THE PHYSICS 11
LAB BOOK
Book 2: Labs 20 – 38
by
S. L. Morris
J. C. Fu
R. F. Whiting
Los Angeles Harbor College
© 2004
TABLE OF CONTENTS
SOUND
20. Standing Waves on Strings – Electric Tuning Fork .................................................... 73
21. The Velocity of Sound in Air – Air Column Resonance .............................................. 76
22. The Velocity of Sound in Metals ................................................................................. 79
23.
24.
25.
26.
27.
28.
29.
30.
31.
MAGNETISM AND ELECTRICITY
Magnetic Field Plotting .............................................................................................. 82
Electric Field Plotting ................................................................................................. 84
Ohm's Law – Series and Parallel Circuits ................................................................... 86
Kirchhoff's Rules ....................................................................................................... 90
AC Circuits and Resonance ...................................................................................... 94
The Magnetic Field of the Earth – Tangent Galvanometer ....................................... 100
The Potentiometer .................................................................................................... 103
The Wheatstone Bridge ............................................................................................ 106
The Heating Effect of an Electric Current ................................................................. 109
LIGHT
32.
33.
34.
35.
36.
Reflection & Refraction – The Optical Disk ............................................................... 112
The Thin Lens – Convex and Concave Lenses ......................................................... 116
Thin Lens – Optical Instruments ............................................................................... 120
Reflection and Refraction at Plane Surfaces ............................................................ 123
Spectral Lines ........................................................................................................... 126
RADIATION
PHYSICS
37. Radiation Detectors – The Geiger Counter .............................................................. 129
38. Radiation Absorption ................................................................................................ 133
Experiment 20
STANDING WAVES ON STRINGS
Electric Tuning Fork
INTRODUCTION
In this experiment the relationship between the tension in a stretched string and the
wavelength of the standing waves produced in it will be investigated.
Standing waves are produced by the interference between two traveling waves with the
same wavelength, velocity, frequency and amplitude traveling in opposite directions. The
equation for the velocity of propagation of transverse waves on a stretched string is:
v
T

where T is the tension in the string and  is the linear density (the mass per unit length of
the string). The velocity of propagation v, the frequency of vibration f, and the wavelength 
are related this way:
v = f
A stretched string has many modes of vibration. It may vibrate as a single segment, in
which case its length is half of a wavelength. It may vibrate in two segments with a node
(zero displacement) at the center as well as at each end; then the wavelength is equal to
the length of the string. The wavelengths of the many modes of vibration are given by the
relation:
2L

n
where L is the length of the string, is the wavelength, and n is an integer called the
harmonic number.
EQUIPMENT & MATERIALS
Electric tuning fork
Stroboscope
Electronic balance
Battery charger
Rod pulley
2 caliper jaws

Heating coil
Ruler

Meter stick
Leads & connectors
50-gram mass hanger
Double-wall calorimeter
- 73 -
Thick string
4-inch "C" Clamp
Slotted masses
Rod pulley table clamp
Scissors
EXPERIMENTAL PROCEDURE
1. Cut off a piece of string about 2 meters long and determine its length, mass and linear
density.
2. Clamp the apparatus to
one end of your table and
clamp the pulley to the
other end, as shown in
Figure 1.
Clamp the
string to one end of the
tuning fork and knot the
other end to the mass
hanger.
Suspend the
string over the pulley, and
adjust the pulley until the
string
is
horizontal.
Record the mass of the
mass hanger.
Fig. 1: Standing Waves on Strings Apparatus
3. Connect the positive terminal of the battery charger (set at 6 volts) to one tuning fork
terminal, connect the other tuning fork terminal to the heating coil and calorimeter filled
with water (used to decrease the tuning fork’s amplitude), and connect the other
terminal of the heating coil to the negative terminal of the battery charger, as shown in
Fig. 1. Set the fork into vibration by adjusting the contact point screw above and to the
left of the two terminals of the tuning fork apparatus, while tapping the tuning fork to
make it vibrate.
4. Measure the frequency of the tuning fork by using a stroboscope. Start with the strobe
frequency set at 4000 cycles per minute, and lower it until one stationary image of the
tuning fork is obtained. When lowering the frequency of the strobe, also observe that a
stationary image is obtained when the strobe frequency is ½, ⅓, ¼, etc., times that of
the tuning fork. Divide the number that appears on the stroboscope by 60 to get the
frequency of the tuning fork in cycles per second (Hertz).
5. Vary the tension of the string by adding masses to the hanger until the string vibrates in
five segments with maximum amplitude. Switch to the 12-volt setting if the vibrations
are too small to see easily. Measure the length of one segment from a point vertically
over the center of the pulley wheel to a node (zero amplitude), to the nearest millimeter
by sliding two caliper jaws over the meter stick. The wavelength will be twice the length
of one segment. Record in the data table the added mass in kilograms. Then record
the total mass m (added mass plus the mass hanger) in the data table. Record the
resulting tension T = mg in Newtons, with g = 9.80 m/s/s.
6. Repeat the procedure for 4, 3 and 2 segments by adding more mass to the pulley.
7. Compare the experimental velocity (v = f) with the theoretical velocity ( v  T /  ) by
computing the percent difference. When you have finished the experiment, empty the
calorimeter, and dry it thoroughly.
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LABORATORY REPORT: STANDING WAVES ON STRINGS
Length of string ___________ m
Mass of string ___________ kg
 = Linear Density of String =
mass of string
__________ kg / m
length of string
Mass of hanger ___________ kg
f = Frequency of vibrating tuning fork __________ Hz
Number of
Segments
= Harmonic
number
5
4
Length of one
segment
(m)
Wavelength  (m)
Velocity from
v = f
(m/s)
Added mass
(kg)
Total mass m (kg)
Tension T
(N)
Velocity from
v=
T/
(m/s)
% difference
- 75 -
3
2
Experiment 21
THE VELOCITY OF SOUND IN AIR
Air Column Resonance
INTRODUCTION
The resonance of sound waves in air columns will be used to determine the velocity
of sound in air. This is accomplished by producing standing waves in air in closed pipes
using sound of a certain frequency.
If a tuning fork is set into vibration and held over an air column, compressions and
rarefactions in the air travel down the tube and are reflected at the closed end of the tube
with a change of phase of 180o. If an integral number of quarter wavelengths just fit into
the tube, a condition called resonance occurs and the loudness of the note from the tuning
fork is increased. The lengths of tube for this resonance condition are given by:
L1 = (1/4), L2 = (3/4), L3 = (5/4, and so forth, as shown in Figure 1 below.
L1 = (1/4)
L2 = (3/4)
L3 = (5/4)
Fig. 1.
The position of the antinode at the open end of the tube is just outside the end of the
tube. This small, extra distance is called the "end correction", e, of the tube and is
proportional to the diameter of the tube. Theoretically, the end correction should be
approximately equal to 0.30 times the diameter of the tube. The actual lengths of the
resonating air column for the first three resonance conditions are given by:
(1/4) = L1 + e
from which:  = 2(L2 - L1),
(3/4) = L2 + e
or
 = 2(L3 - L2),
(5/4) = L3 + e
or
The value for the end correction e of the tube is given by : e =
- 76 -
 = (L3 - L1) .
L2  3L1
.
2
In this experiment, the length of a pipe, closed at the bottom, is
varied by changing the level of the water in the reservoir as shown in
Figure 2. The apparatus consists of a plastic tube about a meter long
mounted vertically on a tripod stand with a rubber hose connecting the
lower end of the tube to the movable reservoir. A tuning fork is held close
to the top of the tube with the prongs vibrating vertically.
The relation between the velocity of sound in air, the frequency of
the wave, and the wavelength is v = f. The velocity v can be calculated if
the frequency f is known and the wavelength is measured.
Fig. 2.
EQUIPMENT & MATERIALS
Resonance tube
Thermometer
2 tuning forks,  450 Hz
600 ml beaker
Rubber mallet
Metric ruler
EXPERIMENTAL PROCEDURE
1. Fill the reservoir when it is lowered all the way to the bottom of the apparatus. Then
adjust the water level in the resonance tube by raising the reservoir until the water level
is about 10 cm from the top of the tube.
2. Strike the tuning fork with the rubber mallet and hold the tuning fork horizontally over the
top end of the resonance tube about 1 cm above the tube so that the prongs vibrate
vertically, as shown in Figure 2. Lower the level of the water in the resonance tube by
lowering the reservoir tank and record the position when resonance is first heard.
(Watch out for harmonics; you should hear a definitely augmented note.)
3. Repeat the procedure two more times for a total of three independent trials and record
the data in the table.
4. Repeat steps 2 and 3 for the second position of resonance. This will be a distance of
½  lower down the tube.
5. Repeat steps 2 and 3 for the third position of resonance. You may need to drain some
water from the apparatus to obtain a large enough value of L 3.
6. Repeat the experiment for the second tuning fork with a different frequency.
7. Calculate values of wavelength, velocity of sound v = f, and the end correction e.
Determine an average value for the velocity of sound.
Theoretically, the velocity of sound in air in units of meters per second is
v = 331.7 + 0.607 T, where T is the ambient temperature of the air in degrees Celsius.
Calculate this theoretical value, and determine the percent difference from your own
value.
Calculate an average of your values of the end correction e. Theoretically,
e = k  (diameter of pipe) where k is a constant of proportionality. Calculate your value
of k, and compare it to the theoretical value of 0.30.
8. Drain and dry your equipment as thoroughly as possible.
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LABORATORY REPORT: THE SPEED OF SOUND IN AIR
Data Table 1: Tuning fork frequency = __________________ Hz
Trial
L1
(m)
L2
(m)
L3
(m)
1
2
3
Average
Average value of  __________ m
Velocity __________ m/s
e = __________ m
Data Table 2: Tuning fork frequency = __________________ Hz
Trial
L1
(m)
L2
(m)
L3
(m)
1
2
3
Average
Average value of  __________ m
Velocity __________ m/s
e = __________ m
________________________________________________________________________
Average value of the velocity of sound __________________ m/s
Ambient temperature ___________________ oC
Theoretical value of the velocity of sound __________________ m/s
Percent difference ___________________ %
Average value for e ___________________ m
Inside diameter of pipe ___________________ m
Constant of proportionality k ___________________
Percent difference between k and 0.30 ___________________ %
- 78 -
Experiment 22
THE VELOCITY OF SOUND IN METALS
INTRODUCTION
This acoustic tube apparatus was used historically to find the velocity of acoustic
(longitudinal) waves in metals by using the known velocity of sound in air. Its use in this
laboratory experiment is to give some direct laboratory experience in measuring the
velocity of acoustic waves in solids in the form of metal rods.
The theoretical velocity of a compressional wave in a metal is given by the following
relation:
Y .

