Montgomery College – Takoma Park/Silver Spring
Physical Sciences Department
FALL 2011
Laboratory Manual
For
General Physics II (Non-Engineering) - PH 204
Written by
The Physical Sciences Department Faculty.
1
CO N T E NT S
ELECTRIC FIELDS .................................................................................................................................... 3
OHM’S LAW ................................................................................................................................................ 7
RC SLOW DECAY .....................................................................................................................................16
ELECTRON CHARGE-TO-MASS (E/M)................................................................................................21
RL CIRCUITS .............................................................................................................................................28
RLC CIRCUITS ..........................................................................................................................................28
RAY TRACING ..........................................................................................................................................42
MIRRORS AND LENSES ..........................................................................................................................42
INTERFERENCE .......................................................................................................................................50
DIFFRACTION GRATING .......................................................................................................................54
MICHELSON INTERFEROMETER .......................................................................................................60
PHOTOELECTRIC EFFECT ...................................................................................................................63
HYDROGEN SPECTRUM ........................................................................................................................78
2
Electric Fields
Objective:
 To map electric field lines from equipotential lines between various electrodes.
Equipment:
 Electric field mapping Equipment
 Galvanometer
 Parallel plate conductor
 Pole-plate conductor



6-V Battery or a DC power supply
Electrical leads
Concentric conductor
Theoretical Background:
Electric charges create an electric field in the region of space surrounding the charge
similar to the gravitational field that exists around a mass. The electric field is a vector
and has both magnitude and direction. The direction of the electric field at a point is
defined to be the direction of the force on a positive test charge placed at the point and
the magnitude of the electric field is given by
E
F
q0
(1)
where q 0 is a positive test charge. These field lines in a region can be mapped by a set of
lines surrounding the charges. The electric field




Lines are drawn such that the line originates from the positive charges and
terminates at the negative charges.
Lines are always perpendicular to the surface of the conductor.
Strength is proportional to the density of the lines.
Lines cannot cross each other.
If a charge is moved between two points along the electric field, the electric field will do
work on the charge. However, the electric field will not do work on a charge that is
moved perpendicular to the direction of the field. Defining the potential difference
between two points as the work done per unit charge against the electric field, the
potential difference will be zero when the charge is moved perpendicular to the field.
Curves for which the charge can be moved without electric field doing work are known
as equipotential curves. These equipotential curves will always be perpendicular to the
electric field lines. By determining these curves, it is possible to obtain a map of the
electric field lines in the region.
In this experiment, a map of the electric field lines will be created for following field
plates:
3
Dipole
Parallel Plate
Point and Plane
Faraday Pail
Procedure:
1. Setup the field mapping board with a parallel-plate conductor under the board and a
graphing paper on the top of the board.
Power supply
_
+
Top view
Bottom view
paper
voltmeter
com
Parallel Plate
V
probe
2. Tape the graphing paper to the mapping board.
3. Turn on the power supply and adjust the power so that the potential difference is
about two to six volts.
4. Move the probe around and locate a point that will give one-half of the power supply
voltage.
5. Mark the point just found with a dot using a pencil through the hole in the probe.
6. Move the probe and search and mark about eight to ten additional points with the
same potential on the sheet.
7. Using the points found, draw a smooth curve through the points. Label the curve
using the potential value.
8. In a similar procedure, map out about 6 or 10 evenly spaced equipotential lines.
4
9. Draw the electrodes that were used on the graphing paper.
10. Using the equipotential map, draw uniformly spaced electric field lines on the
graphing paper.
11. Repeat the experiment to obtain a set of electric field and equipotential lines using
dipole, point and plane, and Faraday pail.
Data Sheet:
Attach the graph paper.
Calculations and Results:
On your graph paper, carefully draw smooth, continuous lines from one electrode to the
other that represents the electric field lines. These lines should start and end
perpendicular to the electrode surface and always cross perpendicular to the equipotential
lines.
Questions:
1. Describe the density of the field lines near the electrodes for the different electrodes.
2. How would the different field densities described above affect the force on a charge?
Note that a force requires both its magnitude and direction to be fully described.
5
6
Ohm’s Law
Objective:
 To determine the validity of Ohm’s law for circuit elements.
 To investigate Ohm’s law for simple series and parallel circuits.
Equipment:
 Resistors
 Voltmeter
 Power supply
 Jumper wires
 Electrical leads
 LEDs
 Lightbulbs






Multimeter
Ammeter
Breadboard
Switches
Alligator clips
Diodes
Theoretical Background:
Conductors have very low resistance to the flow of electricity while insulators have a
very high resistance to the flow of electricity. Resistors are devices that have electrical
properties somewhere between a conductor and an insulator. As such, resistors are often
used to control the flow of electricity. Resistors are found to obey Ohm’s law. Discovered
in 1827 by Georg Ohm, the law states that the voltage across the resistor is directly
proportional to the current through the resistor and is usually written as
V  IR
(1)
where V is the potential difference across the resistor, I is the current through the resistor,
and R is the resistance of the resistor. The SI unit of resistance is ohms () if the
potential difference is measured in volts (V) and the current is measured in Amperes (A).
The Ohm’s law is an empirical statement and is not valid for all devices. The devices that
do not satisfy Ohm’s law are known as non-ohmic devices.
When using multiple resistors, the resistors may be combined in essentially in two
different ways. Two or more resistors may either be combined in series (Fig. 1) or in
parallel (Fig. 2).
R1
R1
R2
R2
Fig. 1: Two resistors in series
Fig. 2: Two resistors in parallel
For series combinations, the effective or equivalent resistance, Req , of the resistors
increases and is given by
7
Req  R1  R2
(2)
whereas for the parallel combination of resistors, the effective resistance of the resistors
decreases and is given by
1
1
1


