1
Created by J. Stoll
WUHS – 2006 ed. 2011
For use with Holt Physics, Serway and Faughn, 2006.
Chapter 17
Ohm’s Law
Electric Power
Activity: Electric Cooking
Chapter 18
Schematic Diagrams and Series Circuits
Applying Ohm’s Law to Series Circuits
Properties of Parallel Circuits
Applying Ohm’s Law to Parallel Circuits
Complex Resistor Combinations
Chapter 11
Simple Harmonic Motion
Types of Waves
Parts of Waves
Superposition of Waves – Interference
Standing Waves
Properties of Sound
Doppler Effect
Sound Levels
Sound Interference
Sound Resonance
Harmonics
Lab: Calculating the Speed of Sound in Air
Chapter 12
2
Electromagnetic Spectrum
Color Spectrum
Linear Polarization of Light
Flat Mirrors
Concave Spherical Mirrors
Drawing Ray Diagrams
Properties of Concave Mirrors
Lens/ Mirror Equation
Convex Mirrors
Chapter 13
Refraction and Snell’s Law
Refraction and the Speed of Light
Critical Angle and Total Internal Reflection
Dispersion of Light and Rainbows
Lenses
Drawing Ray Diagrams for Lenses
Lab: Finding Focal Lengths of Lenses
Chapter 14
Properties of the Nucleus
Rest Energy
Heavy Elements vs. Light Elements
Binding Energy
Nuclear Decay
Nuclear Equations
Measuring Decay
Nuclear Reactions
Particle Physics
Chapter 22
Chapter 13
Color and Light Addition
Color by Subtraction
3
4
When a student is connected into a simple circuit with a generator, what happens to
the current through the student when the voltage is increased? Why? The current
goes up due to the voltage increase which increases the electric pressure.
When a student is connected into the same circuit with the generator and another
student what happens to the current through the students? When more students are
added? Why does it do this? The current decreases. The electrons have to travel
through both students – increasing electric resistance.
As the voltage increases in a circuit for a constant resistance, the current
_increases__.
The relationship in equation form:
I V
As the resistance increases in a circuit for a constant voltage, the current
__decreases__.
The relationship in equation form:
I R
5
What is the electric relationship between current and voltage, and current and
resistance? Directly; inversely
I = V/R
 Combine the two relationships:
Ohm’s Law – the current through an electrical circuit is directly proportional to the
applied voltage and is inversely proportional to the electrical resistance of the
circuit.
 Assumes a constant resistance for different voltages
 Light bulbs do not obey Ohm’s law – increasing voltage, increases the bulb’s
resistance because of an increase in temperature.
o Light bulbs do however obey the Law at specific voltages and it can be
used to calculate the current or resistance at that voltage.
V
I
R
Lig
1. An automobile headlight with a resistance of 8  is placed across a 12V
battery. What is the current through the headlight?
I  V / R  12V / 8  1.5A
2. A flashlight with a 6 V lantern battery has a current of 1.125 A. What is the
resistance value of the light bulb at that voltage?
R  V / I  6V / 1.125 A  5.33
3. A student with a resistance value of 34,000 has a current of 0.008 A flowing
through him. What is the voltage across the student?
V  I  R  0.008 A  34000  272V
Assignment Ch. 17: 27-42, 69
6
What do the numbers at the top of selected light bulbs tell you?
The power of the light bulb – how much relative light it will emit when
connected to 120V
Ex. Different light bulbs
Electric Power – (Watts) – the rate of electrical energy used or radiated per
unit time. (1 Watt = 1 Joule / 1 sec)
* Current is the charge per unit time, and voltage is the energy per unit charge
Recall:
Work = q V;
Power = W/t = q V/t = (q/t) V = I V
1. P = I V
2. P = V2/ R
Substituting in for current: I = V/R; P = V/R x V = V2/ R
3. P = I2 R
Substituting in for voltage: V=I R; P = I (I R) = I2 R
Energy dissipated by electric current:
EE = P t
Electric energy is in units of Joules
Calculate the energy dissipated by a 40 W bulb in 2 hours:
E  P  t  40W  2h  3600s / h  288,000 J
Which of these bulbs have more resistance and current? Assume they are across a
120 V outlet.
Power (W)
7.5
15
40
90
200
Resistance ()
1920
960
360
160
72
Current (A)
0.0625
0.125
0.33
0.75
1.67
7
What can you conclude about the thickness of their filaments?
Smaller light bulbs have a thinner filament -> more resistance
What are fuses and circuit breakers used for in circuits?
To stop the flow of charge when the current becomes too large – current
generates heat which will melt the fuse and break the circuit.
Demo: aluminum fuses and circuit breaker
How much energy does a 60 W light bulb use in a day?
E  P  t  60W  24h  3600s / h  5,184,000 J
 1440Wh  1.44kWh
Why do power companies use kilowatt-hours to charge for electricity used?
A joule is a very small unit of energy. A more convenient unit would be much
larger.
Kilowatt-Hours – unit of energy used by power companies to charge you
money.
1kWh  3,600,000 J
How is electricity transmitted to your homes?
Power lines – thick (about as thick as a quarter) silver-copper alloy with steel
reinforced cable wires
Why would the transmission of energy to your home be at high voltages and low
currents? Hint: recall power equation #3, current determines heat energy loss.
Heat is the number one loss of energy in power lines. Current generates heat,
therefore any reduction in current will mean less energy loss.
Resistance of power cables = 0.2  / 1 km
If your home was 81 km away from the power station, how much power is lost from
the power company in kW? The current of power lines average ~41 A. At cost rate
of 12 cents per kWh, how much money is the power company losing in a day? A
year?
P  I 2  R  412  0.2 / km  81km  27232.2W  27.2kW
E  P  t  27.2kW  24h  652.8kWh  $78.34 / day;$28613.69 / year
Do Lab: Electric Cooking
Assignment Ch. 17: 43-56, 72, 73
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Application of Ohm’s Law, Power, and Electric Energy.
2
I = V/ R;
P = I R;
E=Pt
Using a multi-meter, measure the average current through your hot dog:
I = _______________ A
Record the amount of time, using a stopwatch, needed to cook your hot dog:
t = ___________ s
1. Calculate the resistance of your hot dog when it is connected across 120 V:
2. Calculate the power that heated your hot dog:
3.
Calculate the energy needed to cook your hot dog:
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10
What do architects use to construct buildings?
Blue prints – they have the basic structures with symbols that represent
different objects in the building.
What is a schematic diagram?
A blue print for a circuit.
What do these symbols mean for schematic diagrams?
Wire
resistor
lightbulb
Switch (open) battery
capacitor
What is a series circuit?
A circuit in which all the resistors are connected in-line with each other
creating one current pathway.
What would be the properties of such a circuit?
The properties of a series circuit can be summarized below;
1. Electric current has one single pathway through the circuit. This means that
the current passing through each electrical device is the same.
2. The current is influenced by the resistance of each of the resistors, so that the
total resistance of the circuit is equal to the sum of all the resistance.
3. Ohm’s law applies to each of the resistors in the circuit. The voltage drop or
the volts used by each resistor depends directly on the value of their
resistance. That means that a larger resistor will proportionally use more volts
than a smaller resistor.
4. The sum of the volts used by each of the resistors is equal to the voltage
impressed across the circuit.
VT = V1 + V2 +V3 +…
RT = R1 + R2 + R3 +…
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IT = I1 = I2 = I3 =…
Given the two light bulbs in the sockets - One is 25 W and the other is 60 W. When
placed in series in a 120 V circuit, which one shines the brightest?
a. 25 W bulb
b. 60 W bulb
c. Neither, they both are equally bright
Why does this occur?
The current through each bulb has to be the same – a property of series