v=
where Y is the Young's modulus and  is the density. Take this value of the velocity to
be the theoretical value for computing the percent difference.
For aluminum: Y = 7.0 X 1010 N/m2,  = 2700 kg/m3
For steel: Y = 19.2 X 1010 N/m2,  = 7800 kg/m3
For brass: Y = 9.2 X 1010 N/m2,  = 8400 kg/m3
The velocity v, frequency f, and wavelength , are related by: v = f
The velocity of sound in air varies with the temperature in degrees Celsius as:
v = (331.7 + 0.607 T) m/s
where T is the temperature in degrees Celsius.
EQUIPMENT & MATERIALS
Acoustic tube apparatus
Metal rods (aluminum, steel, brass)
2 Caliper jaws
Thermometer
Meter stick
Cork stopper
- 79 -
Cotton rag
Rosin
EXPERIMENTAL PROCEDURE
1. Clamp the rod exactly at its center, that is, at its length L/2 as shown in the Figure 1.
2. Spread the bottom of the length of the tube with a fraction of a teaspoon of cork dust (a
little goes a long way), and place a cork stopper at the far end of the tube.
Fig. 1. Experimental Apparatus
3. Stroke the rod with a rosined cloth using single straight strokes parallel to the rod. With
the proper technique, you should get intense vibrations and the cork dust will gather in a
pattern showing compressions and rarefactions. The position of the tube itself can be
adjusted lengthwise to produce the best standing wave patterns in the cork dust. The
tube may also be rotated slightly after the stroke to show the pattern more clearly on the
side.
4. The standing waves in a column of air create an alternating series of nodes and
antinodes. At each antinode the air vibrates horizontally, pushing the cork dust away.
The distance between antinodes is half a wavelength. Select one antinode, and
measure the distance from the antinode on its left to the antinode on its right (see Fig.
1). This equals the wavelength in air, air. Use caliper jaws on the meter stick to
measure this as accurately as possible.
5. Calculate the frequency of the sound in air f = v airair. Since the air vibrates because
the rod vibrates, this must equal the frequency of the sound waves in the rod.
6. The center of the metal rod is a node (it can’t vibrate) and the ends are antinodes.
Therefore, the wavelength of the sound in the rod (rod) is twice the length of the rod.
Calculate the velocity of sound in the rod, and compare it to the theoretical value by
computing the percent difference.
7. Repeat the experiment for the two other rods.
- 80 -
LABORATORY REPORT: THE SPEED OF SOUND IN METALS
Ambient temperature __________________ oC
Velocity of sound in air at ambient temperature __________________ m/s
Type of Rod
Aluminum
Length of Rod
(m)
Wavelength of
Sound in Air, air
(m)
Frequency of Sound
in Rod = f = vair/air
(m)
(m)
(Hz)
Experimental Velocity
of Sound in Rod = f rod
(m/s)
Theoretical Velocity
of Sound in Rod =
Y/
(m/s)
Percent difference
- 81 -
Steel
Brass
Experiment 23
MAGNETIC FIELD PLOTTING
INTRODUCTION
A compass is a small horizontal magnetized needle pivoted around its center,
permitting the needle to point in the direction of the Earth’s magnetic field. A magnet is a
bar of metal (usually iron) that has been magnetized, creating a magnetic field around it.
The magnetic field of a bar magnet can be pictured as exiting the bar at its north magnetic
pole, curving around the outside of the bar magnet and re-entering at its south magnetic
pole. A bar magnet in the presence of the Earth’s magnetic field creates a single magnetic
field that is influenced by both sources. In this experiment, you will use the compass to
trace out the magnetic field generated by the Earth and the bar magnet.
EQUIPMENT & MATERIALS
Magnetic compass
Plywood board
11 X 34 drawing paper French curve
Meter stick
Bar magnet
Colored pencils
Masking tape
EQUIPMENT & MATERIALS FOR THE INSTRUCTOR DEMONSTRATION
2 sheets of large drawing paper 5 horseshoe magnets
5 Plexiglas sheets
Iron filings
4 bar magnets
EXPERIMENTAL PROCEDURE
1. Place the plywood board between tables so
as to minimize interference from the metal
bar underneath each table. Place a large
sheet of paper on the board for plotting the
points on the magnetic field lines.
N
Magnetic
North
.
.
.
.
.
.
.
.
2. Determine the direction of magnetic north by
A
A
S
placing the compass on the sheet, and
making sure that no magnets are within a
five-foot radius of the compass. Orient the
board and paper as shown in Figure 1, so the
Earth’s magnetic field runs approximately
Fig. 1.
parallel to the short side of the paper. Place
an arrow in the direction of magnetic north on one corner of the paper, and have all the
members of your lab group print their names there. Place a bar magnet on the west
edge of the paper, oriented as shown in Figure 1. Trace its outline, and label its poles
as ‘N’ and ‘S’. Place eight dots at 10-cm intervals between A and A.
- 82 -
3. Place the center of the compass on the dot nearest the magnet, and make dots as near
as possible to each end of the needle with a pencil. Move the compass needle so one of
these two dots is now under the center of the needle. Make another dot at the forward
end. Continue in this fashion, following up from the previous dot and working both ways
from the original dot, until either the magnet or the end of the paper is reached. Use the
French curve to connect all dots for the line with a smooth curve.
4. Repeat step 3 for the other seven dots, using different colors for each magnetic field
line.
5. Move the compass from A to A, until it seems to rotate aimlessly when tapped, or else
points perpendicular to magnetic north. It will take some careful observation to locate
the best point. At this point, the magnetic field of the magnet cancels the horizontal
component of the magnetic field for the Earth, which is approximately one-fourth gauss
or 0.000025 Teslas. Label this point as the neutral point.
6. Each of the eight magnetic field lines on your paper should have an arrowhead pointed
from the white end to the red end of the compass needle. If there are any large blank
areas on the paper near the magnet, place the compass there and trace out additional
magnetic field lines. There should be enough field lines that you can estimate the
direction of the magnetic field everywhere on the paper.
7. Turn your paper over, then place a bar
magnet on the north edge of the
paper, as shown in Figure 2. Trace its
outline, and label its poles as ‘N’ and
‘S’.
Place eight dots at 10-cm
intervals between B and B, and
between C and C. Repeat steps
No. 3 to No. 6 to find the magnetic
field lines through the dots. Find the
neutral point between points A and A.
.
.
.
.
S
B
.
.
.
.
B
N
Magnetic
North
A
C
.
.
.
A
.
.
.
.
C
.
Fig. 2.
For the instructor; classroom demonstration.
Place magnets of various types under a sheet of clear Plexiglas, and scatter iron
filings on top. Tap the plate until the filings show the shape of the magnetic field clearly.
Try these combinations:
a) horseshoe magnet;
b) two parallel bar magnets with north poles adjacent;
c) two parallel bar magnets with south and north pole adjacent;
d) two horseshoe magnets with unlike poles facing each other about 5 cm apart;
e) two horseshoe magnets with like poles facing each other about 5 cm apart.
- 83 -
Experiment 24
ELECTRIC FIELD PLOTTING
INTRODUCTION
In this laboratory exercise we will determine the configuration of the electric field
lines between electrodes of various shapes which are held at a constant potential. This is
accomplished by plotting a set of equipotential lines (lines of equal voltage), and then
constructing the lines of the electric field which are at right angles to the equipotentials.
Each equipotential line is constructed from a set of equipotential points which are
located by means of the movable probe of the digital voltmeter. The four lines at potentials
of 2, 4, 6, and 8 volts are drawn and used to determine the configuration of the electric
field.
EQUIPMENT & MATERIALS
Electric field plotting apparatus
Hewlett-Packard multimeter
3 sheets of electrode paper
DC Regulated Power Supply
4 banana wires
2 alligator clips
French curve