Req R1 R2
(3)
In this experiment, the several circuit elements will be tested to determine whether or not
the elements are ohmic or non-ohmic. For the second part of the experiment, Ohm’s law
will be investigated for simple series and parallel circuits.
Note
 The current through the resistor must be measured by the connecting the ammeter in
series with the resistor.
 The potential difference across the resistor must be measured by a voltmeter (or
multimeter set to voltage) that is in parallel with the resistor.
Procedure:
Part I: A Single Resistor
1. Using the color code, obtain one of each of the following resistors: 47 , 68 , and
100  resistors. Use a multimeter to measure and record the actual resistances in data
table 1.
2. Create the circuit shown in Fig. 3 with a 100 .
i
+
+
A
V
R1
-
+
Fig. 3: A single resistor circuit
3. Slowly adjust the voltage. Measure and record both the voltage drop across and the
current through the resistor in a data table 5. Take sufficient number of measurement
to obtain an accurate graph.
4. Plot the voltage as a function of the current in full sheet of graph paper. From the
graph, determine the value of the resistance of the resistor.
8
Part II: A Single Resistor with an LED
1. Use a 1000  resistor to create the LED circuit shown in Fig. 4.
i
-
+
+
A
-
V
LED
R1
-
+
-
+
Fig. 4: An LED circuit
2. Slowly increase the power supply voltage. Measure and record both the voltage drop
across and the current through the LED in a data table 3.
3. Record the voltage at which the LED lights up.
4. Now reconnect the LED so that the positive anode is connected to the resistor and the
negative cathode is connected to the ammeter. The LED voltage will be now
negative.
5. Again slowly increase the voltage and record both the voltage across and the current
through the LED data table 3.
6. Plot both the positive and negative voltage vs. current for the LED on a graph paper.
Part III: A Single Light Bulb
1. Measure the resistance of a single bulb.
2. Using the same single bulb, create a circuit as shown in Fig. 5.
i
+
+
A
V
bulb
-
+
Fig. 5: A Single Bulb Circuit
3. Slowly adjust the current. Measure and record both the voltage drop across and the
current through the bulb in a data table 5. Take sufficient number of measurement to
obtain an accurate graph.
4. Plot the voltage as a function of the current in full sheet. Computer software such as
Excel may be used to obtain the graph.
Part IV: Circuit with Two Resistors
1. Sketch a diagram of a circuit consisting of two resistors in series.
2. Create a series circuit using 68  and 100 .
3. Slowly adjust the power supply. Measure and record both the total voltage and
current through the resistors in a data table 5.
9
4. Plot the voltage vs. current and determine the effective resistance of the two resistors
in series.
5. Compare the effective resistance of the two resistors in series with the resistances of
each resistor.
Part IV: Circuit with Two Resistors
1. Sketch a diagram of a circuit consisting of two resistors in parallel.
2. Create a parallel circuit using 68  and 100 .
3. Slowly adjust the power supply. Measure and record both the total voltage and
current through the resistors in a data table 6.
4. Plot the voltage vs. current and determine the effective resistance of the two resistors
in parallel.
5. Compare the effective resistance of the two resistors in parallel with the resistances of
each resistor.
10
Data Sheet:
Data Table 1: Comparison between the color coding and the actual resistances
Resistance (in Ω)
From color coding
Actual Resistance (in Ω)
From multimeter
Data Table 2: The voltage vs. current for a single resistor circuit
Current
in (Amps)
Voltage
in (Volts)
Current
in (Amps)
Voltage
in (Volts)
Data Table 3: The positive and negative voltage vs. current for LED circuit
Positive LED Voltage
V (in Volts)
Negative LED Voltage
V (in Volts)
I (in Amps)
11
I (in Amps)
Data Table 4: The voltage across the light bulb vs. current through the bulb
Voltage
in (Volts)
Current
in (Amps)
Voltage
in (Volts)
Current
in (Amps)
Data Table 5: The total voltage vs. current through two resistors in series
Voltage
in (Volts)
Current
in (Amps)
Voltage
in (Volts)
Current
in (Amps)
12
Data Table 6: The total voltage vs. current through two resistors in parallel
Voltage
in (Volts)
Current
in (Amps)
Voltage
in (Volts)
Current
in (Amps)
13
Calculations:
Show on the graph, the experimental and theoretical calculations for the resistance of the
resistors in series and in parallel circuits. Include the units.
Resistance Color Codes
Example: 47=
Yellow
Color Code
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold
Silver
None
1st band
(1st digit)
0
1
2
3
4
5
6
7
8
9
Violet
2nd band
(2nd digit)
0
1
2
3
4
5
6
7
8
9
14
Black
3rd band
(multiplier)
100 = 1
101 = 10
102
103
104
105
106
107
108
109
10-1
10-2
Silver
4th band
(tolerance)
5%
10%
20%
15
RC Slow Decay
Objective:
 To examine the exponential behavior of current and voltage in RC circuits.
 To determine unknown capacitance via half-life measurements.
 To determine unknown resistance via half-life measurements.
Equipment:
 Digital multimeters (2)
 Breadboard with wire kit
 DC Power supply
 Connecting cables (8)
 Connecting cable adapters




Switches (2)
4.7 MΩ resistor
4.7 µF capacitor
Stopwatch
Theoretical Background:
A capacitor is an electrical element that can store charge. If the capacitor is charged, but
not attached to any circuit, then the charge will remain. However, in real situations the
capacitor slowly drains as the charge leaks to the surroundings. If the ends of the
capacitor are connected, then the charge will immediately be balanced. Between these
two extremes, the rate that the capacitor charges or discharges is a function of the
resistance through which the charge must pass. This function is also based on the total
charge that the capacitor can hold, Qmax.
The amount of charge on each plate of a charging capacitor is given by the exponential
equation:
t
q(t )  Qmax 1  e  


where τ = RC is the time constant (in s) for a given resistance R and capacitance C. The
function for a discharging capacitor is given by:
q(t )  Qmax e
t

For constant values of capacitance, similar exponential relationships can be derived for
both the voltage across the capacitor, and the current through the capacitor.
The “half-life” is the time required for a particular RC circuit to discharge to half of its
starting charge (or voltage):
t 12  RC ln( 2)
16
This means that the amount of time required for the current through, or voltage across, a
discharging capacitor to drop to one-half its starting reference value is a function only of
the resistance and capacitance of the circuit. The same is true for a charging capacitor.
Notice that the half-life is a constant quantity, regardless of starting value. This means
that the time required to drop from, for example, 80% of maximum current to 40% of
maximum is the same time required to drop from, for example, 30% of maximum to 15%
of maximum.
Procedure:
1. Use the multimeter to measure and record the actual resistance of the 4.7 MΩ resistor.
2. Set up the circuit shown below. Leave both switches open for the time being. Set the
ammeter scale to 200 µA, and the voltmeter scale to 20 V. Once you have set up the
circuit, have your instructor check your work before proceeding.
switch 1
+
COM
switch 2
4.7 M
+
4.7 F
25.0 V
COM
3. Turn on the DC power supply and allow it to warm up for a couple of minutes, until a
stable voltage of 25.0 V can be set.
4. Close switch 1. Notice that the complete circuit current will be displayed on the
ammeter, which will be falling as the capacitor charges.
5. Once the current has fallen below 0.5 μA, open Switch 1 to stop the charging process.
6. Close Switch 2. You will now note a voltage for the new RC circuit, consisting of the
capacitor and the internal resistance of the voltmeter. The voltage will be falling as
the capacitor discharges. Once the voltage falls below 1.0 V, open Switch 2.
7. Repeat this process a couple of times to get a feel for the behavior of the falling
current in the first RC circuit as it charges, and the falling voltage in the second RC
circuit as it discharges.
8. Choose a starting current value and close Switch 1. Using the stopwatch, determine
the time required for the current to fall to half of your chosen starting current. Record
the starting current, end current, and time in Table 1.
9. Once the current has fallen below 0.5 μA, open Switch 1 to stop the charging process.
10. Choose a starting voltage and close Switch 2. Using the stopwatch, determine the
time required for the voltage to fall to half of your chosen starting voltage. Record the
starting voltage, end voltage, and time in Table 2.
17
11. When the voltage on the voltmeter falls to less below 1.0 V, open Switch 2.
12. Repeat Steps 8-11 five more times, choosing different starting current and starting
voltage values for each trial. Record your results for each trial in the appropriate
table.
Calculations:
Part 1 – Calculating Capacitance from Half-Life
Using your results from Table 1, calculate an average half-life for your six charging
trials. Use this value to calculate the actual capacitance of the capacitor.
Part 2 – Calculating Voltmeter Internal Resistance from Half-Life
Using your results from Table 2, calculate an average half-life for your six discharge
trials. Use this value, along with the actual capacitance calculated in Part 1, to
calculate the actual resistance of the voltmeter. Remember that the 4.7 MΩ resistor
is no longer part of the RC circuit during discharge.
18
Data Sheet:
Actual Resistance of 4.7 MΩ resistor
Table 1: Charging
Start Current (A)
End Current (A)
Time (s)
End Voltage (V)
Time (s)
Table 2: Discharging
Start Voltage (V)
19
20
Electron Charge-to-mass (e/m)
Objective:
 To observe the effect of a magnetic field on moving charges.
 To determine the charge (e) to mass (m) ratio of an electron.
Equipment:





An e/m tube (evacuated tube with electron gun and low-pressure gas.)
a pair of Helmholtz coils
Power supply unit.
a 6.3 volt AC source for the filament
a 6 volt DC source with sensitive ammeter for Helmholtz coils (about 1 amp DC).
21
Theoretical Background:
The force acting on a charge (q) moving through a magnetic field (B) with a velocity (v)
at any instant is:
(1)
F  q v B sin 
where  is the angle between the charge velocity and magnetic field vectors. The
direction of the force is found using the right hand rule.
While the speed of the charge in question does not change, the direction constantly
changes. Newton’s law requires that a mass acted on by an unbalanced force must
accelerate in the direction of force. Therefore, there exists a net force that is acting on the
charge. The direction of the magnetic force is perpendicular to the direction of the
velocity. The acceleration resulting from this type of force is called centripetal
acceleration. If the field and speed are constant, then the constant centripetal acceleration
leads to a circular path for the particle with the magnitude of the acceleration being
ac 
v2
r
(2)