circuits. If a resistor has more resistance than another, then it will require or
use proportionally more voltage in the circuit. Same current with more voltage
= more power.
What happens to the light bulbs when one of them is unscrewed from its socket?
They all go out.
Why did it do this?
The circuit is now broken and current won’t flow.
Apply Ohm’s Law to series circuits:
Given this schematic diagram:
10 
20 
15 
6V
1. Find the equivalent resistance of this series circuit.
RT = R1 + R2 + R3
= 10 + 20 + 15 = 45 
2. Find the current through the series circuit
I = V/R = 6 / 45 = 0.133 A
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3. Find the voltage drop across each resistor.
V1 = I R1
= 0.133 x 10 = 1.33 V
V2 = 0.133 x 20 = 2.67 V
V3 = 0.133 x 15 = 2 V
4. Compare the individual voltages to the total voltage of the circuit. Does the
property of a series circuit and voltage true?
VT = 1.33 + 2.67 + 2 = 6V; Yes, they add up to the total voltage of the circuit.
5. Find the power dissipated by each resistor.
P1 = I x V = 0.133 x 1.33 V = 0.177 W
P2 = 0.133 x 2.67V = 0.353 W
P3= 0.133 x 2 = 0.266 W
6. Compare the total power of the circuit to the power of each of the resistors,
what can you conclude?
PT = 0.177 + 0.353 + 0.266 = 0.796 W
PT = I x VT = 0.133 x 6 V = 0.798 W
The sum of the individual resistor powers is equal to the total power of
the circuit (excluding rounding errors). This is an example of the law of
conservation of energy.
Go through the practice problems on pg. 650 in groups.
Do Activity: Testing Series Circuits
Assignment Ch. 18: 1-4, 6-11, 16, 17, 27, 29-31
13
Using the resistors from the bin, construct 3 different series circuits, using 3
resistors connected to 3 DCV. DO NOT GO OVER 3 DCV FOR HEALTH AND
SAFTEY REASONS! RESISTORS MAY BECOME VERY HOT AND EMIT
HARMFUL VAPORS!
Fill in the following data tables. Calculate the equivalent resistance of your circuits,
calculate the current through the circuit, and calculate the voltage drops across each
resistor. Then measure the values from your circuit to verify your calculations.
Note; values may be off due to the wires adding a small amount of resistance.
Resistor 1
()
Series Circuit 1
Resistor 2 Resistor 3 Totals
()
()
Calculated Measured
Current (A) Current (A)
Resistor 1
()
Series Circuit 2
Resistor 2 Resistor 3 Totals
()
()
Calculated Measured
Current (A) Current (A)
Resistor 1
()
Series Circuit 3
Resistor 2 Resistor 3 Totals
()
()
Calculated Measured
Current (A) Current (A)
Resistance
Value
Calculated
Volts for each
resistor
Measured Volts
for each
resistor
Resistance
Value
Calculated
Volts for each
resistor
Measured Volts
for each
resistor
Resistance
Value
Calculated
Volts for each
resistor
Measured Volts
for each
resistor
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What kind of circuit is used primarily in homes? Why?
Parallel, we will find out today.
What is a parallel circuit?
A parallel is a circuit where each resistor is connected across the same potential
difference. Each connected resistor forms a ladder like structure called branches.
How would the properties of a parallel circuit differ from a series circuit?
R1
R2
R3
The properties of a parallel circuit can be summarized below:
1. Each resistor connects the two terminals of the power source by ladder like branches of
wires. The voltage applied across these branches is the same voltage applied to each
resistor.
2. The total current supplied by the power source divides among the parallel resistors in the
circuit. Ohm’s law applies to each of the resistors and draws its current from the source.
The currents from each of the resistors added together is equal to the total current drawn
from the source.
3. Each resistor creates a branch or a new pathway for the current flow, decreasing the
overall resistance of the circuit. This means that the total resistance of the circuit is
always less than one resistor or combination of resistors in the parallel circuit. The
relationship of resistance in a parallel circuit can be given by the following equation:
1. VT = V1 = V2 =V3 =…
2. 1/ RT = 1/R1 + 1/R2 + 1/R3 +…
3. IT = I1 + I2 + I3 +…
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Given the two light bulbs in the sockets - One is 25 W and the other is 60 W. When
placed in parallel in a 120 V circuit, which one shines the brightest?
a. 25 W bulb
b. 60 W bulb
c. Neither, they both are equally bright
Why does this occur?
The 60 W bulb shines the brightest because all resistors get the same voltage as the
source. Since the 60 W bulb has the smaller resistance, more current will flow
through it than the other bulb. It will have the most power, = 60W.
What happens when one of the light bulbs is unscrewed from its socket?
The other remains lit.
Why does this occur?
It still has the voltage of the power source across it.
Apply Ohm’s Law to parallel circuits:
Given this schematic diagram:
10 
20 
15 
6V
1. Find the equivalent resistance of this parallel circuit.
1/ RT = 1/R1 + 1/R2 + 1/R3 = 1/10 +1/20 + 1/15 = 0.217
RT = (0.217)-1 = 4.62 
Note: The resistance of a parallel circuit will always be smaller than the resistance
of the smallest resistor in the circuit.
2. Find the current through the parallel circuit
IT = V/R = 6/4.62 = 1.3 A
3. Find the voltage drop across each resistor.
All the resistors have the same voltage as the source = 6 V
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4. Compare the individual currents to the total current of the circuit. Does the
property of a parallel circuit and current true?
I1 = 6/10 = 0.6 A
IT = 0.6 +0.3 + 0.4 = 1.3 A
I2 = 6/20 = 0.3 A
Yes, the total current from the source is the sum
I3 = 6/15 = 0.4 A
of the individual currents.
5. Find the power dissipated by each resistor.
P1 = 0.6 x 6V = 3.6 W
P2 = 0.3 x 6V = 1.8 W
P3 = 0.4 x 6V = 2.4 W
6. Compare the total power of the circuit to the power of each of the resistors,
what can you conclude?
PT = 3.6 +1.8 + 2.4 = 7.8 W
PT = 1.3 x 6V = 7.8 W
Yes, the total power from the source is the sum of the individual powers.
Go through the practice problems on pg. 655 in groups.
Do Activity: Testing Parallel Circuits
Assignment Ch. 18: 12, 18, 19, 28, 39, 40, 48, 49
17
Using the resistors from the bin, construct 3 different parallel circuits, using 3 resistors connected to 3
DCV. DO NOT GO OVER 3 DCV FOR HEALTH AND SAFTEY REASONS! RESISTORS
MAY BECOME VERY HOT AND EMIT HARMFUL VAPORS!
Fill in the following data tables. Calculate the equivalent resistance of your circuits, calculate the
current through the circuit, and calculate the current of each resistor. Then measure the current for your
circuit to verify your calculations. Note: values may be off due to the wires adding a small amount of
resistance.
Parallel Circuit 1
Resistor 1 Resistor 2 Resistor 3 Totals
Calculated Measured
Current (A) Current (A)
()
()
()
Resistance
Value
Calculated
Current for
each resistor
Resistor 1
()
Parallel Circuit 2
Resistor 2 Resistor 3 Totals
()
()
Calculated Measured
Current (A) Current (A)
Resistor 1
()
Parallel Circuit 3
Resistor 2 Resistor 3 Totals
()
()
Calculated Measured
Current (A) Current (A)
Resistance
Value
Calculated
Current for
each resistor
Resistance
Value
Calculated
Current for
each resistor
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Given the three light bulbs in the sockets - One is 60 W and the other two are 25 W.
The 60 W bulb is placed in series with the other two bulbs in parallel. When placed
in a 120 V circuit, which bulb shines the brightest?
a. 25 W bulb
b. 60 W bulb
c. Neither, they all are about equally bright
Why does this occur?
When the two 25 W bulbs are placed in parallel, their overall resistance is cut in
half due to the properties of a parallel circuit. Their overall resistance is now about
the same as the 60 W bulb. Two identical bulbs in series will equally share the
voltage, and have the same current, therefore they will shine equally bright.
Given a complex circuit:
10  15 
50 
10 V
Step 1:
Redraw the circuit as a group of
resistors along one side of the circuit
50 
10 