Ruler
Plain paper
Carbon paper
EXPERIMENTAL PROCEDURE
1. Starting with the dipole electrode configuration (two silver circles), arrange the
apparatus as shown in Figure 1. To do this, place the plain paper on top of the cork
board, place the carbon paper black-side down on the plain paper, and place the
electrode paper on top. Take two pins and the two thin wires inside the electric field
plotting apparatus, and firmly pin one end of each wire to an electrode. The other end
of each should be grasped by an alligator clip connected to a wire, which is in turn
plugged into the DC Regulated Power Supply set between 10.0 volts and 12.0 volts.
Traditionally, red signifies the positive side and black is the negative side. The
electrodes are now charged, and have established an electric field across the electrode
paper.
Plain Paper
Carbon Paper
Electrode Paper
-
+
Voltmeter
10 - 12 V
Fig. 1 Electric Field Plotting Apparatus
(Dipole electrode configuration shown)
- 84 -
Probe
2. Set the multimeter to V
and connect the Common terminal to the negative terminal of
the power supply. Connect a long red wire to the right-side terminal of the multimeter.
This long red wire now serves as the probe; the multimeter will read the voltage (electric
potential) that the probe experiences. The multimeter now functions as a voltmeter.
3. Slide the probe gently along the surface of the electrode paper, until you find a point
near the negative electrode for which the voltmeter reads 2.0 volts. Press downwards
on the electrode, but not too hard. Try not to punch holes in the paper with the probe;
all that is needed is moderate pressure to transfer an impression from the carbon paper
to the plain paper. Find another point approximately one inch away with the same
voltage, and press down moderately to make another impression. Complete this
process until you encircle an electrode, or reach the edge of the page.
4. Repeat step 3 for some other voltages, such as 4.0, 6.0, and 8.0 V. Use additional
equipotentials as needed to delineate the field accurately; there should be no large
blank areas on the white sheet of paper.
5. Connect all of the equipotential points, for a particular voltage, with smooth lines.
Construct the electric field lines by drawing smooth lines perpendicular to the
equipotentials.
6. Trace the outlines of the two electrodes onto the piece of white paper, shade them in,
and label them as + and .
7. Repeat the entire procedure for the two other electrode configurations.
- 85 -
Experiment 25
OHM'S LAW
Series and Parallel Circuits
INTRODUCTION
When a voltage is applied across a circuit element such as a resistor, the current
drawn is directly proportional to the voltage applied. This relationship is known as Ohm's
law and is expressed mathematically as follows:
V = IXR
(Eq. 1)
where V is voltage expressed in volts, R is the proportionality constant called resistance
expressed in ohms, and I is the current in amperes.
If two or more resistors are connected in series, the equivalent circuit resistance is
the sum of the individual resistances (this result is obtained by applying Kirchoff's laws to
the circuit):
Requivalent = R1 + R2 + . . . + RN .
(Eq. 2)
The equivalent resistance for a circuit with resistors in parallel can be obtained
similarly:
1
R equivalent
= 1  1  ...  1 .
R1
R2
RN
(Eq. 3)
In this experiment Ohm's law will be verified both for a part of a circuit and for the
entire circuit by measuring the various currents and voltages. Ohm's law will be used to
find the value of an "unknown" resistance. The instructor will check all circuits before the
switch is closed. The dial on the Hewlett-Packard multimeter should be set at mA to make
it an ammeter, and the middle and right-hand terminals should be used. The dial on the BK
Precision multimeter should be set on 20 V
to make it a voltmeter, and the two rightmost terminals should be used.
EQUIPMENT & MATERIALS
BK Precision multimeter 
Hewlett-Packard multimeter
2 Decade resistance boxes
Leads and connectors
Unknown resistance
DC regulated power supply
- 86 -
Knife switch
EXPERIMENTAL PROCEDURE
A. SERIES RESISTORS:
1. Connect the circuit as shown in Figure 1, using
resistance boxes and an unknown resistor. Close
your switch only when making a reading.
Remember that voltage is measured across the
circuit element and the current is measured through
the element, i.e., you have to break into the circuit
to measure the current with the ammeter. The DC
Regulated Power Supply should be set to 6.0 volts.
200
300
Unknown
A
6V
Fig. 1.
2. Observe the readings of the ammeter when it is placed between the resistors to verify
that the current is the same through every point in a series circuit. Take voltage measurements across each resistor in turn. Use these numbers to fill in Tables 1A and 2A.
3. Verify Ohm's law for each known resistor with these data, in Table 3A. Use Ohm's law
to compute the resistance of the "unknown" resistor.
4. Measure the voltage across the three resistors together (the source voltage) in order to
verify Ohm's law for resistors in series, in Table 4A.
B. PARALLEL RESISTORS:
1. Connect the circuit as shown in
Figure 2. Put the voltmeter across
each resistor in turn, observe and
fill in Table 1B. Also take a reading
across the combined resistors (the
source voltage).
6V
200
300
Unknown
Fig. 2.
2. Find the current through each resistor and the whole circuit with the ammeter.
3. Verify Ohm's law for each known resistor, in Table 3B. Use Ohm's law to find the value
of the "unknown" resistor.
4. Compute the combined resistance from the readings on the ammeter and voltmeter.
Verify the reciprocal resistance law for parallel resistors.
C. SERIES AND PARALLEL RESISTORS IN COMBINATION:
1. Connect the circuit as shown in Figure 3.
Measure the voltage across each resistor
and across the combination. Take ammeter
readings through each resistor. Find the total
resistance from these readings by applying
the laws of series and parallel resistors.
- 87 -
200
300
6V
Fig. 3
Unknown
LABORATORY REPORT: OHM'S LAW
A. SERIES CIRCUIT:
Table 1A: Voltmeter Readings
Table 2A: Ammeter Readings
Across 200
Through 200
Across 300
Through 300
Across Unknown
Through Unknown
Across Combination
Through Combination
Table 3A: Resistance Values
Nominal
From Ohm’s Law
(Use Table 1A & 2A, R=V/I)
Table 4A: Series circuit equivalent resistance:
From R = V/I =
source voltage
current in curcuit
From Eq. 2 and Table 3A
200
300
Unknown
B. PARALLEL CIRCUIT:
Table 1B: Voltmeter Readings
Table 2B: Ammeter Readings
Across 200
Through 200
Across 300
Through 300
Across Unknown
Through Unknown
Across Combination
Through Combination
Table 3B: Resistance Values
Nominal
200
From Ohm’s Law
(Use Table 1B & 2B, R=V/I)
Table 4B: Parallel circuit equivalent resistance:
From R = V/I =
source voltage
current in curcuit
From Eq. 3 and Table 3B
300
Unknown
- 88 -
C. SERIES-PARALLEL CIRCUIT:
Table 1C: Voltmeter Readings
Table 2C: Ammeter Readings
Across 200
Through 200
Across 300
Through 300
Across Unknown
Through Unknown
Across Combination
Through Combination
Table 3C: Resistance Values
Nominal
200
From Ohm’s Law
(Use Table 1C & 2C, R=V/I)
Table 4C: Combination circuit equivalent resistance
From R = V/I =
source voltage
current in curcuit
From Eqs. 2 & 3 and Table 3C
300
Unknown
- 89 -
Experiment 26
KIRCHHOFF’S RULES
INTRODUCTION
A number of simple electrical circuits can be solved mathematically (i.e., finding the value
of the current and its direction through a circuit element) using only Ohm's law; however,
more complex circuits require the use of Kirchhoff’s rules. The first of these is Kirchhoff’s
voltage rule, which is actually a restatement of the law of conservation of energy. It states
that the algebraic sum of the voltages around a circuit loop is equal to zero:
V = 0 .
When moving around a circuit loop, the voltage terms are positive when moving from
negative to positive across a battery, and when moving across a resistor against the flow of
electric current. Otherwise, they are negative.
The second of these rules is Kirchhoff’s current rule, and is in fact a restatement of the law
of the conservation of charge. This rule states that the algebraic sum of the currents into a
junction is zero:
I = 0 .
For each junction, the current terms are positive if the currents flow into the junction, and
negative if they flow out of the junction.
For example, suppose that R1 = 700 , R2 = 200  and R3 = 400 , in the circuit shown in
Figure 1. Adding the voltages around the left-hand loop, starting at the lower left and
moving clockwise, gives
1.5 + I1R1 + I2R2 –1.5 – 1.5 = 0,
so 700 I1 + 200 I2 = 1.5 .
Adding the voltages around the right-hand loop, starting at the lower right and moving
counter-clockwise gives
I3R3 + I2R2  1.5  1.5 = 0,
so 200 I2 + 400 I3 = 3.0 .
At the junction above R2,
I2  I1  I3 = 0,
so I2 = I1 + I3 .
These three equations in three unknowns can be solved to give I 1 = 0.0006 Amps,
I2 = 0.0054 Amps and I3 = 0.0048 Amps.
In this experiment, we will study the application of Kirchhoff’s rules to this circuit by
comparing the observed and calculated values of the currents in the circuits.
- 90 -
EQUIPMENT & MATERIALS
Hewlett-Packard multimeter
3 Decade resistance boxes
DC Regulated Power Supply
1½ V dry cell
Banana wires
2 spade lugs
EXPERIMENTAL PROCEDURE
I1
1. Set up the circuit as shown in
Figure 1.
You should use
small scraps of paper to label
the resistance boxes as R1, R2
and R3 to avoid confusion.
Set the DC Regulated Power
Supply to 3.0 volts, and be
sure to orient its terminals and
the battery terminals correctly.
R1
I2
I3
R2
1.5 V
R3
3.0 V
Fig. 1.
R1
()
100
100
110
120
140
150
150
200
200
220
250
280
300
300
310
400
600
2. Select one row of values of R1, R2 and
R3 from the table at the right:
Set the resistance boxes to their
appropriate resistance.
Measure
these currents experimentally, by
breaking the circuit in turn in each
branch and inserting the multimeter
with its dial set to mA. Be sure to
orient the multimeter correctly, so that
the current as shown in Figure 1 flows