where r is the radius of the circle. Applying Newton’s second law,  Fnet  ma , gives
v2
e vB sin   m
r
(3)
where e is the charge of an electron.
The direction of this force always points toward the center of the circular path. If the
velocity and the magnetic field are perpendicular, i.e.   90 , then equation (3) becomes
e vB  m
v2
r
(4)
Solving for the speed gives
v
erB
m
(5)
The speed of the charge (electrons in this lab) comes from the electron gun. The
electrons are released from a hot metal filament and accelerated through an electric field
(a positively charged grid). The kinetic energy of the moving electrons is due to the
decreasing potential energy associated with the field. The kinetic energy of the electron is
given by KE  eV , or
1
mv 2  eV
2
22
(6)
where V is the potential difference between the charged grid. Solving equation (6) for
the speed gives
v
2eV
m
(7)
Equating the speeds obtained by using Newton’s second law with the speed obtained by
using kinetic energy of the electron leads to
e rB
2 eV

m
m
(8)
Rearranging equation (8), the ratio of the charge on the electron, e , to the mass of the
electron, m , can be found by
e
2V
(9)
 2 2
m r B
The potential difference, V , can readily be measured with a voltmeter. Although the
radius, r , can also be measured, it must be measured very precisely since the radius is
squared in the determination of charge to mass ratio because any error is also squared.
In this experiment, the magnetic field, B , is produced by a Helmholtz coil and its
strength is given by
B
32  10 7  n I
5 5r
(10)
where n is the number of turns and I is the current in the coil. For the coils used in this
lab, the strength of the magnetic field is
B  7.8  10 4 I Weber/m 2
(11)
Finally, substituting B into equation (9) gives:
e
V
 3.29  10 6 2 2
m
r I
23
(12)
Procedure:
1. Connect the Front panel as shown in the figure above. The “B-power supply” is the 0500 V supply. The “heater power supply” is the leftmost 6 V “Filament” supply (the
red and blue plugs equal 6 V). The “coil power supply” is the rightmost 0-20 V
supply. Set the “Coil current adjustment” knob to midway. Turn all power supply
control knobs completely counterclockwise to their lowest settings. Do not turn on
the power supply until the instructor has looked at your your connections.
2. Turn on the power supply and allow the filament to warm up for a minute or two.
Increase the voltage of the 500 V anode supply to approximately 200 V. A blue beam
will appear at the bottom of the tube where the electrons hit the helium atoms.
Slowly increase the rightmost 0-20 V coil power supply until the blue beam is bent
into a complete circle. Slowly vary both the 500 V anode supply and the rightmost 020 V coil supply to get a feel for the range of values that still display a closed circle.
3. Select a fixed voltage. Adjust the rightmost coil supply knob to six different current
settings, carefully measuring the diameter of the circle for each, and record in the data
sheet. A diameter ruler can be seen within the discharge tube, measured in
centimeters from right to left. When taking each measurement, line up the beam
directly with your eye to reduce parallax. You should be able to estimate to a tenth of
a centimeter for each measurement.
4. Repeat Step 3 for a different fixed voltage value.
5. Now, select a fixed current. Adjust the 500 V anode supply to six different voltage
settings, carefully measuring the diameter of the circle for each, and record in the data
sheet.
6. Repeat Step 5 for a different fixed current value.
24
Data Sheet:
Raw Data Part 1: Constant Voltage Diameter Values
V1 =
I (A)
V2 =
diameter (cm)
I (A)
diameter (cm)
1
2
3
4
5
6
Raw Data Part 2: Constant Current Diameter Values
I1 =
V (V)
I2 =
V (A)
diameter (cm)
1
2
3
4
5
6
25
diameter (cm)
Calculations:
Use appropriate units to get e/m in Coulombs/kg. Remember that the original equation is
a function of radius, so your diameter measurements will need to be converted to radius
measurements before you proceed.
1
Determination of e/m from the graph of I 2 as a function of 2 .
r
1
1. Plot I 2 as a function of 2 for each value of V (two total plots). Determine the
r
slope of the best-fit line for each. The slope will be equal to:
slope  3.29  10 6
m
V
e
(13)
2. From the slope of each line, determine the charge-to-mass ratio, i.e. the numerical
value for e / m . Use the two values to calculate an average value for e/m.
Determination of e/m from the graph of r 2 as a function of V .
1. Plot r 2 as a function of V for each value of I (two total plots). Determine the slope
of the best-fit line for each. The slope will be equal to:
3.29  10 6 m
slope 
e
I2
(14)
2. From the slope of each line, determine the charge-to-mass ratio, i.e. the numerical
value for e / m . Use the two values to calculate an average value for e/m.
Comparison with known values
1. Determine the accepted theoretical value for the electron charge-to-mass ratio by
using the known values of electron charge and mass.
2. Determine the Percent Error of both methods with the accepted value of e/m.
Remember that Percent Error is always positive and is calculated as follows:
Percent Error 
Measured Value - Theoretica l Value
Theoretica l Value
 100
Questions
1. Based on your results, is the ΔV or I2 method more accurate in predicting the e/m
ratio? Would you expect either of these methods to be superior? Why or why not?
2. What is the single largest contributor to error in this experiment? Explain your
answer.
26
27
RL Circuits
Objective:
 To study the behavior of an RL circuit
 To determine the time constant of an RL circuit
 To determine the inductance of an unknown inductor
Apparatus:
 PASCO circuit board
 Function generator
 Inductor
 jumper wires




Oscilloscope
Breadboard
Resistor
alligator clips
Introduction and Theory:
Inductor is a coil of wire and is used to store magnetic field. A magnetic field is
generated in an inductor as current passes through it. As the magnetic field increases in
the coil, an induced magnetic field is created in the opposite direction in the coil. This is
referred to as self-inductance. The measure of self-inductance is known as inductance. As
long as there is a change in the current, a magnetic field will be induced in accord with
Faraday’s law of induction. If the current reaches a maximum value and becomes
constant, as in DC circuits, then the induced magnetic field will become zero. If a resistor
is connected in series with an inductor, then the behavior of the circuit is very similar to
that of a RC circuit. The current through the inductor in an RL circuit is given by

i (t )  I 0 1  e  t / 

(1)
where I 0 is the maximum current through the inductor and  is the time constant. The
time constant for a RL circuit is defined as
 
L
R
(2)
If the current is initially zero, then the time constant represents the time required for the
current to reach 63.2% of the maximum current. If the initial current is at maximum
value, then the time constant will represent the time required for the current to drop to
37.8% of the initial value.
Rather than measuring the current through the inductor, it is much simpler to measure the
potential difference across the resistor. The variation of voltage across the resistor is
similar to the variation of the current in the inductor. From Ohm’s law, the voltage drop
across the resistor is given by

v(t )  V0 1  e  t / 
28

(3)
The “half-life” is the time required for the RL circuit’s voltage to reach half of its
maximum value.
In terms of the time constant, the half-life is
t1 / 2 
L
ln 2
R
(4)
By measuring the half-life, either the inductance of an unknown inductor or the resistance
of an unknown resistor can be found.
Procedure:
5. Use multimeter to measure and record the actual resistances of the 100  resistor and
that of the 8.2 mH inductor.
6. Using a PASCO circuit board, create the circuit shown below.
L
+

R
V
Oscilloscope
29
7. Attach the oscilloscope probe between the inductor and resistor and the oscilloscope
ground between the square wave generator ground and resistor
8. Set the function generator to square wave.
9. Use the function generator output knob to set the peak-to-peak voltage to be about
10 V.
10. Adjust the oscilloscope voltage and horizontal time scale to obtain a single trace
similar to either an exponential decay or growth diagram.
11. Measure the half-life from the oscilloscope display.
12. Now place the steel rod inside the inductor core and repeat the
30
Data Sheet:
Resistance of the inductor = _________________________
Frequency
(in Hz)
Resistance of the
Resistor
(in )
Circuit 1 – No
Rod
Circuit 1 – No
Rod
Circuit 1 – No
Rod
Circuit 2 –
Steel Rod
Half-life
(in s)
10
33
100
10
Calculations:
1. Calculate the time constant for the RL circuit.
2. Using the half-life information from the first part, calculate the average actual
resistance of the function generator.
3. Calculate the inductance of the inductor with steel core.
Results:
Time constant
 (in s)
Resistance of the
function generator (in )
Circuit I – 10 Ω
Circuit I – 33 Ω
Circuit I – 100 Ω
Average Resistance of the function
generator
Time constant
 (in s)
Inductance of the core
with steel rod (in )
Circuit II - Steel
Rod
31
32
RLC Circuits
Montgomery College – Takoma Park / Silver Spring Campus
Physical Sciences Department
PH204 – Introduction to Physics for Non-Engineers II
RLC Circuits
Objective:
 To analyze the behavior of RLC circuits
 To determine the resonant frequency
Apparatus:
 PASCO circuit board
 Function generator
 Inductor
 jumper wires