10 V
50 
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50
Step 2:
Identify components in series (if any)
and calculate their equivalent resistance
50 
10 

10 V
50 
50 

10 V
50 
20
Step 3:
Identify components in parallel, and
calculate their equivalent resistance
50 

10 V
50 
 


10 V
Step 4:
Repeat steps 2 and 3 until the resistors
in the circuit are reduced to a single
equivalent resistance


10 V
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

To solve the complex circuit for the voltage drops, current, and power of each
resistor follow the series and parallel rules as you work backwards to the original
circuit.
Start by calculating the current
through your simplified circuit:
50 




V




Apply series circuit rules to solve
for current and voltage drops:
 
10 V


I = 0.2A
V = 0.2 x 25
=5V
I = 0.2A
V = 0.2 x 25
=5V
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The next two steps can be combined to get back to the original circuit since both
parts of the circuit are separate and distinct sections.
Use series and parallel to the corresponding
parts to solve for their
currents and voltage drops.
50 V
10 
10 V

I = 0.2 A I = 0.2A
50 V
You can now calculate the power of each resistor.
See Solution
V1 = 0.2 A x 10 = 2 V
V2 = 0.2 A x 15 = 3 V
V3 = V4 = 5V (property of parallel circuits)
I3 = I4 = 5V/50 = 0.1 A
P1 = 0.2A x 2V = 0.4W
P2 = 0.2A x 3V = 0.6W
P3 = P4 = 0.1A x 5V = 0.5W
PT = 0.4 + 0.6 +0.5 + 0.5 = 2 W
PT = 0.2A x 10V = 2 W
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Solve for the current, voltage drops, and power of each resistor in the following
complex circuit:
10 
22 
100 
33 
9V
See Solution
9V
110 
55
1/ RT = 1/R1 + 1/R2 = 1/110 +1/55 = 3/110
RT = 110/3 = 36.7 
IA = 9V/110 = 0.082A
IB = 9V/55 = 0.163A
V1 = 0.082 x 10 = 0.82V
V2 = 0.082 x 100 = 8.2V
V3 = 0.163A x 22 = 3.59V
V4 = 0.163A x 33 = 5.38V
P1 = 0.082 x 0.82V = 0.067 W
P2 = 0.082 x 8.2V = 0.672 W
P3 = 0.163A x 3.59V = 0.585 W
P4 = 0.163A x 5.38V = 0.877 W
Do Activity: Testing Complex Circuits
Assignment Ch. 18: 14, 15, 20-26, 33, 35, 36
24
Using the resistors from the bin, construct 3 different compound circuits, using 4 resistors
connected to 3 DCV. DO NOT GO OVER 3 DCV FOR HEALTH AND SAFTEY
REASONS! RESISTORS MAY BECOME VERY HOT AND EMIT HARMFUL
VAPORS!
Fill in the following data tables. Calculate the equivalent resistance of your circuits, calculate
the voltage across each resistor, calculate the current through each resistor, and calculate the
current from the power supply. Then measure the current for your circuit to verify your
calculations. Note: values may be off due to the wires adding a small amount of resistance.
Complex Circuit 1
Resistor 1
()
Resistor 2
()
Resistor 3
()
Resistor 4
()
Resistance
Value
Calculated
Voltage
Calculated
Current
Draw your compound circuit:
25
Total
Resistance
()
Calculated
Circuit
Current
(A)
Measured
Current
(A)
Complex Circuit 2
Resistor 1
()
Resistor 2
()
Resistor 3 Resistor 4
()
()
Resistance
Value
Calculated
Voltage
Calculated
Current
Draw your compound circuit:
26
Total
Resistance
()
Calculated
Circuit
Current
(A)
Measured
Current
(A)
Complex Circuit 3
Resistor 1 Resistor 2 Resistor 3 Resistor
()
()
()
4 ()
Resistance
Value
Calculated
Voltage
Calculated
Current
Draw your compound circuit:
27
Total
Resistance
()
Calculated
Circuit
Current
(A)
Measured
Current
(A)
28
What is a pendulum? What is it used for?
A pendulum is a mass at the end of a string or other similar configuration. Was
investigated by Galileo and was found to have a very regular period. It is used for
clocks, determining accelerations, and spin rates.
What force is powering a pendulum?
Gravity. The acceleration is constant
What determines how long it takes to make a complete back-and-forth motion?
The length of the string.
Amplitude – the distance or the size of the wave/vibration from the neutral line. It’s
related to the energy of the wave/vibration.
Period – (T) (units = seconds) the time it takes for a wave/vibration to repeat itself;
the time for one complete oscillation back to the original position.
Frequency – (units = Hz) – the number of oscillations, or waves, or vibrations per
unit time. It can describe the rate of wave production – waves/second = Hz
FT

L
mass
Fg
Small angle approximation of Pendulum motion:
L T
T  2
;