into the right-hand terminal of the
multimeter, and out of the middle
Common terminal.
R2
()
100
200
100
100
120
100
100
200
400
240
100
240
200
200
100
200
160
R3
()
200
600
900
400
320
340
740
400
700
320
500
640
280
680
900
700
400
3. Write down the three Kirchhoff equations, using the nominal values of the resistances
and voltages, as was done in the Introduction, and solve for I1, I2 and I3. Show your
calculations clearly. You might find the method of determinants useful in solving your
system of equations. Calculate the percent difference between these values and the
experimental values.
4. Repeat the entire procedure using a different row of resistance values.
- 91 -
LABORATORY REPORT: KIRCHHOFF’S RULES
Data Table 1
Measured Current (A)
I1
I2
I3
Loop Voltage Equations: ____________________________________
____________________________________
Current Equation:
____________________________________
Calculations:
Calculations Table 1
Calculated Current
(A)
I1
I2
I3
- 92 -
% difference
Data Table 2
Measured Current (A)
I1
I2
I3
Loop Voltage Equations: ____________________________________
____________________________________
Current Equation:
____________________________________
Calculations:
Calculations Table 2
Calculated Current
(A)
I1
I2
I3
- 93 -
% difference
Experiment 27
AC CIRCUITS AND RESONANCE
INTRODUCTION
In this experiment the impedance Z, inductance L and capacitance C in alternating current
circuits will be studied.
The parameters of the circuit will be varied to produce the condition called resonance.
The inductive and capacitive reactance are defined as follows:
Inductive Reactance = XL = 2fL
Capacitive Reactance = XC = 1 .
2fC
XL
The impedance in a series AC
circuit is found by adding the
individual
reactances
and
resistance as vectors as shown
in Figure 1.
Z
XC
XL  XC
R
Fig. 1
Voltages are all equal to the
current I, times the individual or
combined reactances.
They
can be calculated from a
diagram which has the same
form as that shown in Figure 2.
VL = IXL
VC = IXC
Vtotal = IZ
VL  VC
VR = IR
Fig. 2
- 94 -
As the frequency is varied from low to high, a minimum value of total impedance Z is found
1
when XL = XC, or f =
. The value of Z at this resonance frequency is Z = R. If the
2 LC
applied voltage is kept constant, then when Z is a minimum, I will be at a maximum, so both
Z and I have the general form as shown in Figure 3.
Z
I
f
f
Fig. 3
I
Imax
The width of the curves in the
above is of great importance in
such devices as radio and TV
receivers (we only want one
channel at a time), and is
measured by the ratio of the
width to the center frequency, as
shown in Figure 4.
Small R
0.707 Imax
Larger R
f1 fo f2
f
Fig. 4
When the peak is narrow, the circuit
is said to have a high Q, where the
f
quality Q is defined as: Q = f o f .
2
1
A high Q corresponds to a small
value of the total series resistance
(coil resistance plus any other
resistance). Q can also be shown to
be
given
by Q
=
XL
,
R
Z for f = f 2
XL  XC = R
Z for f = f o (Z = R)
Z for f = f 1
45o
45o
XC  XL = R
where
XL = 2foL, with fo being the
resonant frequency.
Figure 5
indicates the relationship between Z,
R, XL and XC as f varies from f1 to fo
to f2.
Locus of points as f varies
Fig. 5
- 95 -
EQUIPMENT & MATERIALS
Simpson 420 function generator
Decade capacitor box
100- composition resistor
2 BNC-to-banana adapters
Coaxial cable, BNC ends
Banana wires
Frequency counter
Inductor, 0.01 Henry
French curve
1 sheet of graph paper
2 multimeters
Oscilloscope
2 alligator clips
Plastic triangle
EXPERIMENTAL PROCEDURE
A. Capacitive and Inductive Reactance
1. Set up the circuit as shown in Figure 6. Both
multimeters must be dialed to V to act as AC
voltmeters. Set the decade capacitance box to
0.5 F. Use alligator clips to connect the 100-
resistor in the circuit. Use the coaxial cable to
connect the function generator’s TTL output to the
frequency counter’s A input, and use the counter
to set the frequencies accurately by using the
“A Input”, setting the counter for a 1 second gate
time, and a frequency setting of <10MHz. Set the
function generator to maximum amplitude.
V
100 
V
5.0 X 107 F
Fig. 6
2. Take voltage readings across the function generator and resistor for each frequency
setting. Frequency settings may be made from 2,000 Hz to 10,000 Hz in 2,000-Hz
steps.
3. From Fig. 2, the voltage across the function generator V fg (= Vtotal) is the vector sum of
the voltage across the resistor VR and the voltage across the capacitor VC. From the
right-angle triangle, Vfg2 = VR2 + VC2. Use this equation and the observed values of
voltage to calculate VC.
4. Ohm’s law for the resistor is VR = IR. Calculate the current through the resistor.
5. Ohm’s law for the capacitor is VC = IXC. Because the resistor and capacitor are in
series, they experience the same current. Calculate the measured reactance X C.
6. Theoretically, the reactance of a capacitor is XC = 1/2fC. Calculate this value and
determine the percent difference between this and the measured value. A reasonable
agreement between these two values of XC validates the vector calculation of VC and
the theoretical calculation of XC. Notice that the equation Vfg = VR + VC, appropriate for
a DC circuit, does not match your data for this circuit.
7. Repeat the above procedure with the 10-mH inductor in the circuit instead of the
capacitor. For an inductor, Vfg2 = VR2 + VL2 and VL = IXL. Theoretically, the reactance
of an inductor is XL = 2fL.
- 96 -
B. RLC Series Resonance
1. Set up the apparatus as in Figure 1, by connecting
the output of the function generator in series to the
Hewlett-Packard multimeter (set to mA to make it an
ammeter), the 10 mH inductor, the decade
capacitance box set to 0.10 F and the 100-
resistor held by alligator clips. Turn on the ammeter
and press the AC/DC button (beside the Range
button) to produce a ~ sign in the display. This
indicates that the ammeter will measure AC instead
of DC current. Attach a BNC-to-banana adapter to
the Ch 1 input of the oscilloscope, and connect its
positive input to the positive output of the function
generator. The TTL output of the function generator
should remain connected to the A input of the
frequency counter.
L
C
A
R
~
Oscilloscope
Ch. 1
Fig. 7
2. Calculate the theoretical values of the resonance frequency f o, the bandwidth and
the quality from the values of resistance, inductance and capacitance.
3. Measure the root-mean-square current I on the multimeter over a range of
frequencies, starting with f = 2000 Hz and increasing by 500-Hz intervals. Maintain
Vtotal at 0.40 V peak-to-peak by monitoring the amplitude of the sine wave on the
oscilloscope and adjusting the amplitude of the function generator. A setting of 0.2
Volts/div gives a convenient size to the sine wave, and should peak 2 squares above
and 2 squares below the center-line. The wave can be centered by rotating the
POSITION dial on the oscilloscope. Place the measurements in Data Table 3.
4. Plot current I vs. frequency f on a piece of graph paper. Obtain extra readings as
necessary near the resonance frequency to clearly define the resonance peak. Use
a French curve to connect the data points as smoothly as possible.
5. Find f1 and f2 from this graph as the frequencies for which I = 0.707 Imax , as shown
in Figure 4. Calculate fo as the average of f1 and f2, and calculate the bandwidth
and quality from the values of f 1 and f2. Find the percent difference of these three
quantities from their theoretical values.
- 97 -
LABORATORY REPORT: AC CIRCUITS AND RESONANCE
Part A:
Data Table 1: Capacitive Reactance
Frequency
(Hz)
2000
4000
6000
8000
10,000
4000
6000
8000
10,000
Voltage across
function generator (V)
Voltage across
resistor
(V)
Voltage across
capacitor
(V)
Current
(A)
Measured
reactance
()
Calculated
reactance
()
Percent difference
Data Table 2: Inductive Reactance
Frequency
(Hz)
2000
Voltage across
function generator (V)
Voltage across
resistor
(V)
Voltage across
inductor
(V)
Current
(A)
Measured
reactance
()
Calculated
reactance
()
Percent difference
- 98 -
Data for Part B:
R = ___________
L = __________
C = ___________
Bandwidth =
fo =
R
= ___________
2 L
1
2 LC
Q=
= __________
2f o L
= __________
R
Data Table 3
Source
Frequency f
(Hz)
I
(A)
Source
Frequency f
(Hz)
I
(A)
2000
2500
3000
3500
4000
4500
5000
5500
6000
6500
7000
7500
8000
Experimental values from graph:
f1 = ________________ Hz
f2 = ________________ Hz
Resonance frequency = fo = ________________ Hz
% difference = ______________
Bandwidth = f2  f1 = ________________ Hz
% difference = ______________
fo
= ________________
f 2  f1
% difference = ______________
Quality =
- 99 -
Experiment 28
THE MAGNETIC FIELD OF THE EARTH
Tangent Galvanometer
INTRODUCTION
A tangent galvanometer consists of a number of turns of copper wire wound on a
circular hoop, with binding posts for selecting the number of turns of wire to be used. In the
center of the hoop is mounted a magnetic compass for determining magnetic deflection.
In this experiment, the magnitude of the horizontal component of the Earth's
magnetic field will be determined, using a tangent galvanometer. From Ampere's law it can
be shown that the magnetic field in the center of a thin coil of wire of N turns is given by the
relation:
B=
o N I
.
2r
where B is the magnetic field in Teslas (10 4 gauss/tesla), N is the number of turns of wire, I
is the current in Amperes, r is the radius of the circular loop in meters, and o is the
permeability of free space which has the value in S.I. units of 4 X 10-7. Since we can
determine the current, number of turns, and the radius of the hoop, the magnitude of the
field in the center of the coil can be determined.
If both the coil and the compass needle are aligned in the direction of the Earth's
magnetic north pole and a current is drawn through the coils, a magnetic field is produced
at right angles to the Earth's field resulting in a deflection of the compass needle, as shown
in the vector diagram:
From the geometry of Figure 1, we have
Magnetic
North
Compass
Needle
BEarth