Oscilloscope
Breadboard
Resistor
alligator clips
Introduction and Theory:
When an AC signal is input to an RLC circuit, voltage across each element varies as a
function of time. The voltage will oscillate with a frequency of the AC signal. Likewise,
the current will also oscillate with the same frequency. Nevertheless, the voltage and
current may not rise and fall at the same time. The voltage and current is said to be out of
phase as shown below.
Figure 1: Voltage and current in an AC circuit
The phase angle  represents the difference between the maximum voltage and the
maximum current. The phase angle will depend on the nature of the circuit.
33
Consider a circuit consisting of a resistor, capacitor, and an inductor in series
Figure 2: RLC series circuit
In an AC circuit, the Ohm’s law cannot be directly applied. However, the law can be
applied for maximum values of current and voltages. The maximum voltage across the
resistor is given by
VR  I max R
(1)
and the maximum voltage across the capacitor is given by
VC  I max X C
(2)
where X C is known as the capacitive reactance and measures the effective resistance of
the capacitor. The value of the capacitance reactance is defined as
XC 
1
2 f C
(3)
Likewise, the maximum voltage across the inductor is given by
VL  I max X L
(4)
where X L is the inductive reactance and is defined as
X L  2 f L
(5)
The maximum voltage of the AC signal is given by
Vmax  I max Z
(6)
where Z is the known as the impedance of the circuit.
Z  R2  X L  X C 
2
34
(7)
The minus sign in front of the capacitive reactance reflects the 180 phase difference
between the voltage across the inductor and the voltage across the capacitor. At a unique
single frequency, X L  X C . This frequency is known as the resonant frequency. At
resonant frequency, the current will be in phase with the source voltage. Setting the
inductive and capacitive reactance equal to each other gives the resonant frequency to be
fr 
1
2 LC
(9)
At resonant frequency, the impedance will be a minimum and the current in the circuit
will be a maximum. The voltage across the inductor-capacitor combination will also be
zero at resonant frequency.
The resonant frequency can be readily observed by using the XY mode on the
oscilloscope. In the XY mode, the display will measure the voltage from one channel as a
function of the voltage from the second channel. The resonance condition will be given
by a single diagonal line on the oscilloscope display.
By measuring the half-life, either the inductance of an unknown inductor or the resistance
of an unknown resistor can be found.
Procedure:
Part I: Resistance of the Function Generator
1. Use multimeter to measure and record the actual resistances of the 100  resistor and
that of the 8.2 mH inductor.
2. Use 100  resistor and the 8.2 mH inductor on the PASCO board to create the RL
circuit shown below.
L
+

R
V
Oscilloscope
3. Attach the oscilloscope probe between the inductor and resistor and the oscilloscope
ground between the square wave generator ground and resistor
4. Set the function generator to square wave.
35
5. Use the function generator output knob to set the peak-to-peak voltage to be about
10 V.
6. Adjust the oscilloscope voltage and horizontal time scale to obtain a single trace
similar to either an exponential decay or growth diagram.
7. Measure the half-life from the oscilloscope display.
Part II: Phase Measurement
13. Use multimeter to measure and record the actual resistances of the 100  resistor and
that of the 8.2 mH inductor.
14. Use a 330 F capacitor, 100  resistor, and 8.2 mH inductor in the PASCO circuit
board to create an RLC circuit shown below.
Figure 3: Oscilloscope connections for the RLC circuit
15. Set the function generator to sinusoidal mode with a frequency of 15 Hz.
16. Connect the alligator clip of the oscilloscope probe to the ground of the function
generator.
17. Use vertical controls and set the coupling for CH 1 and CH 2 to AC.
18. Obtain simultaneous displays of the voltage across the resistor, i.e. current, and the
voltage across the source.
19. Turn the sec/div knob to obtain about two complete cycles on the display.
20. Use the time cursors to measure the phase, t, between the current and the voltage
across the source. Record the phase in the data table.
21. Measure and record the amplitude of the resistor and source voltage.
22. Repeat the phase and amplitude measurements for frequencies of 1500 Hz and 2000
Hz.
Part III: Resonance
1. Adjust the frequency until the current and the voltage across the source are in phase.
2. Press DISPLAY button on the oscilloscope and select XY mode.
3. Record the resonant frequency of the RLC circuit.
4. Replace the 330 F capacitor with 100 F capacitor and determine the resonant
frequency.
36
5. Use a breadboard and create a RLC circuit using a 300  resistor, 470 F capacitor,
and unknown inductor.
6. Measure and record the resonant frequency.
7. Replace the 470 F capacitor with a 1000 F capacitor and again measure the
resonant
frequency.
37
Data Sheet:
Part I: Resistance of the Function Generator
Resistance of the inductor, RL
= _______________
Frequency
(in Hz)
Trial
Resistance of the
Resistor
(in )
Half-life
(in s)
1
2
Part II: Phase Angle Measurement
Resistance of the resistor
=
________________________
Resistance of the inductor
=
________________________
Resistance of the function generator, Part I
=
________________________
Inductance of the inductor
=
________________________
Capacitance of the capacitor
=
________________________
Trial
Frequency
(in Hz)
1
15
2
1500
3
2000
Phase, t
(in
)
Maximum VR
(in
)
Maximum VRLC
(in
)
Part III: Resonant Frequency
Resistance
(in )
Circuit I –
PASCO Board
Circuit II –
PASCO Board
Circuit II –
Bread Board
Circuit II –
Bread Board
Capacitance
(in F)
330
100
470
1000
38
Resonant
Frequency
(in Hz)
Calculations:
4. From the phase measurement, calculate the phase angle.
5. Calculate the theoretical phase angle for each frequency.
6. Use the resonant frequency to calculate the inductance of the inductor for each circuit.
7. Determine the % difference between the expected and the actual phase angle.
8. Compare the value of inductance to the actual inductance of the inductor.
39
Results:
Part I: Phase Angle Measurement
Experimental
Theoretical Phase
Trial
Phase Angle
Angle
1
2
3
Part II: Resonant Frequency Measurement
Theoretical
Inductance
Resonant Frequency
(in mH)
(in Hz)
Circuit I –
PASCO Board
Circuit II –
PASCO Board
Unknown
Inductor
Unknown
Inductor
40
% Error
41
Ray Tracing
Objective:
 To trace reflected and refracted rays of light.
 To determine the index of refraction of a material.
Equipment:




Tracing board
Triangular and rectangular prisms
Ruler
Pen laser




Plane mirrors
Pins
Protractor
Water
Theoretical Background:
Light that strikes a flat, reflective surface (mirror) will reflect at the same angle (incidence)
from the normal to that surface. The distance from the mirror to the image (q) will be the
same as the distance from the mirror to the object (p) where the light started. Any light
that enters a new medium at any angle from the normal of the surface may bend or
refract. The amount of the refraction is based on the two mediums. The index of
refraction (n) is a measure of the speed of a particular wavelength of light in a medium
compared to the speed of light in vacuum (or air). The angle of incidence (incidence) is the
angle the light enters a medium with respect to the normal. The angle of refraction
(refraction) is the angle of the light ray in the new medium with respect to the normal.
incidence 
reflection
n1
n2
refraction
The relationship between the angle of incidence and the angle of refraction is given by
Snell’s Law
n1 sin  incidence  n2 sin  refraction
(1)
If the first medium is air, then the index of refraction will be one. The index of refraction
for the second medium is found to be
42
sin  incidence
(2)
sin  refraction
The direction of the light ray will depend on the geometry of the surface and the indices
of refraction.
n2 
Procedure:
Exercise I: Reflection in a Plane Mirror (Law of Reflection)
1. Set the vertical plane mirror and sheet of paper on the tracing board.
2. Mark the paper where the back of the mirror is. Be careful not to move the mirror
until you are done.
3. Stick a pin 1 through the paper into the board front of the mirror. Then stick a second
pin about one inch away from the first pin, so that it is in line with about a 45o angle
from the mirror as shown below.
p
q
2
1
incidence
refraction
3
eye
4.
5.
6.
7.
4
Look into the mirror until both pins forms a straight line.
Stick in a third pin so that it is in line with the images of the first two pins.
Repeat step 5 with a fourth pin about 1 inch away from the third pin.
The images of the first two pins and the last two pins should be inline (you should
only really see the last pin.
43
8. Remove the pins. Circle the holes where the pins were. Draw a straight line
indicating the back of the mirror.
9. Draw a line through the holes of the first two pins to the mirror line.
10. Draw a line through the holes of the second two pins past the mirror line. This line
should be twice as long as the previous line. These two lines represent the light rays.
11. Draw a line from the intersection of the light rays perpendicular to the mirror and
measure the angle of incidence and the angle of refraction.
Exercise II: Reflection in a Plane Mirror (Parallax)
1. Set the short vertical plane mirror and sheet of paper on the tracing board.
2. Mark the paper where the back of the mirror is. Be careful not to move the mirror
until you are done.
3. Stick a pin 1 through the paper into the board front of the mirror.
p
q
1
2
4. Look into the mirror and move the head from side to side until the pin and its image
are in line.
5. Hold a second “finder” pin behind the mirror, so that it is in line with the first pin and
its image.
6. Move the finder pin forward and back until you find a location where the image of the
first pin and the finder pin stay inline when you move your head side to side.
7. Stick the finder pin in that location. Remove the pins and circle their holes, remove
the mirror, and draw a line indicating the back of the mirror.
8. This method eliminates parallax. Measure the image and object distances.
Exercise III: Refraction in a Rectangular Prism
1. Set the rectangular prism and sheet of paper on the tracing board.
2. Trace the outline of the prism as close to its edges as possible. Be careful not to
move the prism until you are done.
3. Stick a pin through the paper into the board front of the prism. Then stick in a second
pin about one inch away from the first, so that they are in line with about a 45o angle
from the normal to the prism as shown in the figure below.
4. Look into the prism from the opposite side until you can see both pins through the
glass. Adjust the head until the image of pin 2 is exactly behind the image of pin 1.
5. Stick in a third pin so that it is in line with the images of the first two pins.
44
2
1
1
2
3
4
3
4
6. Repeat step 5 with a fourth pin about 1 inch away from the third pin.
7. The images of the first two pins and the last two pins should be inline (you should
only really see the last pin.
8. Remove the pins and prism. Circle the holes where the pins were.
9. Draw a line through the holes of the first two pins to the prism edge where the light
from the pins enters the prism.
10. Draw a line through the holes of the second two pins to the prism edge where the
light from the pins leaves the prism.
11. Draw a line between the intersections of the light rays and prism edges.
12. Draw the normal lines at both edges and measure both angles of incidence and
refraction.
Exercise IV: Minimum Deviation in a Triangular Prism
1. Set the triangular prism on the sheet of paper on the tracing board.
2. Trace the outline of the prism as close to its edges as possible. Be careful not to
move the prism until you are done.
3. Stick a pin through the paper into the board on an edge of the prism. Then stick in a
second pin on the opposite edge of the prism so that the distance from the vertex (A)
to the location of the pin is identical for both pins.
A
1
3
2
deviation
4
4. On the first side, stick a third pin about one inch away from the first pin so that it is in
line with the first pin and the image of the second pin.
5. On the opposite side, stick a fourth pin about one inch away from the second pin so
that it is in line with the second pin and the images of the first and third pins.
6. Remove the prism and pins and circle where the pins were.
45
7. Draw a long line along the first and third pins.
8. Draw a long line along the second and fourth pins until it meets the previous line.
9. Measure the angle of deviation (deviation) using the intersection of these two lines as
the vertex.
10. Repeat steps 1-9 except with the distance from the vertex of the prism to the first pin
greater than to the second pin.
11. Repeat steps 1-9 except with the distance from the vertex of the prism to the first pin
less than to the second pin.
12. Measure the angle (A) at the vertex of the prism.
Calculations:
Refraction: Rectangular Prism
Find the index of refraction for each substance.
Compare the index of refraction for crown glass and calculate the % Error.
Refraction: Minimum Deviation in a Triangular Prism
The index of refraction can be found by: n = sin ½ (Dm + A) / sin ½ A
Use the index of refraction for crown glass and calculate the % Error.
46
Data Sheet:
Exercise I: Reflection in a Plane Mirror (Law of Reflection)
Trial
Angle of Incidence, incidence
Angle of Refraction, reflection
1
2
Exercise II: Reflection in a Plane Mirror (Parallax)
Object distance, p
Image distance, q
Exercise III and IV: Refraction in a Rectangular Prism
Angle of Incidence, incidence
Angle of Refraction, reflection
Rectangular Prism
Exercise III and IV: Refraction in Triangular Prism
Angle of
Angle of
Incidence,
Refraction,
Trial
incidence
reflection
Angle of
deviation,
deviation
1: distance from vertex to pins 1
and 2 are equal
2: distance from vertex to pin 1 is
greater than to pin 2
3: distance from vertex to pin 1 is
less than to pin 2
Results:
Index of Refraction
Rectangular Prism
Triangular Prism
47
% Error
48
Mirrors and Lenses
Objective:
 To determine the focal length of spherical mirrors and lenses.
 To trace light rays for spherical mirrors and lenses.
Equipment:
 Optical bench
 Light source
 Spherical mirrors
 Ruler
 Meter stick




Lens holders
Screen
Convex and concave lenses
Pen laser
Theoretical Background:
A spherical mirror is characterized by a center of curvature, C. The center of curvature
represents the center of the sphere formed by the spherical mirror and the distance from
the vertex of the spherical mirror to the center of curvature is also known as the radius of
curvature, R.
C
F
f
light
R
The focal length of a spherical mirror is one-half of the radius of curvature
f 
1
R
2
(1)
The mirror is known as a concave mirror if the light reflects off the inner surface as in the
figure above, whereas it is called a convex mirror if the light reflects off the outer surface
of the sphere.
Lens consists of two surfaces and can generally be categorized as either converging
lenses or diverging lenses. A converging lens causes light rays traveling parallel to the
principal axis to converge at the focal point whereas a diverging lens causes these same
light rays appears to diverge from the focal point. Both converging and diverging lenses
are characterized by the focal length. An example of a converging lens is a biconvex or
49
convex lens while an example of a diverging lens is a biconcave or concave lens as
shown below.
biconvex
or
convex
biconcave
or
concave
The equation describing the image location is identical for both the thin-lens and a
spherical mirror. The lens equation is
1 1 1
 