g 2
L T2
L gT 2
;
 ;
L
g 4 2 g 4 2
Using the formula given, create a pendulum with a period of one second, ½ second,
and 1 ½ seconds.
What would be the period of these pendulums on the moon where g = 1.63 m/s2?
Assignment Ch. 11: 12-17, 19, 20, 49
29
What is a wave?
It is a periodic disturbance that travels through a medium.
What does it do?
It carries energy away from the initial disturbance.
List some examples of waves:
Water, sound, light, seismic (earthquake), electricity, wind, etc.
What is the source of all waves?
A vibration of some sort.
Periodic Motion - (Pendulum) – the time it takes for a wave/vibration to repeat
itself; the time for one complete oscillation back to the original position.
Demo: super slinky
How do we represent waves?
Demo: marker on white board
- mathematically this is called a: A Sine curve
Wave pulse – A single disturbance in a medium.
Phase - (conceptually represented) – the direction of the wave pulse.
Phase up – (erect, crest, positive phase) – is the phase that is above (+
direction) the neutral position.
Phase down – (inverted, trough, negative phase) – is the phase that is below (direction) the neutral position.
Mechanical waves - (2 types) – a wave created in a matter medium
 matter doesn’t move with the wave - only the energy is transferred!
30
Transverse – the wave propagation is perpendicular to the direction of the
wave speed.
visual representation:
Longitudinal – the wave propagation is parallel to the direction of the wave
speed. (sound is longitudinal wave)
visual representation:
Electromagnetic waves – waves created by vibrating charges and do not require
matter to propagate. EM waves are transverse waves.
Assignment Ch. 11: 22-28
31
How do we represent waves? Sine curve
What do waves transmit? Energy
How fast do waves travel? That is determined by the type of wave and the
properties of the medium.
Each kind of wave possesses the following:
amplitude, crest, trough, neutral line, wavelength
Crest
Amp.
Neutral Line
Trough
Wavelength
Representing longitudinal waves: (Sound)
Compression Expansion
Compressions – areas of higher pressure in a longitudinal wave, they
correspond to the crest of the wave.
Rarefactions - (Expansions) – areas of lower pressure in a longitudinal wave,
they correspond to the trough of the wave.
Note: the neutral is the normal pressure of the undisturbed medium.
Wavelength - (symbol = ) – (units = meters) the distance covered by a wave in
one period.
Period - (symbol = T) – (units = seconds) the time it takes to make one complete
wave or one vibration.
Frequency - (symbol = f) (units = Hz) the rate of waves produced per unit time.
f = waves/time.
Looking at the units, what do you think the relationship is between period and
frequency? f = 1/T
32
Wavespeed - (symbol = v) – (units = m/s) – the rate of distance covered per unit
time by a wave traveling through a medium.
Example: You’re at a Railroad crossing and notice that 2 train cars pass by the
lights in 1 sec. Each train car is 18 m long. How fast is the train going?
v = (2 train cars/ 1 sec.) x (18m / train car) = 36 m/s
Do a unit analysis to find out what the relationship between wavespeed, period,
frequency, and wavelength.
 Wavespeed equation:
v=f 
What determines the speed of the wave?
the type of wave and the property, it has nothing to do with frequency or
wavelength!
What happens when the frequency of the vibration is increased?
Wavelength decreases
What happens when the wavelength is increased?
Frequency has decreased
Examples:
Calculate the wavelength of your favorite tone from the signal generator: The speed
of sound in air is 343 m/s.
Calculate the period of vibration for the speaker producing your favorite tone from
above:
Calculate the wavelength of your favorite FM and AM radio station: The speed of
8
light is 3 x 10 m/s.
Assignment Ch. 11: 29-35, 46-48
33
What are tidal waves and tsunamis?
Large waves that come from the ocean
What are Rogue waves and why are they different than the other waves?
Rogue waves are produced by wave interference.
How are these Rogue waves created?
By waves adding together to make a bigger wave.
Interference - (2 kinds) – when two or more waves meet in the same medium.
Constructive – waves meet in phase and add to create a larger wave
Destructive – waves meet out of phase and subtract to create a smaller wave
or even no wave.
Demo: superslinky in hallway - constructive and destructive
Videos: Rogue Waves
http://www2.waterforduhs.k12.wi.us/staffweb/stoll/Wave%20Videos.htm
What happens when the incident wave from a source interferes with its own
reflected wave? Both wave forms have the same properties and will create areas of
constructive and destructive interference.
Demo: superslinky
Standing wave – a stationary wave form created by interference from a similar
wave or reflected wave.
 parts of a standing wave:
Node – the area with little or no movement in a standing wave. It is created by
destructive interference.
Anti-Node – the area of greatest displacement in a standing wave. It is created by
constructive interference.
Video: Tacoma Narrows Bridge
http://www2.waterforduhs.k12.wi.us/staffweb/stoll/Wave%20Videos.htm
What is the relationship between the number of AN’s and the frequency of the wave
produced? 1 AN = ½  therefore; 2AN = 1 . It is a direct relationship: double the
AN’s by doubling the frequency.
34
1/2  standing wave:
1  standing wave:
1 1/2  standing wave:
Measuring a slinky’s wavespeed using standing waves:
1) Measure out 5 meters, and stretch the super slinky out to that length. Create a
1/2  standing wave:
See example Solution
2) Measure the frequency of the standing wave using a stopwatch:
10 vibrations/ _________ sec.
3) Calculate the wavelength of the standing wave:
4) Calculate the wavespeed of the superslinky:
v = f 
Do the same for a 1  standing wave and 1 1/2  standing wave, and compare their
wavespeeds. What do you notice about their frequencies?
Assignment Ch. 11: 36, 37, 40-43
35
36
What is sound? A longitudinal wave created by a series of compressions and
expansions in a medium.
Demo: paper towel in doorway
As you increase the frequency what happens to the wavelength of sound?
The wavelength decreases
How is sound created? A vibrating source.
Demo: wave generator and speaker
How is sound represented? A sine curve, however the crest and trough are
physically different than a transverse wave, but retain all wave properties.
Crest – compression areas
Trough – expansion areas
Different materials have a different speed of sound in them. Air at room
0
temperature (20 C) and 1 atm pressure, speed = 343 m/s. In general, the speed
0
increases 0.59 m/s for every 1 C increase.
* increase the temp. ----> increases the # of molecular collisions - air is more elastic
Pitch - a term used to describe sound frequency - Hz
* Hearing range for humans (varies by age and gender)
----> 20 Hz – 20,000 Hz
Demo: sound generator
Infrasonic – sound frequencies lower than 20 Hz
Ultrasonic – sound frequencies greater than 20,000 Hz
Speed of sound in water = ~1500 m/s (NOT surface waves!)
 the molecules are closer together----> molecules transfer energy faster
Speed of sound in metals = ~5000+ m/s
 the atoms are very close together, and metals are very elastic!
Back in the 1800’s and early 1900’s people put their ears to the railroad track. Why
did they do that? Sound travels easier and farther through metals than any other
material.
Assignment Ch. 12: 1-5, 8, 9, 39
37
What happens to sound if the source or observer is moving?
The pitch of the source appears to change.
Demo: Mr. Doppler, Video
Doppler Effect – the apparent shift in frequency due to the motion of the source
and/or the observer.
toward – higher frequency
away – lower frequency
 works for all types of waves! - transverse, longitudinal, and electromagnetic
wave speed
1
2
Boats on water, radar/Laser guns
 Boat 1 travels against the velocity of the wave crests. Boat 1 will encounter
more _______ wave crests per unit time.
 Boat 2 travels with the velocity of the wave crests. Boat 2 will encounter
less _______ wave crests per unit time.
Each boat will perceive a different frequency than the frequency measured by a
stationary observer.
What happens when the boat or any other source travels faster than the wave speed
of the material? Since the wavespeed is determined by the properties of the
material, the motion of the source does not change the properties. The source causes
the waves to overlap constructively creating a very high crest in front of the source,
followed by a very large trough.
In water = bow wave
In air = shock wave - i.e. sonic boom
Video clips: aircraft breaking the sound barrier
Assignment Ch. 12: 6, 7, 11, 12
38
How do we measure the amount of sound coming from a source?
Measure the difference in pressure from the crest and trough.
Amplitude – a sound wave amplitude is determined by the relative pressure
difference caused by the compression or expansion of a sound wave.
Higher pressure > more energy > louder sound
Decibels – (dB) – the unit used to measure the relative loudness of sounds based on
a logarithmic scale of base 10. For a given sound, every 10 dB increase means the
sound is 10x more intense.
 exponential scale: 20 dB is NOT twice as intense as 10 dB
 20 dB is 10x more intense than 10 dB, and 30 dB is 100x more intense than a
10 dB sound.
Demo: Sound meter
Examples:
1. How many times more intense
is a rock concert to a physics
class?
Physics class = ________ dB
2. How many times more intense
is a physics class to a
whisper?
3. How many times more intense is a physics class to a jet?
Assignment Ch. 12: 17, 18
39
How do piano tuners tune a piano? They listen for beats.
 they use a property of sound interference
What is interference?
When two or more waves meet in the same medium.
What will happen when these two sound waves meet?
Area of Decreased
Area of Increased
Pressure (Destructive)
Pressure (Constructive)
Beats – wave interference created by waves with similar frequencies.
 beat frequency = |(f1 - f2)|
Demo: wave generators, resonance boxes, tuning forks, beat freq. animation
1. What would be the beat frequency of a 520 Hz tuning fork sounding at the
same time as a 512 Hz tuning fork?
8 Hz
2. If you heard a 5 Hz beat frequency, and you had the 520 Hz tuning fork, what
would be the possible frequencies of the other tuning fork?
525 Hz, 515 Hz
Assignment Ch. 12: 29, 37, 38
40
How do musical instruments work?
They use a property of resonance – which means “to sound again.”
What is first needed to produce sound?
a vibration
How would you make sound louder?
Influence more air.
Forced Vibration – using a vibrating source to move a larger surface area.
Example: sounding board
 special form of forced vibration
Demo: tuning forks and resonance boxes
Resonance – if the natural vibrating frequency of an object is equal to the vibrating
source, a sound standing wave is produced.
Sound resonance applications: Tuned Intakes, Tuned exhausts
 air column resonance
Demos: PVC pipe resonances with tuning forks and wave generator
Standing Waves – a wave form created by interference by a reflected wave.
Closed Tube Resonance – a sound wave in a column of air that is reflected and
phase shifted, resonances go up by odd integers of the 1st resonance (fundamental)
 2 AN = 1
1st Resonance – tube length resonates a ¼ wavelength of the sound wave.
41
2nd Resonance - tube length resonates a ¾ wavelength of the sound wave
 Resonances are separated by ½ wavelength intervals
Open Tube Resonance – a sound wave in a column of air that is open at both ends
and when reflected does not phase shift, the resonances go up by integer multiples
of ½ wavelengths.
1st Resonance – tube length resonates a ½ wavelength of the sound wave.
2nd Resonance – tube length resonates a 1 wavelength of the sound wave.
 Resonances are separated by ½ wavelength intervals
42
1. What is the resonating frequency of the 45 cm PVC pipes for a closed tube?
190.6 Hz
See solution
