNe laser light) we can measure distance

changes of only 158 nm.

012-04630G Microwave Optics

Exp 10 – Fiber Optics

Exp 11– Brewster's Angle

Notes – on Procedure

Answers – to Questions

①Glare off water from a low source is primarily hori-

zontal in polarization, so sunglasses should be de-

signed to block horizontally polarized light.

Notes – on Procedure

②The meter reading with the “optical fiber” bag in place

can more than double the unobstructed meter reading.

This is because the bag prevents the normal spreading

of the beam, and directs all the microwave radiation

into the receiver horn.

③The bag can direct the beam through a full 90° turn

without measurable attenuation, if the curvature is

gradual.

④The signal begins to be attenuated with a radius of cur-

vature of about 5 cm, and drops off rather suddenly from

there. It is difficult to get consistent results, though.

Answers – to Questions

①Theoretically one can use the radius at which the mi-

crowaves begin to “leak” to determine the index of

refraction of the material. In reality, this is quite diffi-

cult. Our values for n using this method range from

1.1 to 1.4.

②The styrene pellets are very small, compared to the

microwave wavelength. Compared to visible

wavelengths, the pellets are enormous. Because of

this size difference, optical radiation is scattered by

the pellets and microwave radiation is transmitted.

Additional Idea

This apparatus may also be used as a demonstra-

tion of how the plane of polarization can be ro-

tated by multiple reflections. Rotate the transmitter

or receiver 90° to each other, so that no signal gets

through. Now put the bag of pellets between the

two. If the bag is held straight, there will be a zero

meter reading; but if the bag is curved into a spiral,

there will be a non-zero reading.

②Theoretically, one could do this by finding the

point at which there was no transmission of verti-

cally polarized light. We have not been able to get

good results in this experiment, however.

General Notes

①The index of refraction of the polyethylene is 1.5.

(Calculated from the dielectric constant at 10 GHz)

②One must be careful on this experiment to note that

there are actually two effects which are being mea-

sured. In addition to the Brewster’s angle reflection,

there is a certain amount of interference between the

front- and rear-surface reflections from the polyethyl-

ene. This interference causes extra peaks at 13.8° and

67.2°, and a local minimum at 43.6°. The interference

is notable enough that you may want to demonstrate

that, instead of the Brewster’s angle.

①-⑤

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Microwave Optics

Exp 12– Bragg Diffraction

Notes – on Procedure

①The polarization angle of the transmitter and receiver

(horizontal or vertical) does not matter.

⑤

Peaks occur at 18°, 24°, and 45°. These correspond to

plane spacings of 4.6cm, 3.4cm, and 4.0 cm (n = 2 for

the 45° peak) The actual spacing is 3.8 cm The first

peak is apparently a reflection off a different plane

than the one we’re measuring.

⑥110 Plane:

The peak at 29° gives a plane spacing of 2.9 cm; the

actual spacing is 2.7 cm

Answers – to Questions

①Other families of planes would be the 111 plane, the

101 plane, and so on. These would be difficult to ob-

serve with this apparatus due to the small size of our

“crystal”.

②Not knowing the orientation of the interatomic planes

of the crystal would increase the complexity of the

analysis. We could orient the crystal so that there was

maximum transmission; this would indicate to us a

100 plane. From there, we could try different angles

until we had enough data to assemble a likely picture

of the atomic spacing in the crystal.

➤ ➤

➤ NOTE: 10-15% error is reasonable for this

experiment.

012-04630G Microwave Optics

Appendix

Replacing the Receiver Battery

The Receiver is powered by two 9-volt alkaline batteries.

To replace them, simply remove the back panel of the Re-

ceiver (the panel with the rotational scale) by removing

the four screws. Install the new batteries, place them into

the holder as shown below, and replace the panel.

➤➤

➤ NOTE: We highly recommend that you use only

alkaline batteries.

Adjusting the Receiver

①Meter mechanical zero adjustment:

a. Turn the INTENSITY control to OFF.

b. The mechanical zero adjustment is located on the

meter, centered just below the meter face. With the

meter level and in the horizontal position, use a

small (1/8”) flat-blade screwdriver to adjust the

meter needle to read as close to 0 as possible.

②Electronic offset null adjustment:

a. Make sure the Transmitter is OFF by unplugging

it.

b. Turn the INTENSITY control to the 1X position.

c. Turn the VARIABLE SENSITIVITY control all

the way clockwise to its maximum setting.

d. The offset null adjustment is located through a

small hole just above the receiver antenna. Use a

small (1/8”) flat-blade screwdriver to adjust the

meter reading as close as possible to 0.