p q f
(2)
where p is the object distance, q is the image distance, and f is the focal length. If the lens
is not a thin lens, then the focal length is determined by
1
1 
f  n  1  
 R1 R2 
(3)
where n is the index of refraction of the lens, R1, and R2 are the radius of curvature of the
two surfaces.
Procedure:
Exercise I: Focal Length of Concave Spherical Mirror
1. Choose a distant light source, i.e. ( p   ) as the object.
2. Place the mirror with the concave side facing the light source.
3. Place the screen near the mirror slightly away from the principal axis such that the
screen does not block the light from the source.
4. Obtain an image of the light source onto screen.
5. Measure and record the focal length of the spherical mirror.
50
f
C
p=
q=f
Exercise II: Focal Length of a Convex Spherical Lens
1. Choose a distant light source, i.e. ( p   ) as the object.
2. Place a strong convex lens into the lens holder on the optical bench as shown below.
3. Obtain an image of the distance object onto an image screen behind lens.
4. Measure and record the focal length of the spherical convex spherical lens.
5. Likewise, determine the focal length of a weak convex lens.
Distant
light source
Lens
Image
screen
Exercise III: Focal Length and Magnification for a Concave Mirror
1. Insert the light source and the object into one end of the optical bench as shown
below.
2. Place the mirror about 50 to 70 cm from the light source.
3. Adjust the location of the image screen until a sharp image is formed. Measure and
record the object distance, image distance, object height, and the image height in the
Data Table A.
4. Measure and record object and image distances for five additional configuration.
5. Record whether the image is erect or inverted and real or virtual for each case.
Bulb Object
Image
screen
Mirror
6. Now adjust the location of the mirror such that the object distance is smaller than the
focal length found in Exercise I.
51
7. Look directly at the mirror. Qualitatively describe and record the resulting image in
the Data Table B.
Exercise IV: Focal Length and Magnification for Converging Lens
1. Place the object, i.e. the light source, lens, and the screen as shown below.
2. Adjust the location of the screen to obtain a sharp image. Measure and record the
object distance, image distance, object height, and image height in Data Table C.
3. Measure the object and image distances for five additional arrangements.
4. Record whether the image is erect or inverted, real or virtual.
Bulb Object
Image
screen
5. Now adjust the location of the lens such that the object distance is smaller than the
focal length found in Exercise II.
6. Look directly at the through the lens. Qualitatively describe and record the resulting
image in the Data Table D.
7. Repeat steps 1 to 3 to determine the focal length of a second convex lens.
Lens
Exercise V: Combination of Two Converging Lens
1. Place the object, i.e. the light source, lens, and the screen as in Exercise IV.
2. Put a second convex lens near the first convex lens. Record the distance between the
lenses.
3. Adjust the lenses and the screen until a sharp image is formed on the screen.
4. Measure and record the object distance, image distance, object height, and the image
height.
Calculations:
For exercise III:
 Use the mirror equation to determine the focal length of the mirror for each trial.
 Determine the average focal length of the mirror along with the standard deviation
for the focal length.
For exercise IV:
 Use the lens equation to determine the focal length of the lens for each trial.
 Determine the average focal length of the lens along with its standard deviation.
For exercise V:
 Calculate the expected image location for the combination of the lenses.
 Compare the expected magnification with that actual magnification.
52
Data Sheet:
Exercise III:
A. Concave Mirror: Object distance Larger Than Focal Length
Image
Object
Image
Object
Real or
Trial distance, p, distance, q,
height, h,
height, h,
virtual
(in cm)
(in cm)
(in cm)
(in cm)
Upright
or
Inverted
1
2
3
4
5
6
B. Concave Mirror: Object distance Less Than the Focal Length
Real or
Upright or
Magnified or
Virtual
Inverted
Reduced
p<f
Exercise IV:
C. Convex Lens 1: Object distance Larger Than Focal Length
Image
Object
Image
Object
Real or
Trial distance, p, distance, q,
height, h,
height, h,
virtual
(in cm)
(in cm)
(in cm)
(in cm)
1
2
3
4
5
6
D. Convex Lens: Object distance Less Than the Focal Length
Real or
Upright or
Magnified or
Virtual
Inverted
Reduced
p<f
53
Upright
or
Inverted
E. Convex Lens 2: Object distance Larger Than Focal Length
Object
Image
Trial distance, p, distance, q,
(in cm)
(in cm)
1
2
3
4
5
6
Exercise V:
A. Lens Combination
Distance
Object
Image
between
distance, p,
distance, q,
the lenses
(in cm)
(in cm)
(in cm)
Object
height, h,
(in cm)
Results:
Exercise III:
Trial
Focal length
from mirror equation
(in cm)
1
2
3
4
5
6
Average
54
Image
height, h,
(in cm)
Real or
virtual
Upright
or
Inverted
Exercise IV:
Lens 1
Trial
Lens 2
Trial
Focal length, f1,
from thin lens equation
(in cm)
1
1
2
2
3
3
4
4
5
5
6
6
Average
Average
Exercise V:
Measured focal length, f,
(in cm)
Expected focal length, f,
(in cm)
55
Focal length, f2,
from thin lens equation
(in cm)
Percent error
56
Interference
Objective:
 To study the interference of light passing through a double-slit.
 To determine the separation between two slits.
 To measure the wavelength of green light.
Equipment:
 He-Ne laser
 Green laser
 White sheet of paper
 Meter sticks and rulers
 Clamp




Metal stand
Double slits
Optical bench
Laboratory jacks
Theoretical Background:
When two or more waves combine or interfere with one another, their amplitudes add or
superimpose. When the two waves are in phase, then the amplitude of the resulting wave
will be larger the amplitude of the either wave and is known as the constructive
interference. In contrast, if the two waves our out of phase, then the waves tends to
cancle each other and is known as a destructive interference. As in other waves, light
waves will interfere to form bright (constructive) or dark (destructive) spots or fringes.
The position of the bright fringe from the central maximum fringe is given by
(1)
d sin   m
where d is the distance between the slits,  is the angular position of the fringe,  is the
wavelength of the light used, The value m specifies the order of the fringe. The position
of the dark fringe is given by
1

d sin    m  
2

(2)
Pm
ym
d

L
CAUTION: DO NOT LOOK INTO THE LASER AND DO NOT
POINT LASER AT OTHERS!
57
Procedure:
1. Mount the double-slit on the optical bench.
2. Place a He-Ne laser on the laboratory jack and direct a laser beam onto the center of a
double-slit, labeled A, so that an interference pattern is seen on a wall.
3. Turn off the laser and tape a sheet of paper onto the wall where the interference
pattern is observed.
4. Turn the laser back on. Record the distance from the slit to the interference pattern, L,
in Data Table 1.
5. Mark the center of the bright bands on both sides of the central maximum with a
sharp pencil. The marks should be small.
6. Label the center spot as m = 0 and spots adjacent to the center spots as m = 1, 2,
3, and so on.
7. Let the position of the central maximum to be x = 0. Measure the distance between
the nth order from either side of the central maximum. Record the distances in Data
Table 2.
8. Repeat steps 1 to 6 using double-slits B and C.
9. Repeat the experiment using a green laser.
Calculations:
 Using the wavelength of the He-Ne laser to be 632.8 nm, calculate distance between
the slits for the double slits A, B, and C.
 For each double-slit used, calculate the wavelength of the green laser.
58
Data Sheet:
Data Table 1: Distance between the Slits and the Screen
He-Ne Laser
Green Pen Laser
Slit
Slit-Screen distance, L,
in (cm)
Slit-Screen distance, L,
in (cm)
A
B
C
Data Table 2: He-Ne Laser
Double-slit A
Distance
between
nth maxima
in (mm)
Double-slit B
Double-slit C
nth maxima
in (mm)
nth maxima
in (mm)
1st order
2nd order
3rd order
4th order
5th order
6th order
7th order
Data Table 2: Green Pen Laser
Double-slit A
Double-slit B
Distance
Between
nth maxima
in (mm)
nth maxima
in (mm)
1st order
2nd order
3rd order
4th order
5th order
6th order
7th order
59
Double-slit C
nth maxima
in (mm)
Results:
He-Ne Laser
Double-slit A
Double-slit B
Double-slit C
Slit separation, d
in (mm)
Green Pen Laser
Data from DoubleSlit
Wavelength, 
in (nm)
A
B
C
Average
Wavelength
Question:
1. Which measurement is most critical in the experiment?
2. How does the pattern change if the distance from the slit to the screen is made
smaller?
3. What happens to the pattern as the distance between the slits is increased?
60
61
Diffraction Grating
Objective:
 To measure the spacing of a diffraction grating
 To measure the groove spacing of a CD and a DVD
Equipment:
 Diffraction grating
 He-Ne and green lasers
 CD and DVD
 Ringstand