2. What is the resonating frequency of the 45 cm PVC pipes for an open tube?
381.1 Hz
See solution
3. What air column length for a closed tube will resonate at 512 Hz?
16.7 cm
See solution
4. What air column length for a closed tube will resonate at 293 Hz?
29.3 cm
See solution
43
Is there more than one frequency that will resonate in a given air column?
Yes, the resonances from other frequencies will also resonate
Fundamental - (fo = 1st resonance/ harmonic for a given pitch) –
the lowest frequency that will resonate in a column of air.
Harmonic –
the higher multiples of the fundamental frequency that resonate in a column of air.
 different “C” key = integer multiple frequency for same note
Demo: different “C” tuning forks
Closed Tube Harmonics - f1 = 1fo ; f2 = 3 fo ; f3 = 5 fo; .....
Open Tube Harmonics - f1 = 1fo ; f2 = 2 fo ; f3 = 3 fo; .....
1. Calculate the fundamental frequency for an open and closed tube of length 45
cm. (See previous notes)
190 Hz, 380 Hz
2. Calculate the second and third harmonics for both kinds of tubes.
Closed: 570 Hz, 950 Hz
Open: 760 Hz, 1140 Hz
Demo: PVC tube and wave generator PVC pipe drum
Let’s answer the first question: How do musical instruments work?
* all musical instruments need a vibration.
* a certain column of air will have natural resonating frequencies (harmonics) all
sounding at the same time.
* the fundamental is the most pronounced (its resonance loses the least sound
energy) with each successive harmonic being the next pronounced.
* the super-positioning of all the harmonics give the instrument its characteristic
sound quality.
44
A flute has a high fundamental followed by higher harmonic frequencies, therefore
it will have naturally high sound qualities. A tuba has a low fundamental followed
by low harmonic frequencies that have diminishing energies for high frequencies,
therefore the tuba will have naturally low sound qualities.
Physics of Sound Video
Do Lab: Calculating the Speed of Sound in Air
Assignment Ch. 12: 20, 21, 24-28, 34-36
45
To calculate the speed of sound in air by applying a property of closed tube
resonance.
The fundamental wavelength of a closed tube is equal to four times the length of the
air column.
=4L
By knowing the frequency for the fundamental of the closed tube, and measuring
the length of the air column, one can calculate the value of the speed of sound in air.
v = f  = f (4 L)
There is a correction to the air column length, due to the width of the air column,
which must be added to the measured air column length for a proper calculation.
The correction factor is 40% of the diameter of the air column or:
L = l + 0.4 d
Therefore, the speed of sound in air is given by the equation, with the correction
factor:
v = f  = f (4 L) = f ( 4 (l + 0.4 d) )
You will be using a PVC tube ~ 0.45 m in length, and a 1 L graduated cylinder
filled with water to simulate a variable closed tube. The length of the air column in
the PVC pipe is varied by pulling the pipe in and out of the water in the graduated
cylinder.
1) Measure the PVC tube inner diameter using a ruler or meter stick. This will be
used for the 3 different tuning forks since you will be using the same tube for each
tuning fork.
d = ____________ m
2) Select one of the tuning forks from the card board box and record its frequency
in the table. This will be the fundamental frequency for your air column.
46
3) Strike the tuning on the rubber hammer provided and hold the tuning fork above
the top of the PVC pipe. Pull the PVC pipe up or down in the water until the loudest
tone is made. At the point of loudest tone, resonance, measure the distance from the
top of the PVC pipe to the top of the water level in the graduated cylinder. This is
the air column length l.
4) Select two other different tuning forks from the box, and do the same procedure,
recording the measured values in the table.
Tuning
Length of
Fork
air column
Frequency
=l
Corrected Calculated Calculated
Air
fundamental Speed of
column
wavelength Sound in
Length = L
=4L
Air = v
288 Hz
512 Hz
47
o
1) The accepted value for the speed of sound in air is 331.5 m/s at 0 C and 1 atm of
o
pressure. The speed of sound in air is increased 0.59 m/s per 1 C in dry air. Use the
air temperature you measured to calculate the theoretical speed of sound in air.
Theoretical speed of sound in air = _____________ m/s
2) Do a percent error analysis for each tuning fork to see how close you were to the
theoretical accepted value for the speed of sound in air.
% Error = |(actual - theoretical)|
theoretical
3) How does your calculated experimental value for the speed of sound in air
compare to the theoretical value?
4) What were some of the errors involved in the lab experiment? Any assumptions?
5) What other experiment could you do to find the speed of sound in air?
48
49
What is light?
Electromagnetic transverse wave composed of oscillating electric and magnetic
fields.
What did Einstein propose in 1905?
Tiny bundles of vibrating energy called photons. Ex, water waves are composed of
tiny moving molecules of water.
What creates light?
Vibrating or accelerating charges.
Are there different kinds of light?
Yes, their properties or effects on matter are different and can be plotted into a
spectrum.
Electromagnetic Spectrum – a frequency chart of the different kinds EM waves
based on their properties
 transverse wave
radio
infrared
ultraviolet
gamma
4
9
12
14
15
17
20
24
0----10 ------10 -----10 --------10 -----10 --------10 -----10 -----10 ----->
microwave
|
|
x-ray
cosmic
visible
What are the uses for light?
 The agreed upon speed of light is 299,792,458 m/s by international standards.
 The measure of the speed of light is done by atomic clocks. The time it takes
light to travel exactly 1 meter = 1/ 299,792,458 seconds.
8
 Usually the speed of light, c = 3 x 10 m/s
50
Red light  = 700 nm,
Violet light  = 400 nm
Calculate the frequency span of the color spectrum:
n = x10-9
f = 4.29 x 1014 Hz ----- 7.5 x 1014Hz
Calculate the wavelength of the highest frequency light known to man.
24
f = 1 x 10 Hz
= 3 x 10-16 m
Calculate the wavelength of one of the lowest frequencies of light which is in the
radio band emitted by power lines through AC current at 60 Hz.
= 5 x 106 m
Light Ray Model – (light ray approximation)
light travels in straight line paths (particle property of light)
Demo: Pinhole camera
Assignment Ch. 13: 1, 2, 7, 10-13
51
What happens when one of the polarizers is turned 90 degrees relative to the other
polarizer? The light dims and then is totally blocked.
What happens when you view the light reflections from the desk tops through the
polarizer? Rotate the polarizer. The light from the reflections are blocked.
What happens when you view an LCD screen through a polarizer
Light is blocked, the screen turns black
What can you conclude about an LCD screen?
The liquid crystal and the crystal panel are polarized.
What happens when you view the sky on a sunny day through a polarizer?
The air from the upper atmosphere polarizes the light from the sun.
Why do all of these occur?
They all are different applications or examples of polarized light.
Polarization – the vibration of transverse waves in a uniform direction.
 Light is a transverse wave - this is a property of only transverse waves.
Light emitted from bulb is
radomly polarized
Only vertically polarized light
is allowed to pass through
Polarizer resonates in only
one direction all other light is absorbed
 Polarizers aligned perpendicularly will –
absorb all the light
 A perfect polarizer will only absorb 1/2_______ the light from a randomly
polarized source.
Assignment Ch. 13: 39, 43-45
52
How do mirrors work?
The loosely bound outer electrons in metal are free to vibrate at the same
frequency as the incoming light wave.
What happens when you view at a window from inside your house at night? Why
does it do this?
You see a partial reflection. It does this because light is being transmitted from
a less dense material to a more dense material. Some light is allowed through
but some light gets reflected.
What is the light ray model for light?
Light travels in straight lines.
What happens when light encounters matter?
1. absorbed – light is in resonance and is turned into heat.
2. transmitted – light passes from atom to atom in the new material, the light
is not in resonance with the material
3. reflected – light is absorbed and re-radiated by the freely vibrating
electrons on the material’s surface.
Demos: laser on mirror, light ray box on mirror
Law of Reflection –
a light wave is reflected at an angle equal to the angle of the incident light wave
as measured relative to the normal.
Normal –
the imaginary perpendicular line that can be drawn from the surface at the
point where the light ray meets the surface.
 parallel light rays reflect in a specific way
Two kinds of reflections:
 Regular –
parallel light rays reflect parallel, they create a virtual image. Ex. mirror
 Diffuse –
parallel light rays reflect in different directions. Ex. We see each other and
other objects by diffuse reflections
53
Identify the angle of incidence, angle of reflection and the normal in the diagram:
Images – a point where light rays converge or appear to converge
2 types:
1. Virtual Images – an image located behind a mirror’s surface where light
rays appear to converge. You have to look into the mirror to see this
image.
2. Real Images – an image located in front of the mirror’s surface where
light rays converge. The image can be projected onto a screen.
Magnification –
a ratio of the size of the image relative to the size of the object.
Images can be:
 Erect –
images that are virtual are in the same direction as the object.
 Inverted –
images that are real are projected upside-down.
What kind of images do plane mirrors produce?
Virtual, Erect, M = 1: the image appears to be behind the mirror the same
distance as the object in front of the mirror, and is the same size and direction
as the object.
Assignment Ch. 13: 14, 16, 17, 19
54
What happens when you view yourself in the large concave mirror?
When it is close enough you see a virtual, enlarged image.
Why do they produce images like these?
A curved mirror reflects light in front of the mirror creating real images – a
real focal pt.
What happens when the hovercraft is sent down the hallway toward the curved end?
The hovercraft will bounce off of the curved wall and go through the same
point on the normal axis.
 Recall: the Law of Reflection –
light reflects at equal angles
Demo: concave mirror, hovercraft at the end of the hall
r
f
C
C
Principal Axis
C = center of curvature (circle radius)
f = focal point
Principal Axis –
the imaginary perpendicular line to the surface of the curved mirror that goes
through the center of curvature, and focal point.
Focal Point –
the point where light rays converge to form real images.
 Equation for focus:
2f=C
55
Every point on an object reflects light in all directions and those light rays are
reflected from a mirror. It is easier to simplify the object images by applying one of
the properties of light rays coming from an object. You need only 2 light rays to
determine the properties of the images from the object:
Principles for Drawing Ray
Diagrams
Light Rays travel in straight lines
from all points
Parallel Light Rays will converge
at the focal point
Light Rays that go through the focal point will
reflect as parallel lines
A light ray will travel through the center of
curvature to the same point on the object’s
image.
56
Identify the images produced in each of these situations, whether they are real or
virtual, erect or inverted, enlarged or reduced: Mirror Interactive
a. If the object (O) is outside of the C:
Image properties: inverted, reduced (M<1), real
C
f
b. If the O is between the C and f:
Image properties: inverted, enlarged (M>1), real
C
f
c. If the O is inside the f:
Image properties: erect, enlarged (M>1), virtual
C
f
Demos: images with concave mirror
57
Finding the magnification and location of an image using geometry:
1 1 1
 