BEarth = Bcoil / tan
Bcoil
Fig. 1.
EQUIPMENT & MATERIALS
Tangent galvanometer
20- rheostat
Ruler
DC Regulated Power Supply
Reversing switch 

Dip needle
- 100 -
Leads & connectors
Ammeter
EXPERIMENTAL PROCEDURE
1. Set up the galvanometer so that the wires are oriented parallel to the Earth's magnetic
field as indicated by the compass. The galvanometer can be placed on a piece of
plywood between tables so as to keep it away from iron, pipes or other magnetic
material (this includes the rheostat which becomes an electromagnet when current is
drawn through it).
Rheostat
2. Connect the rest of the circuit
as shown in Figure 2.
Loosely braid the wires to the
galvanometer in order to
cancel the field produced by
the relatively heavy current in
the wires.
A
Reversing
Switch
Tangent
Galvanometer
Fig. 2
3. Using the 10-turns binding posts (the middle and right posts), pass a current through the
galvanometer and adjust the rheostat until the needle is deflected through 45 o. At this
value of current, the field of the coil is equal to the field of the Earth. Now reverse the
direction of the current and see if the needle is 45 o in the other direction, if it is not, then
the galvanometer was probably not accurately aligned in the North-South direction. Redo the procedure until you get a deflection that is as close as possible to 45 o in each
direction. Record the values of current in the laboratory report. Sketch a vector
diagram for this situation. Calculate the field strength of the coil and record it in the
laboratory report.
4. Repeat the above procedure using the 15-turns binding posts (the left and right posts).
Somewhat less current will be required here. Then repeat the procedure using the 10turns binding posts, only this time obtain equal deflections of 63.5o. The current for this
deflection should produce a field that is twice as strong as the Earth's. Sketch a vector
diagram.
6. Using a magnetic dip needle (compass needle mounted vertically), determine the
direction of the field dipping into the Earth. From the horizontal component obtained
above and the angle of dip, determine the magnitude of the Earth's magnetic field
vector. In the Los Angeles area, the expected value for this is 4.8 X 10 -5 teslas.
- 101 -
LABORATORY REPORT: TANGENT GALVANOMETER
Data Table:
Number of
Turns
Deflection
10
45o
15
45o
10
63.5o
Current
Bcoil
Calculations and Diagrams:
Angle of Dip __________________
Calculation and Diagram:
Magnitude of Earth's Magnetic Field Vector__________________
- 102 -
BEarth
Experiment 29
THE POTENTIOMETER
INTRODUCTION
The potentiometer is an instrument that is used to measure the potential difference (the
voltage) across the electrodes of a cell. The advantage of using this instrument rather than
a voltmeter lies in the fact that a potentiometer measures the true (or no-load) voltage; that
is, no current is drawn from the cell when a measurement is made. On the other hand, a
voltmeter will draw some current from the cell when a measurement is made. Also, the
internal resistance of a cell gradually increases with the use of the cell. This resistance
produces an internal voltage drop (or IR drop from V = IR) when current runs through the
circuit. A balanced potentiometer has no current, and so it avoids these problems.
In this experiment, the slide-wire is calibrated by using a Students’ standard cell. The
potential difference of a good dry cell is measured, and then the potential difference of a
dead dry cell is measured.
EQUIPMENT & MATERIALS
Slide-wire potentiometer
Wirewound rheostat, 20 
1 fresh and 1 dead 1½ V dry cell
Hewlett-Packard multimeter
DC Regulated Power Supply
7 banana wires
8 spade lugs
Students’ standard cell
Cadet galvanometer
EXPERIMENTAL PROCEDURE
1. Measure the voltage of the two cells provided with the voltmeter, and record these
values in the laboratory report.
2. Examine the right-hand side of Figure 1. Set the DC Regulated Power Supply to 4.0
volts, and connect its terminals to the lower terminals of the rheostat. An electric
current will constantly run through the rheostat, and the voltage of the tap (the rheostat’s
upper terminal) can be varied from 0 to 4.0 volts. Connect the negative (zero-voltage)
terminal to the 0.000-meter side of the slide-wire potentiometer and the tap to the 2.000meter side. You will soon be adjusting the rheostat’s tap to make the voltage at the
2.000-meter side exactly equal to 2.000 volts. Assuming that the Nichrome wires are
uniform and undamaged, the voltage at every point of the wires will then equal the
reading of the meter stick beneath it.
- 103 -
Fig. 1: Slide-wire Potentiometer Arrangement
3. Place the metal key on the potentiometer so that its movable front end taps the
Nichrome wire at a position equal to the voltage listed on the Students’ cell, to the
nearest millimeter. The Students’ cell is designed to maintain its nominal voltage, as
long as no current runs through it. Connect the key to the positive terminal of the
Students’ cell, and connect this in series to the galvanometer and the negative (black)
terminal of the DC Regulated Power Supply, as shown in Figure 1.
4. Check that the two buttons on top of the galvanometer are rotated into their upper (lesssensitive) positions, and lower the metal key to tap the Nichrome wire at the correct
position. The galvanometer needle will deflect if the potentiometer is not correctly
calibrated. Move the rheostat’s tap until the galvanometer’s needle barely moves as the
key is lowered and raised. Rotate the top left-hand button on the galvanometer to place
it in its lower (more-sensitive) position, and continue to adjust the rheostat’s tap until the
needle is undeflected. The potentiometer is now calibrated. The galvanometer
experiences no current, because the wire connecting the key to the Students’ cell
experiences the same positive voltage at both ends.
5. Return the galvanometer button to its less-sensitive position, and replace the Students’
cell with a good dry cell. Adjust the position of the key to minimize the galvanometer
needle’s deflection. Do not scrape the key along the wire, as this would damage the
wire and destroy its uniformity. Move the key, then lower and raise it before moving it
again. When the galvanometer needle barely deflects, rotate the left-hand button on top
of the galvanometer to its lower position, locate the point of no deflection, and record it.
This gives you an accurate voltage of the battery, when no current is being produced
from it.
6. Repeat steps 4 and 5 with the Students’ cell for calibration, and with the worn-out dry
cell to get another measurement. Notice that the voltages you have obtained, accurate
the nearest millivolt, are similar but probably not identical to the voltmeter readings you
obtained at the beginning of the lab.
7. Return the galvanometer buttons to their less-sensitive position, and remove all spade
lugs and wires from the equipment.
- 104 -
LABORATORY REPORT: THE POTENTIOMETER
Standard Cell Voltage (Marked on Cell) ____________________________ Volts
Voltage of New Dry Cell from Voltmeter ____________________________ Volts
Voltage of Dead Dry Cell from Voltmeter ___________________________ Volts
Measurement Involving Standard Cell:
Position for Final Balance ___________________________ meters
Measurement Involving New Dry Cell:
Position for Final Balance ___________________________ meters
Voltage of Cell ___________________________ Volts
Measurement Involving Dead Dry Cell:
Position for Final Balance ___________________________ meters
Voltage of Cell ___________________________ Volts
- 105 -
Experiment 30
THE WHEATSTONE BRIDGE
INTRODUCTION
The Wheatstone bridge is a circuit used to
measure the resistance of an unknown
resistor by comparison to an accuratelyknown or standard resistance.
I1
I1
R2
R1
G
Figure 1 is a diagram of a bridge circuit. For
the null or balance condition, no current must
flow through the galvanometer. For this
condition to occur, the potential drop across
R1 must equal that across Rs, hence we
have:
I1R1 = I2Rs.
(Eq. 1)
Rs
Ru
I2
I2
Fig. 1. Wheatstone Bridge Circuit
A similar condition holds for the other half of the bridge and we have:
I1R2 = I2Ru.
(Eq. 2)
Dividing the first equation by the second yields:
R1
R2
R
R
= R s , therefore Ru = Rs R2 .
u
1
Therefore, if any three resistances are known, the fourth can be calculated.
The purpose of this experiment will be to measure the resistance of unknown resistors by
using the slide-wire form of the Wheatstone bridge. Differing proportions of the wire will
constitute R1 and R2. A decade resistance box will serve as the standard resistance Rs.
Once a value for the unknown resistance Ru is determined, the value will be compared to
that obtained using an ohmmeter.
The resistivity of several wires will be determined and compared to the accepted values.
The resistivity , is defined as:
=RA,
L
where R is the resistance of the wire, L is the length of the wire in meters, and A is the
cross-sectional area of the wire in m2.
- 106 -
EQUIPMENT & MATERIALS
Slide-wire potentiometer
Decade resistance box
Hewlett-Packard multimeter
DC Regulated Power Supply
4 spade lugs & 2 alligator clips
Resistance spools
Galvanometer
Knife switch
8 banana wires
EXPERIMENTAL PROCEDURE
1. Connect the circuit as in Figure 2, using a spool of nickel silver (an alloy) for the
unknown resistor, and a decade resistance box (set initially at 10 ) for the standard
resistor. Keep your wires as short as possible. Have your instructor check your circuit
before closing any switches.
2.0 volts
R1
R2
L1
L2
G
Rstandard
Runknown
Fig. 2. Wheatstone Bridge Schematic Diagram
2. Use the galvanometer first as a voltmeter (no buttons on top of the galvanometer
depressed) and move the slide back and forth (do not scrape the wire) until an
approximate balance is obtained. If the balance is too far to one end of the meter stick,
change your value of standard resistance in order to get it closer to the center.
3. Now depress the left-hand button on the top of the galvanometer to change it to a moresensitive position and carefully obtain a balance. Record this position as the actual wire
lengths L1 and L2 in the laboratory report. If the potentiometer wire is uniform, then
L2 / L1 = R2 / R1 . Disconnect the unknown resistor from the circuit, and connect the
unknown resistor to the ohmmeter (the multimeter set to ) to measure the resistance
directly. If the ohmmeter reading is significantly different from your calculated Ru, check
your calculations and your circuitry.
4. Use your value of Ru and the information on the spools to compute the resistivity of the
different wires.
28-gauge wire has a cross-sectional area of 8.044 X 108 m2.
30-gauge wire has a cross-sectional area of 5.067 X 108 m2.
5. Repeat this procedure for another nickel silver spool and then for a copper spool.
6. Compare your values of resistivity with the accepted values by computing the percent
difference.
- 107 -
LABORATORY REPORT: THE WHEATSTONE BRIDGE
Data & Calculations Table:
Resistance Spool
Description
Balance Position
On Wire
(cm)
Wire Length, L1
(cm)
Wire Length, L2
(cm)
Nickel Silver
Nickel Silver
Copper
Length ______________
Length ______________
Length ______________
Wire Gauge __________
Wire Gauge __________
Wire Gauge __________
3.3 X 107
3.3 X 107
1.7 X 108
Standard Resistance
Rs
()
Unknown Resistance
Ru = R s
L2
L1
Resistance by
Ohmmeter
()
()
Calculated
Resistivity
(-m)
Accepted
Resistivity
(-m)
Percent difference
- 108 -
Experiment 31
HEATING EFFECT OF AN ELECTRIC CURRENT
INTRODUCTION
Energy is dissipated as heat when current flows through a resistance coil. In this
experiment, a coil is immersed in water and by measuring the temperature of the water
before and after the current is applied, the heat transferred by the coil can be calculated.
From measurements of the voltage and current, the mechanical energy in Joules needed to
produce the effect can be calculated:
Eq. 1
Energy in Joules = (Current in Amps) X (Voltage in Volts) X (Time in seconds)
Energy in calories = (Mass of H2O) X (Specific Heat of H2O) X (Temperature Change of H2O)
Eq. 2
The result of dividing the energy in Joules by the energy in calories is the mechanical
equivalent of heat.
The accepted value of the mechanical equivalent of heat is 4.186 J/cal.
EQUIPMENT & MATERIALS
Heating coil
Battery charger, 6V and 12V
BK Precision multimeter
Hewlett-Packard multimeter
Double-wall calorimeter
Thermometer
Double-pan balance
Ice cubes
Stop clock
Knife switch
Leads & connectors
600 ml beaker
EXPERIMENTAL PROCEDURE
1. Set up the apparatus as is indicated in Figure 1
with the battery charger set at 6 volts, and with
the switch kept open. Have the instructor
check and approve your circuit.
The BK
Precision multimeter should be set to 20V
to
be the voltmeter, connected by the two
terminals on its right-hand side. The HewlettPackard multimeter should be set to 10A to be
the ammeter, connected by its Fused and
Common terminals.
V
A
Calorimeter
+
-
6 and 12 volts
Fig. 1.
- 109 -
2. In a beaker, mix some ice water with tap water until the temperature is ~15 oC below
room temperature. This is the chilled water that you will use in the experiment.
3. Determine the mass of the inner cup of the calorimeter without the fiber ring. Fill the
inner cup to two-thirds full with the chilled water. Determine the mass again. The
difference in the two masses is the mass of the water. Add 12 grams to this before
writing the result in the data table, to compensate for the energy that will be absorbed
by the heating coil, the lid and the inner cup of the calorimeter.
4. Insert the thermometer through the lid of the calorimeter, so that the bulb of the
thermometer is level with the bottom of the heating coil. Carefully place the lid and coil
into the calorimeter. Stir the water by moving the plunger up and down for 5 seconds.
This will ensure a uniform temperature throughout. Obtain the initial temperature
reading, to the nearest tenth of a degree.
5. Close the switch and start the stop clock simultaneously. Measure the current flowing
through the coil (4 – 6 amps) and the voltage across the coil (4 – 6 volts). The voltage
and current should remain constant while the water is being heated. Continue stirring
the water by moving the plunger up and down.
6. When the temperature is about 10oC above room temperature, open the switch and
stop the stop clock simultaneously. Stir the contents and measure the final
temperature.
7. Calculate the number of Joules of electrical energy consumed using Eq. 1.
8. Calculate the number of calories of heat energy that flowed into the calorimeter using
Eq. 2. The specific heat of water is 1.000 cal/goC.
9. Calculate the mechanical equivalent of heat, and its percent difference from the
accepted value.
10. Repeat steps 2 through 9 with the battery charger set to 12 volts. When finished, dry
your equipment completely before putting it away.
- 110 -
LABORATORY REPORT: HEATING EFFECT OF AN ELECTRIC CURRENT
Data & Calculations Table:
Trial
1
Mass of inner cup of calorimeter
(g)
Mass of inner cup of calorimeter plus water
(g)
Mass of water
(g)
Initial temperature of water
(oC)
Current through coil
(A)
Voltage across coil
(V)
Final temperature of water
(oC)
Time of heating
(s)
Electrical energy
(J)
Heat energy
Experimental mechanical equivalent of heat
(cal)
(J/cal)
Percent difference
- 111 -
2
Experiment 32
REFLECTION & REFRACTION
The Optical Disk
INTRODUCTION
In this experiment we will study the principles of reflection and refraction with an apparatus
called an optical disk. This is a vertically-mounted disk, with a graduated scale around the
edge, slits at the side for splitting a light beam into rays, and screws to support lenses and
mirrors on the disk face. A box of special accessories, including a variety of lenses and
mirrors, will provide the needed items for use with the optical disk.
EQUIPMENT & MATERIALS
Optical disk apparatus
Inside caliper
Pasco light source
Optical disk accessory kit
Battery charger, set at 12 volts
Ruler
Lab jack
EXPERIMENTAL PROCEDURE
A. PLANE MIRROR:
1. Darken the room by closing the blinds and turning off the lights. Plug the light source
into the battery charger set to 12 volts, and slide the rod on the back of the light source
in or out to form an image of the filament on a distant wall. The light rays are now
parallel, and the screw beneath the rod should be tightened to maintain this condition.
Adjust the slotted plate so only the central slit is open, and rotate the optical disk so that
the zero axis points directly at the central slit. This will be the principal axis of the
optical systems. Adjust the lab jack and light source so that a ray of light shines through
the central slit and runs along the zero axis of the disk. Fasten the plane mirror to the
disk along the principal axis, rotated into position with the reflected ray overlapping the
incident ray, and then clamped firmly. Measure the angle of incidence and the angle of
reflection when the optical disk is rotated to three different positions. How well is the