Laboratory jacks
Clamps
Meter stick and ruler
Theoretical Background:
Diffraction refers to the apparent bending of a wave after encountering a small obstacle.
The phenomenon can be explained with Huygen’s principle where every point of a
wavefront acts as a point source for new waves. These waves after passing the obstacle
will interfere with one another producing a series of bright and dark fringes. For a
diffraction to be noticeable, the size of the barrier must be of the same order as the
wavelength.
Figure 1: Diffraction
The diffraction pattern can be created using a device known as a diffraction grating which
consists of either a transparent or a reflective material with uniformly multiple slits or
grooves. For a transparent grating, the light that strikes the grating passes through the
grating and will be bent as shown below.
62

d
d sin
Figure 2: Features of a diffraction for a grating
The resulting interference pattern can be observed on a distant screen placed in front of
the grating. A constructive interference will occur when the path difference between the
light passing through the grooves is a multiple of the wavelength of the light
d sin   m
(1)
where d is the distance between the adjacent slits,  is the angle between the normal to
the grating surface and the location of the maximum, m is known as the order number,
and  is the wavelength of the light.
m=2
2
1
m=1
m=0
laser
grating
screen
Figure 3: Diffraction Setup
The wavelength of a light can be determined by shining a light at a grating with a known
groove separation and measuring the angular position of the mth maxima. Likewise the
grating spacing, d, can be found if the wavelength of the light and the location of the mth
maxima are known.
In this experiment, the groove spacing of several different materials will be found.
63
Procedure:
PART I – Grating Spacing of a Diffraction Grating
1. Place the laser on the laboratory jack and shine a laser beam onto a distant screen.
WARNING: DO NOT LOOK DIRECTLY INTO THE LASER!
2. Position the grating of known groove spacing just in front of the laser such that laser
beam goes through the grating and shines onto the wall. Note the location of the
interference pattern.
3. Turn off the laser.
4. Tape a blank sheet of paper onto the wall at the location of the interference pattern.
5. Turn the laser back on. Mark the location of the center of the bright fringes.
6. Measure the distance from the grating to the screen.
7. Measure and record the distance from the center of the pattern to the maxima on both
sides in
8. Repeat steps 1-7 using a green laser.
PART II – CD Groove Spacing
9. Place a CD about 30 cm in front of the laser.
10. Place a screen directly in front of the laser such that the laser beam reflects back onto
the screen.
11. Aim the laser beam such that the beam reflects off the CD from the grooves near the
outer edge.
12. Measure and record the distance between the screen and the CD.
13. Record the position of the maxima on both sides of the central maximum.
14. Repeat steps 5-8 using a DVD.
64
Data Sheet:
Part I. Grating Spacing of a Diffraction Grating
Part A. Determination of the Grating Spacing
He-Ne laser wavelength, He-Ne =_________________
Maxima
xleft (in cm)
xright (in cm)
1
2
3
4
Distance from the grating to
the screen, L
Part B. Determination of the Wavelength for Green Laser
Grating spacing of the grooves, d =_______________
Maxima
xleft (in cm)
xright (in cm)
1
2
3
4
Distance from the grating to
the screen, L
65
Part II. Determination of the Groove Spacing for CD and DVD
He-Ne laser wavelength, He-Ne =_____________________
Groove Spacing for CD
Maxima
xleft (in cm)
xright (in cm)
Groove Spacing for DVD
Maxima
1
1
2
2
3
3
4
4
Distance from the
grating to the screen, L
xleft (in cm)
xright (in cm)
Distance from the
grating to the screen, L
Calculations:
Show calculation for the determination of the slit spacing for the diffraction grating.
Use the calculated grating spacing to determine the wavelength of the green light.
Determine the groove spacing for both CD and DVD.
Results:
Part I:
He-Ne Laser: Grating Spacing
average
grating spacing, d
(in mm)
Grating spacing,
daverage
66
Green Laser: Wavelength Determination
wavelength, 
average
(in nm)
Wavelength,
average
CD and DVD Groove Spacing:
Groove spacing
(in mm)
CD
DVD
Questions:
1. How does the groove spacing of CD compare with that of DVD?
2. Estimate how much more data one can fit on a DVD compared to a CD. Assume that
the light source for a DVD player is the same as a CD and that data is equally spaced
along the grooves.
67
68
Michelson Interferometer
Objective:
 To observe interference pattern.
 To measure the wavelength of monochromatic light.
Equipment:
 Precision Michelson interferometer
 Green laser

He-Ne laser
Theoretical Background:
The Michelson Interferometer is a device which splits a monochromatic light into two
independent rays and then recombines them to produce an interference pattern as shown
in Fig. 1. The rays are directed along separate paths, one of which can be precisely
changed. The rays are then recombined and superimpose. The resulting interference
pattern can be viewed on a screen.
Fringe pattern as
seen on the screen
Fig. 1: Precision Interferometer
Precisely changing the path of one of the rays can control shifting of the interference
pattern. The wavelength of the monochromatic light is found by measuring the distance
the path must change for one ray that causes the pattern to shift in and out of phase. The
light is split 90o by beam splitter. One ray goes through the beam splitter to a fixed
mirror and the other to a “movable” mirror. The light from the fixed and movable mirror
is reflected directly back to the beam splitter where they recombine. The resulting
interfering beam can be viewed on a screen. The position of the movable mirror can be
adjusted using a micrometer. The distance that the mirror has moved can be determined
from the ratio of the micrometer adjustment to mirror adjustment. The light ray must
travel twice the distance that the mirror moves (out and back). Thus for any number of
phase shifts (between two dark or bright lines) the wavelength can be found from the

2l
m
69
(1)
where m is the number of phase shifts, l is the distance that the mirror has moved.
Procedure:
This apparatus is very delicate and sensitive. Do not move, bump, or try to adjust it
other than described below.
1. Remove beam splitter. Fasten the diverging lens straight on the base plate.
2. Adjust the laser so that the beam reflected from the movable mirror strikes the center
of the diverging lens.
3. Remove the diverging lens by loosening the screw holding the lens.
4. Adjust the movable mirror so that the distance between the plate holding the mirror
and the plate holding the screws is about even (5 – 6 mm).
5. Place the beam splitter without tightening the screws. The partially reflecting surface
should be in the direction of the angle scale. Adjust the beam splitter so that the two
brightest points visible on the viewing screen are located on or almost on a vertical
line. Tighten the screw holding the beam splitter onto the base plate.
6. Use the adjusting screws to move the adjustable mirror until the two brightest points
on the screen overlap each other. Flickering of the bright spot indicates interference.
7. Secure the diverging lens back into the beam and secure it
8. Look at the viewing screen. If you and your lab partners cannot see the fringes, ask
your instructor. Do not try to change the settings or adjust the mirrors.
9. Locate the micrometer and slowly turn the barrel while watching the fringes move.
Notice that the fringes go by very quickly. Proceed when you can control the
micrometer and see one fringe go by the arrow in the lens.
10. Read the initial position of the micrometer.
11. Count 30 fringes go by while slowly turning the micrometer.
12. Read the final position of the micrometer.
13. Repeat steps 3-5 two more times.
14. Record the type of monochromatic light (He-Ne laser or Na vapor).
70
Data Sheet:
Ratio of micrometer adjustment to mirror adjustment: _________________
Position of
Micrometer
Trial
1
2
3
Initial
Final
Type of monochromatic light:
CALCULATIONS:
Determine the optical path difference between the two rays.
Find the wavelength experimental using the average micrometer distance.
Determine the % error of the wavelength for the source that you used.
RESULTS:
Trial
Experimental wavelength, experiment al
Optical path length
1
2
3
Average
Wavelength
71
72
Photoelectric Effect
Objective:
 To determine the Planck’s constant
Equipment:

PASCO Photoelectric Effect apparatus
Introduction and Theory:
When light strikes a metal surface, an electron may be emitted from the surface. The
emitted electron is known as the photoelectron. This effect is known as the photoelectric
effect. The correct explanation for the effect was first given by Albert Einstein.
In this experiment, the photoelectric effect will be performed to determine the Planck’s
constant. The energy carried by the light, E, striking the metal surface is given by
E  hf
(1)
where f is the frequency of the light and h is the Planck’s constant. The light transfers an
energy to the electron in a discrete unit. Some of this energy is used to remove the
electron from the metal and the rest of the energy goes into the kinetic energy of the
released electron. Applying conservation of energy gives
hf  KEmax  
(2)
where  is known as the work function and is the minimum amount of energy that a
photoelectron must absorb in order to escape from the metal surface. The kinetic energy
of the photoelectron will be a maximum when the electron leaves the surface. The
photoelectron travels to the collector plate leading to a current which can be measured,
Figure 1.
Incoming light
Collector plate
Photoelectron
Power supply
Ammeter
Figure 1: Schematic diagram for the photoelectric effect
73
Note that the collector plate is connected to the negative of the variable power supply.
The potential supplied by the variable power supply is a retarding potential. If this
potential difference provided by the variable power supply is large enough, it is possible
to prevent the photoelectrons from reaching the collector plate. The potential difference
at which this occurs is known as the stopping potential. At this stopping potential, the
kinetic energy of the photoelectron is a maximum and is given by
KEmax  eVs
(3)
where Vs is the stopping potential. The wavelength and the frequency of the light are
related through
c  f
(4)
The conservation of energy given by equation (2) can then be written as
Vs 
h