f q p
 Where, p is the object distance, and q is the image distance, and f is the focal
length of the lens/mirror.
1
1
1


focal _ length image _ dist . object _ dist .
Equation for finding the magnification and orientation of an image:
M
h  q

h
p
 Where, h’ is the image height, h is the object height.
image _ height
image _ dist .
magnification 

object _ height
object _ dist .
p
h
h’
q
58
A 10 cm tall object is placed at various distances in front of a concave mirror with a
radius of 15 cm. Find the image distance, height, and magnification for each object
distance of 20 cm, 10 cm, and 5cm.
See Solution 1
See Solution 2
See Solution 3
Assignment Ch. 13: 23, 24, 28-32, 34, 35, 46, 47, 49, 52
59
What is a convex mirror?
A mirror that “bulges” outward like a part of a silvered ball
Demo: convex mirror
Why do they produce images like these?
All light rays diverge and appear to come from a point behind the mirror.
Properties of Convex Mirrors:
 Light rays always diverge
 Focal point is behind the mirror therefore, focal point is always = -f
 Forms images smaller than normal and are virtual images.
Follow the same ray diagram rules to find the properties of the images formed by
convex mirrors:
f
C
Calculate the focal point of a convex mirror with a radius of 30 cm. A 10 cm object
is placed 50 cm away from the mirror. What will be the virtual image height and
location of the object?
See Solution
Assignment Ch. 13: 25, 26, 36, 50, 51, 57
60
61
What happens when a pencil is placed in a beaker of water?
It appears to be broken and bent.
Why do you see fish underwater at a different location than where it actually is at?
The light rays are bent away from the original location.
Refraction – the bending of light rays due to the difference in density between
transparent materials.
Refraction animation
 The incident light is parallel to the light ray transmitted on the other side when
the object’s sides are parallel
 The amount a light ray is refracted depends on the difference in densities of
the two materials.
o Less dense to more dense – the light is bent toward the normal.
o More dense to less dense – the light is bent away from the normal.
What happens to the light rays as the angle of incidence is increased from 0 to 90
degrees? The light rays are bent more and more away from the normal
Demo: light ray box on glass
Diagram of a light ray through a more dense material:
The incident light ray is parallel to the
transmitted light ray on the opposite side of the
glass
Air
Glass
Air
62
Snell’s Law - describes the amount light will be refracted based on a material’s
index of refraction.
* The index of refraction is a unit-less number that is a property of the
transparent material and is found experimentally. The index of refraction is
related to how fast light will travel in a medium
Air = n = 1
ni sin i  nr sin  r
 Where ni is index of refraction for the incident material, and nr is the index of
refraction for the new material.
63
Calculate the index of refraction of glass and plastic using a laser pointer and block of the
material.
64
What is the speed of light?
3 x 108 m/s or 186,000 miles/sec in a vacuum.
What happens to the speed of light as it enters a new material?
It gets slower.
Why does it do this?
The material is more dense and it takes light longer to jump from atom to atom
through the material.
If this occurs, then as light enters a new material the frequency of the light must
remain the same (red light is still red light in glass).
f air  f glass
v
f

therefore,

Recall: v  f  
c
air

v glass
c
 glass
v glass

air nr

 glass ni
 The ratios are a constant = index of refraction
 ni = usually air = 1
c
v glass
 nr
Examples: Find the speed of light in water, glass, and another substance.
vw = 2.26 x 108 m/s, vg = 1.974 x 108 m/s
What is the index of refraction of a material whose speed of light is 1.87 x 108 m/s?
nr = 1.604
Assignment Ch.14: 1-5, 10-14, 39-42, 50
65
How does fiber optics work?
They work on a physics principle called total internal reflection.
What happens to the light beam as the glass is rotated 90 degrees?
The light beam is refracted to a larger and larger angle until the light beam is
reflected back into the glass.
Demo: light beam on prism, fiber optic strand
Critical Angle - the angle at which the refracted angle is 90 degrees.
air
glass
 only occurs when light travels from higher to lower indices of refraction.
Total Internal Reflection –
occurs when angle of the light wave in the more dense medium is greater than the
critical angle. It creates a perfect reflection with no energy loss.
Application to Snell’s Law: ni sin  i  nr sin  r
1. Calculate the critical angle (c) for air and glass.
41.1 degrees
2. Calculate the critical angle for air and water.
48.75 degrees
Video: Lightspeed
Assignment Ch. 14: 27, 35, 36-38, 51, 56, 58, 59
66
Why do we see rainbows?
Light refracts in the water droplets.
Demo: rainbow pictures
What happens when white light travels through a prism?
The light gets separated into the different colors.
Why does it do that?
Each frequency of light has a slightly different speed through the material. It will
then refract at slightly different angles.
Demo: light ray box and prism
Dispersion – occurs when white light is refracted into the different color
frequencies. Red frequencies can travel through transparent materials slightly faster
than the higher, violet frequencies. The violet refracts more than red.
 Related to the index of refraction –
 Each light frequency experiences a slightly different index of refraction – red
light is smallest, violet light has the largest.
 Each light frequency will travel at slightly different velocities through
material.
Application to Snell’s Law: Rainbows
Water Droplet
White light
Violet
Red
67
Calculate the speed of light for red and violet light in crown glass:
Red light n = 1.514, Violet light n = 1.528
vr = 1.982 x 108 m/s
vv = 1.963 x 108 m/s
Why are sunrises/sunsets red?
The atmosphere refracts light like a lens. It disperses the blue the most (why the sky
is blue) and red the least. The red passes almost straight through to our eyes.
What are Mirages?
Light waves that are refracted due to the less dense (hotter air) near the ground.
What creates them?
Light is bent upward towards our eyes. The light that would normally be absorbed
by the ground is totally internally reflected up to our eyes.
Demo: mirage images
Assignment Ch. 14: 28-30, 49
68
What is a lens? a circularly curved piece of glass.
What are they used for? For focusing light rays or magnifying images.
What are they made out of?
Commonly made out of glass, but technically any type of transparent material
that has a different index of refraction.
Lens – a curved piece of transparent material that refracts light through or
away from a focal point.
 Lenses have two focal points on either side
Two kinds of lenses:
1. Convex – a lens that is thicker in the center, it bulges outward.
 Bends light inward – has a focus
Concave – a lens that is thinner in the center than the outside edge, curves
inward.
 Bends light outward – always disperses and only creates virtual images.
69
The ray diagrams for lenses are very similar to those drawn for spherical mirrors.
However, the light rays are not reflected but refracted through the focus on the
opposite side of the lens.
Recall the lens/mirror equations:
h
q
M  
h
p
1 1 1
 
f q p
p
h
h’
q
Principles for Drawing Ray Diagrams for Lenses
Light Rays travel in straight lines from all points
Parallel Light Rays will converge at the focal point
Light Rays that go through the focal point will refract as
parallel lines
A light ray that travels through the center of the lens will
travel in a straight line.
70
Identify the properties of a convex lens: Lens Ray Diagram Interactive
1.
2f
f
f
2f
2f
f
f
2f
2f
f
f
2f
f
2f
2.
3.
Identify the properties of a concave lens:
1.
2f
f
71
1. A convex lens with a focal length of 15 cm is placed 50 cm from a 10 cm high
object. Calculate the image location, height, and the lens magnification.
q = 21.4 cm, M = -0.43, h’ = -4.3 cm, real, inverted, reduced image
2. Calculate the image location, height, and magnification if the object from #1
is placed 20 cm from the lens.
q = 60 cm, M = -3, h’ = -30 cm, real, inverted, enlarged image
3. A concave lens with a focal length of 15 cm is placed 20 cm in front of a 20
cm high object. Calculate the virtual image location, height, and
magnification.
q = -8.57 cm, M = +0.43, h’ = +8.6 cm, virtual, upright, reduced image
Assignment Ch. 14: 15-18, 24-26, 43-46, 48
Lab: Finding Focal Lengths of Lenses
72
Purpose: To calculate the focal lengths of various lenses, find their magnification given their
lens arrangement, and verify the magnification by direct measurement.
Theory: The focal length of a lens can be calculated based on the object and image positions
measured relative to the lens. The lens/mirror equation will be used to calculate the focal length.
The magnification of the image will also be calculated and verified by directly measuring the
size of the image formed on the screen.
h
q
M  
h
p
1 1 1
 