law of reflection obeyed? Set the slit opening for 3 slits and check to see if parallel rays
are still parallel after reflection from a plane mirror.
B. SPHERICAL MIRROR:
1. Trace the outline of the spherical mirror, and draw a line perpendicular to the surface
near each edge. These two lines intersect at the center of curvature, the point that is
equally distant from every part of the mirror. Measure the radius of curvature, which is
the distance from the center of curvature to any part of the mirror, to the nearest
millimeter.
- 112 -
2. Remove the plane mirror from the optical disk, and bolt the spherical mirror to the
optical disk, along the principal axis and close to the slits. Rotate the mirror so that the
ray along the principal axis (the middle of the three rays) is reflected back along the
principal axis. Use the inside caliper to measure the focal length, from the focal point to
the center of the spherical mirror. Theoretically, the focal length is exactly half the
radius of curvature. Compare your theoretical and experimental values.
3. Remove the slotted plate entirely and draw the resultant spherical aberration (lack of
sharp focus due to the mirror surface not being parabolic) by moving the lab jack up and
down, and drawing the reflected rays with a ruler.
4. Return to having 3 slits open, and use the convex side of the mirror to repeat the setup
step 2. The focal point can be found by aligning a ruler to a reflected ray and noting
where it crosses the principal axis.
C. REFRACTION:
1. Remove the mirror, and use two bolts to clamp the semi-circular (plano-convex) lens to
the optical disk, with the flat end along the 90o line and facing the light source. Adjust
the equipment to create a single central ray, traveling along the principal axis into and
out of the lens. Rotate the optical disk, and read the angles of incidence and refraction
directly from the edge of the optical disk. Notice that the ray is bent only where it enters
the lens, as the angles of incidence and refraction at the circular surface are zero, so
the angle of refraction is correctly measured by the edge of the optical disk. Obtain
three measurements and compute the index of refraction for the glass from the
equation:
of the angle of incidence
Index of refraction = sine
.
sine of the angle of refraction
2. Rotate the optical disk 180o so that the circular edge faces the light ray, and notice that
the same pairs of angles are obtained.
D. TOTAL INTERNAL REFLECTION:
1. Observe the light ray as it emerges from the flat side of the plate. Vary the angle of
incidence, noting how the intensity of the refracted ray varies. Place the red plastic strip
over the slit, rotate the optical disk until the refracted beam disappears, and measure
the critical angle of incidence. Repeat with the blue plastic strip, and account for the
different values.
2. Now use the 90o prism so the long face is vertical and closest to the slits. Rotate the
optical disk shell to obtain a single ray that is not along the principal axis, and trace its
path to show that the ray experiences total internal reflection. Turn the disk through
135o so the ray falls perpendicularly on one face, and trace the totally reflected ray.
This is the principle used in creating reflections in prism binoculars, for example.
- 113 -
LABORATORY REPORT: OPTICAL DISK
Data for Part A: LAW OF REFLECTION – PLANE MIRROR
Comment on how well the law of reflection is obeyed.
Angle of
Incidence
Angle of
Reflection
_____________________________________________________
Comment on how parallel the rays are after reflection.
_____________________________________________________
Data for Part B: FOCAL LENGTH – SPHERICAL MIRROR
Trace of Spherical Mirror:
Sketch of Spherical Aberration:
Incident rays
principal
axis
Incident rays
Concave Mirror
Convex Mirror
Radius of curvature
Theoretical focal length
Measured focal length
Data for Part C: REFRACTION – PLANO-CONVEX LENS
Angle of Incidence
Angle of Refraction
Angle of Incidence (= Angle of Refraction from previous table)
- 114 -
Index of Refraction, n
Angle of Refraction
Data for Part D: TOTAL INTERNAL REFLECTION – PLANO-CONVEX LENS & 90o PRISM
Plano-convex Lens:
Comment on how the intensity of the refracted ray changes as the incident angle increases.
______________________________________________________________________
Critical angle of incidence using the red plastic strip.
____________________________________________________________________________________
Critical angle of incidence using the blue plastic strip.
____________________________________________________________________________________
Account for any difference in the above two angles.
____________________________________________________________________________________
90o Prism:
Sketchs of Single Ray Undergoing Total Internal Reflection:
Principal
axis
Principal
axis
- 115 -
Experiment 33
THE THIN LENS
Convex and Concave Lenses
INTRODUCTION
The relationship between the object and image distances from a lens and the focal
length of the lens is called the thin lens equation:
(1/s) + (1/p) = 1/f
Eq. 1
where s is the object distance, p is the image distance and f is the focal length (see Fig. 1).
This equation will be investigated to determine if, indeed, the sum of the reciprocals of the
measured object and image distances equals the reciprocal of the focal length of the lens.
In this experiment, light from an illuminated object will be passed through a lens and,
when possible, brought to focus on a frosted glass screen. The nature of images produced
will be studied as the distance of the object from the lens is varied. The images should be
described as real (visible on a screen) or virtual (seen as an image in an eyepiece), erect
(both image and object pointed upwards) or inverted (image and object pointed in opposite
directions), and magnified (in size) or reduced (in size).
EQUIPMENT & MATERIALS
1 convex lens, 15-cm
1 concave lens, 10-cm
2 lens holders
1 support rod, 12-inch
Optical bench
4 optical bench clamps
Metric ruler
1 reflective glass plate
Object lamp
Gooseneck lamp
Frosted screen
3 sheets of graph paper
EXPERIMENTAL PROCEDURE
1. Close most of the blinds and turn off the room lights. Mount the convex (thickest in the
middle) lens and the screen onto lens holders held in place with clamps on the optical
bench, with the lens closest to the window.
2. To determine the focal length experimentally, bring the image of the farthest convenient
object that is outside the window to the clearest focus on the screen. The distance from
the lens to the image is the focal length. Notice that in the thin lens equation, s must
equal infinity for your measurement of p to give f exactly. In practice, if s >> p, p  f.
- 116 -
3. Mount the illuminated object on a clamp, on the opposite side of the lens from the
screen. Place the illuminated object at each of the following positions from the lens in
turn, and move the screen until the real image appears as sharp as possible.
a. farther than twice the focal length
b. at twice the focal length
c. between twice the focal length and the focal length
Record the distance from the object to lens and from lens to screen. Describe the
image as real or virtual, erect or inverted in orientation, and magnified or reduced in
size.
4. Use Eq. 1 to calculate the focal length f. If Eq. 1 is accurate, your values of f should not
deviate much from the value you obtained in step 2.
5. For cases 3a, 3b and 3c, find the image distance graphically by drawing a ray diagram
to scale. Draw the lines as carefully as possible using a ruler. Use your measured
object distances and focal lengths. Compare the graphical image distance with the
measured image distance by calculating the percent difference. The image (real or
virtual, erect or inverted, magnified or reduced) in your ray diagram should match your
description from step 3.
As an example, study the ray diagram in Figure 1 that shows an object placed 40 cm in
front of a lens with f = 15 cm. As you may notice, two rays can be used to locate the
image: A parallel ray from the object passes through the focus and since the lens is
"thin", a second ray passes straight through the center. The image is drawn where
these two rays cross. The image can be described as real, inverted and reduced.
p
s
f
f
object
focus
principal
axis
focus
image
Fig. 1
- 117 -
6. Place the object lamp at 10.0 cm, the 10-cm concave lens at 60.0 cm, the reflective
glass plate at 70.0 cm and the 12-inch support rod at 100.0 cm. Handle the reflective
glass plate by its edges only, and orient its more reflective side towards the rod.
Looking through the glass plate from the 100.0-cm side of the optical bench, you should
be able to see the small virtual upright image of the object lamp through the concave
lens, and the reflected virtual image of the rod. Turn the holder of the glass plate
slightly to place the two images exactly on top of each other. If necessary, place a
sheet of white paper below your eyes to provide a contrasting background for the rod, to
make it easier to see.
As you move your head to the left and right, you will notice that the two virtual images
do not stay together, an effect called parallax. Slowly move the rod towards the mirror
until the two images do not move relative to each other. The two virtual images are now
at the same location in space.
Calculate the location of the rod’s virtual image, which is as far behind the reflective
glass plate as the rod is in front of it. As this is the same location as the lamp’s virtual
image, you can calculate the distance of the lamp’s virtual image from the concave lens.
This is the image distance of the lamp, and it is a negative number. Use the thin lens
equation to calculate the focal length of the lens (also a negative number), and calculate
the percent difference of this result from its nominal value of -10.0 cm.
- 118 -
LABORATORY REPORT: THIN LENS
Focal length of lens from step 2 _________________
Data Table
Case
Object distance
(cm)
Image distance
(cm)
Nature of image (circle one)
Focal length
from Eq. 1
(cm)
Image distance according
to ray diagram
(cm)
a
b
c
Real or Virtual
Real or Virtual
Real or Virtual
Erect or Inverted
Erect or Inverted
Erect or Inverted
Magnified or Reduced
Magnified or Reduced
Magnified or Reduced
Percent difference between
image distances
Location of rod ___________________
Location of rod’s reflected virtual image ___________________
Object distance of lamp
+ 50.0 cm
Image distance of lamp ___________________
Focal length of lens ___________________
Percent difference ___________________
- 119 -
Experiment 34
THE THIN LENS
Optical Instruments
INTRODUCTION
Both a microscope and a telescope will be constructed from simple lenses and the
image system of each will be studied. Since a simple magnifier serves as the eyepiece for
both the microscope and the telescope, a simple magnifier will be studied first and then
applied to the other two optical instruments.
Measurements of magnification will be made in the laboratory and then checked
against the theoretical results determined algebraically. Theoretically, (1/s) + (1/p) = 1/f,
where s is the object distance (between the object and the lens), p is the image distance
(between the image and the lens), and f is the focal length of the lens.
Experimentally, the magnification measures the apparent increase in size:
M = size of image / size of object. Theoretically, M = - p/s.
EQUIPMENT & MATERIALS
Optical bench
Paper number line
3 optical bench clamps
Metric ruler
3 Lens holders
4 lenses (+5, +10, +30, -10 cm)
Masking tape
EXPERIMENTAL PROCEDURE
A. SIMPLE MAGNIFIER:
1. Examine a biconvex lens (thick in the middle, thin near the edge) with a focal length of
5 cm. Hold it close to a printed page, adjusting the position of the lens so that the most
distinct image is seen in the center of the lens. Measure and record the distance
between the lens and the paper.
2. While viewing the image most distinctly through the center of the lens, examine the
appearance of the letters viewed near the edge of the lens. Move the lens vertically
until the letters seen near the edge are in good focus and re-measure the distance
between the lens and the paper. These two numbers are different because a simple
lens like this, with spherical surfaces, has a shorter focal length for light that travels near
the edge of the lens than for light through its center.
- 120 -
3. View the sample of graph paper through the lens until it is in good focus over most of
the lens. Compute the image distance and the theoretical magnification, by measuring
the object distance and assuming that the focal length is +5.0 cm. Estimate the
magnification experimentally by seeing how many unmagnified squares on the graph
paper fit into one magnified square. Do the two results agree?
B. THE MICROSCOPE:
1. Accurately measure the focal length of a 5-cm biconvex lens and a 10-cm biconvex
lens, using the procedure of Experiment 33, step 2 (the focal length equals the image
distance for a distant object). Mount the 10-cm lens (which will serve as the eyepiece)
at the origin of the optical bench, and mount the 5-cm lens (which will serve as the
microscope objective) at a distance f o+ fe in front of the eyepiece, where f o is the focal
length of the objective and f e is the focal length of the eyepiece. Mount a metric ruler
vertically several centimeters beyond the objective.
2. Place your eye close to the eyepiece and slide the ruler back and forth until an inverted,
enlarged image is seen distinctly. Estimate the magnification experimentally by seeing
how many centimeters of the ruler, seen unmagnified through one eye, appear to fit in
one centimeter of the magnified image seen through the other eye. Take a few minutes
to practice viewing with both eyes simultaneously, to get an accurate estimate of M.
Theoretically, M = - fe / fo. The value of M should be negative, because the image is
inverted. Do the two results agree?
C. THE TELESCOPE:
1. Use the 5-cm biconvex lens for the eyepiece and the 10-cm biconvex lens for the
objective, separated by a distance f o+ fe. Remove the ruler and its lens holder. View
the paper number line, taped to a wall, and adjust the system until a distinct image is
seen. Estimate the magnification from the relative sizes of object and image as was
done with the microscope. Compare this estimated magnification with the theoretical
magnification M = - fo / fe.
2. Substitute the 30-cm biconvex lens for the objective and repeat step 1.
3. Set up a Galilean telescope, using a 30-cm biconvex lens as the objective and a 10-cm
biconcave lens as the eyepiece. Repeat step 1, with fe = - 10 cm. This gives a positive
value for M, implying that the image is erect.
- 121 -
LABORATORY REPORT: OPTICAL INSTRUMENTS
A1. Distance between lens and
paper for image at center of lens.
_________________
A2. Distance between lens and
paper for image at edge of lens.
_________________
A3. Measured object distance
_________________
Calculated image distance
_________________
Calculated magnification
_________________
Estimated magnification
_________________
Do the magnifications agree (within reason)? _________________
B.
Focal length of eyepiece
_________________
Focal length of microscope objective _________________
Estimated magnification
_________________
Theoretical magnification
_________________
Do the magnifications agree (within reason)? _________________
C1. Focal length of eyepiece
_________________
Focal length of telescope objective _________________
Estimated magnification
_________________
Theoretical magnification
_________________
Do the magnifications agree (within reason)? _________________
C2. Focal length of eyepiece
_________________
Focal length of telescope objective _________________
Estimated magnification
_________________
Theoretical magnification
_________________
Do the magnifications agree (within reason)? _________________
C3. Focal length of eyepiece
_________________
Focal length of telescope objective _________________
Estimated magnification
_________________
Theoretical magnification
_________________
Do the magnifications agree (within reason)? _________________
- 122 -
Experiment 35
REFLECTION & REFRACTION
AT PLANE SURFACES
INTRODUCTION
In this experiment the laws of reflection and refraction will be investigated by means of ray
tracing.
In the experimental procedure using the plane mirror, it will demonstrated that:
(a) the angle of incidence is equal to the angle of reflection;
(b) the angle of reflection changes when the mirror is rotated through an angle;
(c) the virtual image in a mirror has the same orientation in back of the mirror that it has in
front.
The index of refraction n of a glass plate will be determined from Snell's law;
n=
sine of the angle of incidence .
sine of the angle of refraction
The index of refraction of a glass prism will also be found by using the minimum deviation
formula.
EQUIPMENT
Cork board
Wooden block
Glass plate and triangle
Small 360o protractor