Replacing the Receiver Battery

➤➤

➤CAUTION: The electronics of the Transmitter

and Receiver assemblies contain diodes that are not

easily repairable. An attempt to repair diode assem-

blies may void your warranty.

➤➤

➤NOTE: Abnormal behavior (weak or erratic

meter readings, etc.) may be caused by weak batter-

ies. Please make sure your batteries are good before

giving us a call.

012-04630G

Microwave Optics

Schematic Diagram, Microwave Transmitter

Schematic Diagram, Microwave Receiver

Schematic Diagrams

012-04630G Microwave Optics

Replacement Parts List

Pasco Part No. Description Oty.

Transmitter

003-04319 Transmitter Assembly 1

113-132 Resistor, 1.3K, 1/4W, 5% 1

113-221 Resistor, 220 OHM, 1/4W 5% 1

113-471 Resistor, 470 OHM, 1/4W, 5% 1

430-085 IC-LM317T Positive V Reg. 1

445-005 Module, Microwave Transmitter 1

956-04311 Schematic, Microwave Transmitter 0

Receiver

003-04313 Receiver Assembly 1

004-04312 Receiver P.C.B. Assembly 1

113-153 Resistor, 15K, 1/4W, 5% 1

113-184 Resistor, 180K, 1/4W, 5% 1

113-621 Resistor,620 OHM 1/4W 5% 1

123-013 Resistor, 562K 1/4w 1% MF 1

123-016 Resistor, 51.1K 1/4w 1% MF 1

142-028 Trimpot, 50K 1T .5W CERM SA 1

216-026 Capacitor, 1000pF 5% 25V 1

412-012 Zener Diode, 1N751A 5.1V 5% .4W 2

430-086 IC-LF356N FET OP-AMP DIP 1

510-019 Switch, Rotary, 2POLE 6POS 1

527-001 L.E.D, Red 1

555-02811 Printed Circuit Board 1

113-152 Resistor, 1.5K, 1/4W, 5% 1

113-300 Resistor, 30 OHM, 1/4W, 5% 1

123-2001 Resistor, 2K 1/4W 1% MF 1

140-01716 Modified Pot - 5K 1

140-040 Pot, 5K 1

445-006 Module, Microwave Receiver 1

525-008 Meter 1

710-04313 Wire List, Microwave Receiver 0

956-04312 Schematic, Microwave Receiver 0

Components

003-01748 Assembly, Partial Reflector 2

003-02090 Assembly, Receiver/Transmitter Stand 2

003-02091 Assembly, Component Holder 2

003-02092 Assembly, Rotating Component Holder 1

003-02093 Assembly, Fixed Arm 1

003-02094 Assembly, Goniometer 1

003-02100 Assembly, Rotating Table 1

003-02116 Assembly, Styrene Pellets 1

003-02817 Assembly, Slit Extender Arm 1

540-002 Battery, 9 Volt, Alkaline 2

540-007 AC Adapter, 120VAC, 9VDC 1

or 540-013 AC Adapter, 220/240VAC, 9VDC 1

648-01749 Metal Reflector 2

648-02042 Slit Spacer, Narrow 1

648-02043 Slit Spacer, Wide 1

648-02052 Polarizer Screen 2

648-02082 Ethafoam Prism 1

735-027 Plastic Bag, 2 1/2” X 24” 4

➤ ➤

➤ NOTE: Replacement

parts can be purchased

from PASCO or at most

electronic stores.

012-04630G

Microwave Optics

Notes

012-04630G Microwave Optics

Technical Support

Feedback

If you have any comments about the product or

manual, please let us know. If you have any

suggestions on alternate experiments or find a

problem in the manual, please tell us. PASCO

appreciates any customer feedback. Your input helps

us evaluate and improve our product.

To Reach PASCO

For technical support, call us at 1-800-772-8700

(toll-free within the U.S.) or (916) 786-3800.

fax: (916) 786-3292

e-mail: techsupp@pasco.com

web: www.pasco.com

Contacting Technical Support

Before you call the PASCO Technical Support staff, it

would be helpful to prepare the following information:

➤If your problem is with the PASCO apparatus,

note:

-Title and model number (usually listed on the

label);

-Approximate age of apparatus;

-A detailed description of the problem/sequence of

events (in case you can’t call PASCO right away,

you won’t lose valuable data);

-If possible, have the apparatus within reach when

calling to facilitate description of individual parts.

➤If your problem relates to the instruction manual,

note:

- Part number and revision (listed by month and

year on the front cover);

- Have the manual at hand to discuss your

questions.

PASCO scientific 080187 Gun Diode Microwave Transmitter User Manual 012 04630G cov p65

PASCO scientific Gun Diode Microwave Transmitter 012 04630G cov p65

Users Manual

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