f q p
Set-up/Procedure:
lens
Meter stick stand
Light bulb
Screen
Measure the size of the 15 W light bulb from the top of the bulb to the location where the glass
bulb meets the base.
_______________ cm
Given the set-up illustrated above:
1. Place the object at a convenient location on the meter stick (ex. 20 cm mark).
2. Place the lens at a convenient location in front of the object (lightbulb).
3. Slide the screen back-and-forth on the meter stick until a sharp image of the lightbulb is
formed. Pay particular attention to the image of the filament because the filament is
located in the center of the lightbulb.
4. Measure the image distance from the screen to the lens.
5. Measure the height of the image produced on the screen, from the top to the bottom.
6. Repeat this process for each of the remaining lenses
73
Calculate the focal length of each of the 6 numbered lenses. Also calculate the magnification of
the image formed on the screen and then compare it to the actual magnification of the image.
How close were you to the actual magnification? Do an error analysis of each lens to
quantitatively define how well you did your calculations.
Lens
Focal
Magnification Actual
% Error
Length (cm)
Magnification
1
2
3
4
5
6
74
75
What is happening when the Geiger counter is placed near the radioactive source?
It will start clicking.
What is making those sounds?
Small charged particles (or gamma rays) that are being shot outward from the
nucleus at a very high speed.
Demo: detector and source
Stable vs. Unstable Atoms, what makes an atom unstable?
Generally, if the electrostatic repulsion of the nucleons is stronger than the nuclear
force the nucleus will decompose into a more stable state.
Before these questions can be completely understood we need to understand some
of the properties and the fundamental structure of atoms.
Fundamental Structure of Atoms
76
Atoms have the majority of their mass located in the center of the atom called the
nucleus.
Relative size of atoms: If the nucleus of a hydrogen atom were the size of a ball
bearing 1cm in diameter, where would the electron be located? Proton = 1.6 fm and
hydrogen atom = 10-10 m
D = 625 m
Representing the atomic structure of atoms:
The atoms represented on the periodic table on pg. 872-873 in your textbook have
different chemical properties based on the number of electrons that are orbiting
around the nucleus. However, the nuclear structure determines what kind of atom it
is based on how many protons exist in the nucleus.
207
82
Pb
207 = A = mass number
82 = Z = atomic number
What is the difference between these two numbers?
The number of neutrons in the atom.
These numbers represent the different kinds and number of nucleons in an atom.
Nucleon –a massive particle located in the nucleus of an atom.
Proton – a nucleon with a positive charge of 1.6 x 10-19 C
Neutron – a nucleon that has no net-charge.
A Z N
Calculating the number of neutrons in an atom:
 where, A, Z, and N are all positive integer numbers – can’t have ½ proton!
77
Isotope –
atoms with the same atomic number but with different mass numbers due to
differing numbers of neutrons.
Nuclear Density = 2.3 x 1017 kg/m3
How much would a ball bearing with a diameter of 1cm weigh if it had the same
density of a nucleus?
1.204 x 1011 kg = 2.65 x 1011 lb.
Atomic Mass Units – (amu = “u” ) – the SI unit of mass used to measure the
masses of nucleons.
1 neutron ~ 1 proton ~ 1 u 1 u = 1.66053886 x 10-27 kg
1 electron ~ 5.5 x 10-4 u
1 proton = 1.007825 u
1 neutron = 1.008665 u
Electron Volts – (eV) – a unit used to measure the rest energy of particles. It is
used to relate the amount of energy a particle possesses due to its mass.
One eV is the energy one electron will give up when moving across a potential
difference of 1 Volt.
Assign. HW Ch.22: 1-3, 33, 34
78
What did Einstein Propose in 1905 in his Theory of Relativity?
Einstein proposed that the rest mass of an object is actually a measure of the
energy an object possesses.
Mass/ Energy Equivalence – ER = mc2 - a derivation of Einstein’s special
theory of relativity that explains how mass is not conserved in nuclear
reactions but the mass of an object is due to the energy it possesses, based on
the constancy of the speed of light.
Where, c = 299 792 458 m/s
 Converting mass in amu to eV of energy:
1.66053886 x10 27 kg299792458m / s 
1u 
 931.49MeV
1.60217653x10 19 J / eV
M = 1 x106
2
Nucleon
Mass (kg)
Mass (u)
Rest Energy
(MeV)
Proton
1.6735 x 10-27 kg
1.007825 u
938.78 MeV
Neutron
1.6749 x 10-27 kg
1.008665 u
939.56 MeV
Electron
9.109 x 10-31 kg
5.4858 x 10-4 u 0.511 MeV
Calculate the rest energy of each of the above atomic particles:
79
What makes a nucleus stable? Why don’t they fly apart and disintegrate?
The strong nuclear force between the protons and neutrons.
Remember Coulomb’s Law? What is the repulsive force between protons?
Fe = ?
Fe = kq1q2, where k = 9 x 109
d2
Calculate the repulsive force between one of the protons in a Uranium nucleus:
1f = 1 x 10-15 m
Diameter of 1 proton = 1.6 fm ;
1 uranium nucleus = 15 fm
See Solution
How fast would the proton have to travel to be absorbed by a Uranium nucleus?
Recall, KE = PE
See Solution
Strong Nuclear Force – the strongest of the natural forces that keeps nucleons
bound together against the electric force of repulsion.
 Short range force ~ 1fm
Stable light elements: Z = N ; # of protons = # of neutrons
Stable heavy elements:
Z < N ; # of protons < # of neutrons
 Neutrons add strong nuclear __________ without adding the electric force.
 More protons = more electric repulsion _____________
80
 For atoms where the number of neutrons greatly outnumber the number of protons, they
are unstable due to a property where neutrons need to be bonded to protons, neutrons by
themselves are unstable and will transform into a proton and an electron
Conceptually:
= neutrons
= protons
 For Z > 83 – nucleus is not stable – strong nuclear force only acts to a
distance of adjacent nucleons – neutrons keep protons together.
81
What is the atomic mass of 2 protons? 2 neutrons? What about a Helium atom?
(see Appendix H, pg. 874)
2(1.007825u) + 2(1.008665u) = 4.03298u
He = 4.00260u
When compared together what accounts for the mass discrepancy?
The amount of energy released when combining these particles together or in
reverse – the amount of energy needed to strip them apart.
Binding Energy – the energy released when nucleons form a more stable, less
energetic nucleus. The energy released is equal to the mass deficit according to
Einstein’s special theory of relativity. It is also the energy needed to completely
break apart an atom.
Ebind  mc2
Where m = mass deficit
m  Z (m p )  N (mn )   atomicmass
Ebind  m(amu)  931.49MeV / u
82
9
Ex. Calculate the binding energy per nucleon for 4 Be and
235
92
U in MeV.
See Solution
See Solution
23
Special Case 11 Na and
atoms? Why?
23
12
Mg . What are the binding energies for each of these
Na = 186.6 MeV – has less # of protons and more neutrons which makes it more
stable – less repulsive force and more strong nuclear force – more energy required
to rip it apart
Mg = 181 MeV
Isobars – atoms that have the same atomic mass but different atomic numbers
Assign. HW Ch.22: 5 - 9
83
What is radioactivity? Why does it do this?
Atoms that emit particles, or gamma rays from their nucleus to create a more
stable atom.
About 400 stable nuclei exist, however, there are 100’s of unstable nuclei and they
break apart into other more stable particles.
Radioactivity – the emission of particle(s) and energy from the nucleus that
break it down into a less energetic and more stable nucleus.
 Nucleus before decay is called the ____ Parent ___ nucleus.
 Nucleus after decay is called the _____ Daughter ___ nucleus.
All radiation gives off energy according to E = mc2
Three basic types of radiation:
Alpha – () – a type of radiation that is composed of 2 protons and 2 neutrons
– essentially a Helium nucleus.
 Charge = +2
 Results in– decreasing
the atomic number by 2
and decreasing the mass
number by 4
84
Beta – () – 2 types of decays: the emission of particles that changes the atomic
number but does not change the nucleon number.
B- - (beta minus) – the emission of an electron and a small neutral
particle called a neutrino (actually an anti-neutrino)
 Charge = -1
 Results in – the
decomposition of a
neutron into a proton in
the nucleus – increasing
the atomic number by 1
B+ - (beta plus) – the emission of a positron and a neutrino
 Charge = +1
 Occurs only when the available nuclear energy is > 2 mec2
= 2(0.511 MeV) = 1.022 MeV
 Results in – the
decomposition of a proton
into a neutron – decreasing
the atomic number by 1
85
* Anti-matter – predicted by Schrodinger when he applied his wave
equation to quantum mechanics. In this theory, all particles have an antiparticle, that when combined, annihilate each other and change their mass
into energy.
Positron – (e+) – an anti-electron - a particle that has the same mass, but
opposite charge and magnetic moment of the electron.
Gamma – () – the emission of gamma ray photons by an excited (more
energetic) state of an atom. The nucleus re-arranges itself more compactly.
 Charge = no charge
 Results in – a less
energetic nucleus.
 the nucleus rearranges itself making it more stable and compact in the nucleus
– it loses energy in this process which emits a high energy photon.
Conceptually:
Neutrons and protons
are touching but not
in the most stable state
Neutrons and protons
squeeze together more
compactly decreasing
their distance of separation
Assign. HW Ch.22: 10, 13, 14, 17, 18
86
Recall balancing reaction equations in Chemistry – Do you remember the rules that were used
to balance the equation?
The same basic rules apply to nuclear equations as well. (sometimes referred to as nuclear
chemistry)
Energy/ Mass Conservation:
The total amount of energy, including the rest energy of mass before a nuclear
reaction, is equal to the total amount afterwards.
Charge conservation:
The net-charge before a nuclear reaction is equal to the net-charge afterwards.
Spin (magnetic moment) Conservation: every particle has a certain magnetic value
or spin. The net-magnetic moments of the particles before a reaction, is equal to the
net-magnetic moments afterwards.
* not specifically covered in this text.
U  ? He U  He  Th
238
4
238
4
234
92
2
92
2
90
Calculate the energy released in this reaction using the binding energy of the given
atoms. Where does this energy go?
See Solution
87
C  ? e C  e   N
14
0
14
0
14
6
1
6
1
7
* electron has significantly less mass than the parent nucleus and is not a factor in
the mass of the daughter nucleus
 a neutron is converted into a proton by emitting an electron, recall the neutron
has no net-charge.
12
7
N  ? 10 e127N  10 e  126C
 a proton is converted into a neutron by emitting a positron (anti-electron)
Neutrino – ( ) - a small fast moving neutral particle, predicted by Enrico Fermi,
emitted when a beta decay or an electron capture occurs.
 mass << mass of electron
 does not interact well with matter
 anti-neutrino - ( )
B C  e    C  C  
12
12 *
0
12 *
12
5
6
1
6
6
*denotes an excited state – the nucleus rearranges itself more compactly.
88
Identify the type of decay and the amount of energy released in the reaction.
227
223
87
1. 89
Ac  ? Fr
See Solution
98
Tc  ? 42
Mb
98
2. 43
See Solution
Decay Series – a chart illustrating the possible decays from a parent nucleus to the
final most stable daughter nucleus.
Decay Series Animation
Assign. HW Ch.22: 11
89
When will an unstable atom decay? It is all based on probability. No one knows
exactly when the decay will occur, but when a large number of atoms are present,
you can measure when a decay will most likely occur based on an average.
 A probability of decay gives a better idea when a larger number of these
atoms are present
Becquerel - (Bq) – SI unit of activity – the rate of decays per unit time = 1 decay/
second.
Atomic Decay Animation
 rate of decays / second
 Curie - (Ci) – original unit of decay = 3.7 x 1010 Bq, is approximately the
activity of 1 g of radium.
 1 Ci = 3.7 x 1010 Bq
Half-Life – (T1/2) – the time it takes ½ of the atoms in a sample to decay into a
daughter atom.
1 T1/2 = 1/2 of the atoms are still present
2 T1/2 = 1/4 of the atoms are still present
3 T1/2 = 1/8 of the atoms are still present
Equation for finding half-life:
T1 / 2 
ln 2