4 sheets of 11 X 17 paper
Plastic triangle
Plane mirror

Colored pencils
Masking tape
7 common pins
Ruler
PROCEDURE
A. Plane Mirror
1. Draw a straight line across the
middle of your paper, placed on
top of the corkboard, and draw a
triangle in front of the line with
vertices A, B, and C labeled on
the paper. Support the mirror
vertically by taping it to the
wooden block so that its back
(reflecting) surface is on the line
as shown in Figure 1a.
A
R2
mirror line
A
R1
C
L2
L1
B
Fig. 1a
- 123 -
A
2. Place a pin at vertex A of the triangle
and place a reference pin R1 about
10 cm in front of the mirror and to
the right as shown in Figure 1b. Use
another pin L1 to line up the
reference pin R1 and the image A of
the vertex pin in the mirror. Repeat
for R2 and L2.
mirror
P
line
R1
R2
L1
A
L2
Fig. 1b
3. Use a colored pencil to draw each line segment R1L1 and R 2 L 2 to the mirror surface
and extend them as dashed lines behind the mirror until they meet. Label this point on
the paper as A, the image of vertex A behind the mirror. Remove the pins at A, L 1 and
L2, and repeat the procedure for vertices B and C, using pencils of different colors.
Connect the vertices of the virtual image behind the mirror.
4. Now draw a line from vertex A to where the line segment R1L1 meets the mirror surface
at point P; this is the incident ray. The line R1L1 is the reflected ray. Use the plastic
triangle to draw a line that passes through the point P, perpendicular to the mirror line.
This line is called the normal. The angle between the incident ray and the normal is
called the angle of incidence. The angle between the reflected ray and the normal is
called the angle of reflection. Measure these two angles, and write them on the paper.
According to the law of reflection, they should be equal.
5. Now fold your paper at the mirror line and see how closely your virtual triangle matches
your real one.
6. On a second sheet of paper, set up the
mirror and mirror line as before. Place a
large dot on the center of the mirror line
on the paper. Place pins A and B in the
paper as shown in Figure 2, lined up
with the dot. Now align two more pins C
and D so that all four pins line up when
viewed through the mirror. Rotate the
mirror about its center dot through an
angle of about 15o and line up two more
pins E and F to get a new reflected ray.
Draw the new mirror line, and the line of
incidence and the two lines of reflection.
Measure and write down the mirror
angle  and the angle  between the two
reflected rays. According to the law of
reflection,  = 2.
- 124 -

F

E
D
C
Fig. 2
B
A
B. Glass Plate
1. Place the glass plate on a third sheet of paper and
draw its outline. Use the plastic triangle to square
off the corners of this outline, and place tick marks
exactly 1.0 cm from the right side, on the upper and
lower sides. Draw a long straight line through these
tick marks, as shown in Fig. 3. This line will be a
normal for the rays.
A
B
C
A B
C
P
2. Draw three differently-colored lines to point P for
the angles A = 15o, B = 30o and C = 45o, and
place pins A, B and C on them. Place a pin P at the
intersection of the glass plate and the normal.
Place pin A against the glass plate in line with the
images of pins A and P as seen through the glass
plate. Do the same for pins B and C. Draw PA  ,
PB  and PC with the appropriate colors, then
measure the three angles of refraction A, B and
C, and write them on the paper. Calculate the
index of refraction for each of the three cases using
Snell’s law. Show your work on the sheet of paper.
C
B
A
C B A
Fig. 3
C. Prism
1. Place a prism on a fourth sheet of paper and
draw the prism’s outline, as shown in Figure 4.
Use a ruler to draw the corners (the vertices)
accurately, and place two pins A and B exactly
5.0 cm from the upper vertex. Locate C by lining
up B with A as seen through the prism. Do the
same for D. Now all four pins should line up
when viewed from C. Note the rainbow of colors
from D, due to dispersion.

D
A
B

C
2. Measure and place on the drawing the vertex
angle  of the prism and the deviation angle ,
and use the minimum deviation formula to
compute the index of refraction n:
n =

2

sin 2
sin
Fig. 4
Your drawings are the data sheets for this experiment. Make sure the name of every
member of your lab group is on the first of the four pages
- 125 -
Experiment 36
SPECTRAL LINES
INTRODUCTION
Electrons of gases can be raised to excited states if the atoms in the gas absorb
energy during collisions. The electrons are said to have been raised from their "ground
state" to "excited states". When these electrons fall back to a lower-energy excited state or
to the ground state, particles of light called photons are emitted. Such photons have
unique wavelengths and the set of spectral lines so produced is a signature of the atoms
that are excited.
In this experiment, energy is supplied to a hydrogen gas by high voltage. The
electrons are excited and fall back almost instantly, emitting photons. This light can be
separated into its individual spectral lines using a diffraction grating. The wavelength of
each line can then be calculated from the diffraction equation.
EQUIPMENT & MATERIALS
Spectrum tube power supply
Hydrogen discharge tube
Lens holder and support stand
2 Meter sticks
2 Ring stands
2 Buret clamps
Paton-Hawksley grating
Gooseneck lamp
Lab jack
EXPERIMENTAL PROCEDURE
1. Set up the apparatus as shown in
Figure 1. Place the spectrum
tube power supply on the lab jack,
and place the grating so that it is
exactly 50.0 cm in front of the
meter stick and at the same
height as the meter stick. Handle
the grating with care, as the
surface can be easily damaged.
Align the discharge tube so that it
is directly behind the 50.0-cm
mark of the meter stick, as viewed
through the grating. Perform the
experiment in a darkened room
and use the reading lamp to
illuminate the gradations on the
meter stick. Avoid touching the
two terminals of the power supply
as it operates at a high voltage.
Fig. 1
- 126 -
2. For each of three spectral lines (red, turquoise, and blue), take readings of the meter
stick to the nearest millimeter, both to the left and to the right, with your eye as close to
the center of the grating as possible. As soon as the measurements have been made,
turn off the power supply and then proceed to the calculations. Let the spectrum tube
cool down before removing it.
3. Figure 2 is a schematic representation of the first-order diffraction for our setup.
d
0th Order