f 
e
e
(5)
In this experiment, you will determine the Planck’s constant by measuring the stopping
potential for various wavelength of light.
Procedure:
1. Cover both the window of the mercury light source enclosure with the mercury cap
and the window of the photodiode enclosure with the photodiode cap as shown
below.
covered
74
2.
3.
4.
5.
Turn on Power and Mercury Lamp on the h/e power supply.
Turn on the photoelectric apparatus by pushing in the power button.
Allow the light source and the apparatus to warm up for about 20 minutes.
Set the Voltage Range Switch on the far right of the panel to -2 - +2 V and the
Current Range switch on the far left of the panel to 10-13.
6. Disconnect the ‘A’, ‘K’, and ‘down arrow’ cables on the back panel of the apparatus
to set the current amplifier to zero.
7. Press the Phototube signal button in to Calibration.
8. Adjust the Current Calibration knob until the current is zero.
9. Press the Phototube Signal button to Measure.
10. Reconnect the ‘A’, ‘K’, and ‘down arrow’ cables on the back panel of the apparatus.
ALWAYS HAVE A FILTER ON THE WINDOW OF THE PHOTODIODE
ENCLOSURE, AND PUT THE CAP ON THE MERCURY LIGHT SOURCE
WHENEVER FILTER OR APERTURE IS CHANGED.
11. To start the measurement, uncover the window of the photodiode enclosure. Place 4
mm diameter aperture and the 365 nm filter onto the window of the enclosure.
12. Uncover the window of the Mercury light source.
13. Adjust the Voltage Adjust knob until the current on the ammeter reads zero.
14. Record the magnitude of the stopping potential for the 365 nm wavelength in Data
Table 1.
15. Cover the window of the Mercury light source.
16. Replace the 365 nm filter with the 405 nm filter.
17. Repeat steps 13 – 16.
18. Repeat the measurement procedure for 436 nm filter, 546 nm filter, and 577 nm filter.
19. Repeat the data measurement for 2 mm diameter aperture.
75
Data Sheet:
Data Table 1: Stopping Potential of Spectral Lines, 4 mm Diameter Aperture
Wavelength,
 (in nm)
Frequency,
  c  (  1014 Hz )
Stopping Potential,
V (in V)
1
2
3
4
5
365.0
404.7
435.8
546.1
577.0
Data Table 2: Stopping Potential of Spectral Lines, 2 mm Diameter Aperture
Wavelength,
 (in nm)
Frequency,
  c  (  1014 Hz )
Stopping Potential,
V (in V)
1
2
3
4
5
365.0
404.7
435.8
546.1
577.0
Calculations:
1. From the data, determine the frequency of the light.
2. Plot the stopping potential versus the frequency of the light (  1014 Hz ).
3. Determine the slope of the best-fit line through the data points on the graph.
4. Show calculations for the Planck’s constant and the work function of the
photocathode.
5. Calculate the work function from the graph of stopping potential vs. frequency.
76
77
Hydrogen Spectrum
Objective:
 To observe the emission spectrum of hydrogen
 To measure the wavelength of the emission lines for hydrogen spectrum
 To compare the measured energies of the photons with Bohr’s prediction
Equipment:
 Spectrum tube power supply
 Transmission diffraction grating


Hydrogen discharge tube
Wooden spectrometer apparatus
Theoretical Background:
Light is an electromagnetic wave. The wavelength of visible light ranges from about
400 nm for blue-violet to 700 nm for red. It is possible to separate the light into its
constituent components. The pattern of resulting colors after separation is called a
spectrum. There are three different types of spectra. These are continuous spectra,
bright-line (emission), and dark-line (absorption) spectra.
A hot dense gas object will produce a continuous spectrum whereas a hot transparent gas
will produce an emission spectrum. A continuous band of colors are visible in a
continuous spectrum. In an emission spectrum, a series of bright lines are visible against
a dark background. In contrast, a series of dark lines are visible against a continuous
spectral background for a absorption spectrum. The dark lines seen in the absorption
spectrum represents the wavelengths of the light which are absent. By observing the
spectrum, it is possible to determine the properties of the light source. This is the method
which is used to determine the features of the distant stars and galaxies as well as objects
in our solar system.
The emission spectrum of hydrogen has four strongly visible lines. These lines have
wavelengths of 656.3 nm (red), 486.1 nm (blue-green), 434.1 nm (blue-violet), and 410.1
nm (violet). Balmer, in 1885, discovered that the wavelength of the light can be found
from
78
1 
 1
 RH  2  2 

n 
2
1
(1)
where n are integers with values of 3, 4, 5,  and RH  1.097  107 m-1 is known as the
Rydberg constant. The correct explanation for the perplexing equation was given by Bohr
in 1913.
Bohr assumed that the electron orbiting the nucleus travels in a circular orbit. He further
assumed that the radius of the orbit can have only certain values, i.e. the orbits were
quantized. The orbital state was characterized by the principal quantum number n (
n  1,2,3,  ) with the total energy of the hydrogen given by
En  
me k e2 e 4 1
2 2 n 2
(2)
where me is the mass of the electron, k e is the Coulomb constant, e is the magnitude of
the charge of an electron, and   h 2 where h is the Planck’s constant. In terms of the
Rydberg constant, the total energy of the hydrogen atom is given by
E n  hcRH
1
n2
En  
or
13.6
eV
n2
(3)
If n is larger, then the electron is at a higher state and the atom will have greater energy.
When an electron undergoes a transition from a higher state with higher energy to a lower
state with lower energy, then the atom will emit a photon of energy
E  E i  E f
(4)
where
E  hf
or
E  h
c

(5)
From equations (3) and (5), the energy of the emitted photon is
 1
1 
  RH  2  2 
n


 i nf 
1
(6)
If the electron undergoes a transition to a state n f  2 , then equation (6) reduces to
Balmer’s formula.
In this laboratory, a transmission diffraction grating will be used to produce bright-line
spectra from hydrogen gas-discharge tubes. A transmission diffraction grating is a just a
piece of material having a large number of equally separated slits. Typical distance
79
between the slits – grating spacing – is on the order of the wavelength of the light and
varies from about 500 nm to 2000 nm .
Procedure:
1. Place the grating in the grating slot of the apparatus.
2. Measure and record the distance from the grating to the slit, L , in data table.
3. Record the number of lines per unit length, n, for the transmission grating.
4. Use extreme caution when using spectrum-tube power supply. Do not touch the
supply electrodes while the supply is turned on. Replace the discharge tubes only
when the power supply is turned off.
5. Place the hydrogen discharge tube in the tube holder of the spectrum-tube power
supply.
6. Align the light source such that the slit, as seen through the grating, is as brightest as
possible as shown below.
meter stick
Balmer line
eye

grating
Hydrogen gas
L
7. Look straight through the grating.
8. A first-order Balmer lines should be visible on the left and the right sides of the
discharge tube.
9. Measure and record the position of Balmer lines on the left, x left , and the right, x right ,
of the slit in Data Table 1.
10. Replace the hydrogen source with another source.
11. Measure and record the location of the strongest visible line.
80
Data Sheet:
Data Table 1: Hydrogen Spectrum
Distance from the slit to the grating, L = ______________
Number of grating per unit length = ___________________
Color
xhigh
xlow
xaverage
xlow
xaverage
Red (left)
Red (right)
Blue-Green (left)
Blue-Green (right)
Blue-Violet (left)
Blue-Violet (right)
Violet (left)
Violet (right)
Data Table 2: Unknown Spectrum
Color
xhigh
Calculations:
 From the number of lines per unit length on the grating, calculate the distance
between the slits on the grating.
 Show calculations for the wavelength and the frequency of each line.
 Using the frequency, calculate the experimental value of the energy of the emitted
photon corresponding to each line.
 Determine the theoretical value of the emitted photon energy.
 Calculate the percent error between the expected and the experimental photon
energies.
 Determine the wavelength of the unknown source. Using the spectrum chart, identify
the element in the second discharge tube.
81
Results:
Results Table 1: Hydrogen Spectrum
wavelength
Color
average

frequency
f
Eexperimental
Etheoretical
frequency
f
Eexperimental
Etheoretical
Red
Blue-Green
Blue-Violet
Violet
Results Table 2: Unknown Spectrum
wavelength
Color
average

82