Grating
1st Order
Fig. 2.
4. The wavelength  of each line in the spectrum is given by the grating equation:
n = d sin 
where n is an integer 1, 2, 3, etc.; d is the grating groove spacing and  is the angle
subtended by the spectral line as shown in the diagram above. The reciprocal of the
number of grooves per meter is d, the spacing between grooves.
For example, if the grating has 600 grooves per millimeter, there are 600 grooves per
1,000,000 nanometers, so the spacing between grooves would be d = 1,000,000/600 =
1667 nanometers.
5. The diffraction grating may not be exactly parallel to the meter stick, so line No. 5 of the
data table gives the best estimate of how much the light is deflected, not line No. 3 or
line No. 4. Calculate the wavelength for the three lines and enter the results in the data
table. The accepted value for the Balmer series of the hydrogen spectra (excited state
to a lower-energy excited state) is given below. Report the percent difference in the
laboratory report.
H  (red) = 656.3 nanometers
H  (turquoise) = 486.1 nanometers
H  (blue) = 434.1 nanometers
- 127 -
LABORATORY REPORT: SPECTRAL LINES
Spacing Between Grooves on the Grating: d = __________ nanometers
Data and Calculations Table:
Red
1. Left
(cm)
2. Right
(cm)
3. 50.0 minus (No.1)
(cm)
4. (No. 2) minus 50.0
(cm)
5.
No. 3  No. 4
(cm)
2
6.
No. 5
( = Tan )
50 .0
7.  = Arctan (No. 6)
(o)
8. Sin 
9.  = d sin 
Percent difference
(nm)
(%)
- 128 -
Turquoise
Blue
Experiment 37
RADIATION DETECTORS
The Geiger Counter
INTRODUCTION
When unstable atomic nuclei disintegrate, they eject alpha particles (two protons
and two neutrons bound together), beta particles (electrons) and gamma rays (energetic
particles of light) at high speed. We cannot see this radiation directly, but a Geiger counter
can detect the passage of such particles and count them individually. This experiment is
designed to help you understand the operation of the Geiger counter, and to confirm the
inverse-square law governing the radiation of these particles.
EQUIPMENT & MATERIALS

Geiger tube (cardboard cover removed)
Nucleus pulse-counter
Thallium-204 beta source
Lead carrying case
Clear plastic triangle
1 sheet of graph paper
Shims
Meter stick
EXPERIMENTAL PROCEDURE
1. Attach the BNC connector from the Geiger counter to the back of the Nucleus pulsecounter. Lay the Geiger tube on its side, and level it by placing shims underneath the
back of the tube. Place a meter stick in front of the Geiger tube, with the 0-mm edge of
the meter stick directly under the black aperture of the tube that covers the detector. Be
careful not to touch or poke the black aperture, as it is easily damaged.
2. Set the Time dial on the Nucleus pulse-counter to Manual and set the High Voltage
dials to read the nominal plateau voltage listed on the Geiger tube. Plug in the pulsecounter’s power cord, press the Power button, then press Stop, Reset, and Count.
Remove the Thallium-204 disk from the lead carrying case, and notice that the counter
changes rapidly when the unlabeled face of the disk is moved close to the aperture.
Nearest face
of disk
Aperture
Geiger Tube
Detector
d
x
3. When a high-speed particle from the Thallium-204 disk passes through the aperture and
strikes the detector, a pulse of electricity is sent to the counter, increasing the count
by 1. Placing the disk close to the aperture allows a large fraction of the beta particles to
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be detected. You may gain some appreciation of how tiny atoms are by contemplating
that each count represents a disintegrating atom, and the fragment of Thallium-204
embedded in the plastic disk has been producing beta particles, day and night, for many
years.
4. Set the Time dial to 0.5 minutes and place all radioactive disks in the lead carrying
case. Make five measurements of the ambient radiation (the background radiation,
which is detected even when no disks are present) by pressing the Reset and Count
buttons, and waiting until the red light over the Stop button appears. Average these five
measurements and round to the nearest integer.
5. Place the unlabeled face of the Thallium-204 disk at various distances between 100 mm
and 10 mm from the aperture and count the number of beta particles detected. Subtract
the average number of counts due to ambient radiation to obtain the corrected number
of counts, due to the disk alone. The distance from the aperture to the nearest face of
the disk should be measured to the nearest millimeter. Place these results in Table 1,
and use these values of N to calculate 1/ N .
6. We might expect the number of counts to vary according to an inverse-square law. To
see if this is true, let N stand for the number of detections due to the Thallium-204 disk,
and let m stand for a proportionality constant. If the distances of the detector and the
disk from the aperture are d and x respectively, as shown in the diagram on the
previous page, then
1
N= 2
.
m ( x  d) 2
This equation may be rewritten as
1
N
= mx + md.
Plot a graph of 1/ N as a function of x, and fit the data points to a straight line. Find the
slope m, and the y-intercept md. Calculate the value of d.
Comment on whether or not the value of d seems reasonable. The detector within the
Geiger tube actually runs horizontally along the entire length of the tube. Comment on
how this may have affected your graph.
7. The Geiger counter permits us to learn something about the nature of these particles by
studying their statistics. For example, are these particles emitted in groups, or is each
particle emitted independently? According to statistics, if the particles are emitted
independently, the standard deviation of individual readings should be approximately
equal to the square root of the average of the readings. Take ten readings with the
Thallium-204 disk as close to the aperture as possible. Find the standard deviation ,
from
10
2
 (x i  x ave )
=
i 1
10  1
and compare it to the square root of xave.
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LABORATORY REPORT: RADIATION DETECTION
Geiger tube # _____
Counts obtained during
0.5-minute intervals due
to ambient radiation
Nucleus pulse-counter model # _____
______, ______, ______, ______, ______.
Average number of counts
due to ambient radiation
(rounded to nearest integer) ______
Table 1
Distance from aperture
x
(mm)
Measured Number of
Counts During
0.5-minute Interval
Corrected Number of
Counts During
0.5-minute Interval
N
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1
N
Slope = m = ____________ mm-1
y-intercept = md = ________
d = ___________ mm
Comments:
Ten measurements
of Thallium-204
________, ________, ________, ________, ________,
________, ________, ________, ________, ________.
xave = ____________
x ave = ____________
 = ____________
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Experiment 38
RADIATION ABSORPTION
INTRODUCTION
In this experiment, we shall study the absorption of beta particles and gamma rays
by various materials. The most difficult to stop are the gamma rays, which are
electromagnetic waves of very short wavelength and consequently high energy. Since
these rays are neither attracted or repelled by Coulomb forces, they pass easily through
most matter, but stop eventually.
The most easily absorbed are the alpha particles; a few centimeters of air will
suffice. The reason for this is that they are relatively massive, and a positively-charged
alpha particle will interact with the negative electrons of atoms and produce an ionizing
path. Such a particle soon loses its energy through such collisions, and stops.
Intermediate between the difficult-to-stop gamma rays and the easily-stopped alpha
particles are the fast-moving electrons called beta particles. Since these are negative, they
are repelled by the electron clouds around atoms but can be stopped by a few meters of air
or a few millimeters of aluminum, losing energy from collisions.
EQUIPMENT & MATERIALS

Geiger tube (cardboard cover removed)
Lead carrying case
Nucleus pulse-counter
Clear plastic triangle
Thallium-204 beta source
Cesium-137 gamma source
2 sheets of graph paper
15 sheets of cardboard
15 sheets of aluminum
15 sheets of lead
Micrometer
Meter stick
Sample holder
EXPERIMENTAL PROCEDURE
1. Connect the Geiger tube to the Nucleus pulse-counter, plug in the pulse-counter’s
power cord, turn the pulse-counter on and set the High Voltage dials to read the
nominal plateau voltage listed on the Geiger tube. Set the Time dial to 0.5 minutes.
Place the tube on end so it faces downward, and place the plastic sample holder in the
lowest slot.
2. Obtain five measurements of the ambient background radiation, and average them to
the nearest integer.
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3. Place the Cesium-137 gamma source, unlabeled face up, in the bottom slot of the
sample holder and measure the number of counts by pressing the Stop, Reset and
Count buttons. Place three sheets of cardboard in the uppermost slot, and measure the
resulting number of counts. Add three sheets in each lower slot and measure the count
rate until all five slots are filled. Subtract the ambient count from these counts to get the
corrected counts. Calculate the natural logarithms of these corrected counts.
4. Use the micrometer to measure the thickness of the uppermost trio of sheets, to the
nearest hundredth of a millimeter. Then add the next trio of cardboard sheets to get a
cumulative thickness, and write down this total thickness beside the counts that were
obtained when this thickness was in place. Continue this process to obtain the
thickness appropriate for each reading.
5. The number of particles in a beam after passing through a thickness x of absorbent is
N = Noe-x ,
where  is the linear absorption coefficient of the material for this type of emission.
Taking the natural logarithms of both sides gives
ln (N) = (-)x + ln (No) ,
which is the equation of a straight line with slope -.
Plot a graph of ln (N) vs. x, on half a sheet of graph paper, excluding the x = 0 value.
Notice that your number of counts for x = 0 is very high. This is because Cesium-137
also emits beta particles, which are stopped by the first three sheets of cardboard. Fit a
best-fit straight line through the other data points, and determine the value of  (the
negative of the slope).
6. The half-value thickness of a material is the thickness for which the intensity of a beam
decreases by one-half. When N = No/2, these equations give
Half-value thickness = ln (2)/ = 0.693/.
Calculate the half-value thickness of this material for this type of radiation.
7. Repeat steps 3 to 6 with aluminum sheets, and then lead sheets. You will probably find
that lead has the smallest half-thickness. It doesn’t take much lead to stop a significant
amount of radiation, which is why lead is used to make carrying cases for radioactive
samples.
8. Repeat steps 3 to 6 with Thallium-204 as the source, by sliding a single sheet of
cardboard into each slot. Plot these results on half a sheet of graph paper. Notice that
the half-value thickness of cardboard for these beta particles is much smaller than for
the more-penetrating Cesium-137 gamma rays.
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LABORATORY REPORT: RADIATION ABSORPTION
Geiger tube # _____
Nucleus pulse-counter model # _____
Number of counts during a 0.5-minute
interval due to ambient radiation
______, ______, ______, ______, ______.
Average number of counts due to ambient
radiation (rounded to nearest integer)
______
Table 1. Cesium-137 gamma source through cardboard
Thickness of Absorbent
Measured Number of
Counts During
0.5-minute Interval
(mm)
Corrected Number of
Counts During
0.5-minute Interval
N
ln (N)
0.00
 = ___________ mm-1
Half-value thickness = ___________ mm
Table 2. Cesium-137 gamma source through aluminum
Thickness of Absorbent
(mm)
Measured Number of
Counts During
0.5-minute Interval
Corrected Number of
Counts During
0.5-minute Interval
N
0.00
 = ___________ mm-1
Half-value thickness = ___________ mm
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ln (N)
Table 3. Cesium-137 gamma source through lead
Thickness of Absorbent
Measured Number of
Counts During
0.5-minute Interval
(mm)
Corrected Number of
Counts During
0.5-minute Interval
N
ln (N)
0.00
 = ___________ mm-1
Half-value thickness = ___________ mm
Table 4. Thallium-204 beta source through cardboard
Thickness of Absorbent
Measured Number of
Counts During
0.5-minute Interval
(mm)
Corrected Number of
Counts During
0.5-minute Interval
N
0.00
 = ___________ mm-1
Half-value thickness = __________
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ln (N)