Where, , is the decay constant for the specific type of atom.
90
How to find the value of 
N  Nt
t is the time
period for the
decays
N is the number of
parent nuclei
N is the number of daughter
nuclei
 or the number of parent
nuclei
 that have decayed
 A larger decay constant (the rate of change will be quicker.
 A smaller decay constant (the rate of change will be slower.
Rearranging the equation gives:
N

 N  activity
t
Activity is the rate of decays per unit of time = Becquerel
Integrating both sides of this equation over a period of time (t) gives:
N f  Ni e
Nf is the number of
nuclei left after a
period of time -t
 t
Ni is the number of
original parent nuclei
Calculate the activity of Ra-226 whose half-life is 5.0 x 1010 s, and beginning with
3.0 x 1016 atoms.
See Solution
Calculate the number of atoms of Rn-222 left after 12 days. The half-life is 3.82 d,
and the initial number of atoms in a sample is 4.0 x 108 atoms.
See Solution
Lab: Fanta-astic Decay lab
Assign. HW Ch.22: 15, 16, 22-24, 44, 45
91
Modified from http://www.albany.edu/faculty/jae/quarknet/html/soda.html
Purpose: to demonstrate that the bubbles, made by pouring a fresh bottle of Fanta or Coke, pop randomly and
thus the foam head decays exponentially just as particles decay randomly.
Materials: bottle of Fanta, Coca-Cola, or other soda, funnel if necessary, graduated cylinder, foam drinking
cup, dry erase markers, stopwatch, scientific calculator
Procedure: Each lab group needs at least three students: one to pour the soda and time, and two observers to
mark the top and bottom of the foam at time intervals.
1. Set up the graduated cylinder with a funnel over it as shown.
2. Using soda from a foam cup, pour soda into the graduated
cylinder quickly but carefully to create a lot of soda foam. Mark
the top and bottom of the foam immediately and begin timing.
3. The timer calls “Go!” every 5 sec. At each call from the timer,
the observers mark the volume at the top of the foam and at the
bottom of the foam on the graduated cylinder using a dry erase
marker.
4. The observers mark down the volumes every 5 sec.
5. Repeat steps 3 and 4, continue until the foam is just about all
gone.
6. Students should find the volume of the foam for each time
entered by subtracting the bottom volume from the top volume.
They should then calculate V/Vi , where Vi is the first recorded
volume of the foam.
7. Calculate the natural logarithm of the volume fraction,
ln (V/Vi ).
8. Graph your data on the computer and use a best fit graph, exponential decay, for your first set of data and
Linear, for ln(V/Vi), for the second set.
With the data recorded, students should graph V/VO as a function of time. They should attempt to verify that the
curve is similar to exponential decay and try to calculate the half-life from the curve by finding the time at
which the value of V/Vi is equal to 0.5 . They should also graph ln (V/Vi ) as a function of time.
If the decay is a true exponential, this graph should be a straight line with a negative slope. The negative of the
slope = the decay constant for that soda.
Record  for your soda,

 = _____________
V f  Viet
Vf
Vi
92
e
 t
ln
Vf
Vi
  t
Time
Top Volume
(mL)
Bottom Volume
(mL)
Net
(sec)
V/Vi
ln (V/Vi)
Volume (mL)
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
Vi =
of your soda and compare the value with the time when V/Vi = 0.5 by marking it on
your graph.
Use your decay equation: T1 / 2 
ln 2

of your soda foam in pops/sec. Each mL of foam has approx. 1400 bubbles.
Act. =  N, where N is the number of bubbles:
93
What happens when two atomic nuclei interact? This occurs naturally as well as
artificially. When close enough, the strong nuclear force will attract the other nuclei
and will combine into one. The new atom will most likely be unstable and emit
radiation or other types of particles.
In 1919 Rutherford performed the first artificial nuclear reaction using a small
particle accelerator.
4
14
1
2
7
1
With the actual intermediary atom of Flourine-18
4
14
18
1
2
7
9
1
Remember your nuclear equation rules: the nucleon (A) total is equal on both sides
of the reaction, as well as the atomic number (Z).
He  N  H  ?
He  N  F  H  ?
Flourine-18 disintegrates almost immediately into two stable nuclei –
a hydrogen (proton) and oxygen
What will be the following reaction products? Would they be stable? What are the
energies released in this reaction? (if any) Explain.
4
12
6
1. 2
See Solution
He  C  ?
H  Li  ?  ? 24He
1
7
3
2. 1
See Solution
94
Neutron Capture - the absorption of a free neutron by the nucleus of an atom
 Neutrons do not interact electrically with the nucleus. When close enough, the
strong force pulls the neutron into the nucleus.
1
0
?
140
93
1
n 235
U

?

Ba

Kr

3
92
?
56
36
0n
or
90
Cs  37
Rb  2 01n
144
55
 reaction creates an average of 2 ½ neutrons per reaction. The free neutrons
then react with other uranium-235 atoms which fission as well creating a
chain reaction.
 Uranium-238 absorbs neutrons without fissioning, therefore uranium ore is processed to
increase the percentage of uranium-235.
95
Breeder Reactors are designed to increase nuclear fuel efficiency. The energy that
would be normally lost by free neutrons is absorbed by other atoms to create new
fissile fuel. This results in less radioactive waste.
 The nuclear core has some uranium-238 and is lined with uranium-238. The
following reaction occurs with the free neutrons:
1
0
239
239
0
n 238
U

U

Pu

2
92
92
94
1 e
 After 2 beta decays the uranium-239 is turned into plutonium-239
 The plutonium is then harvested and used as fuel.
n Th U  2 e
1
232
233
0
0
90
92
1
After harvesting the uranium-233, it is then placed back into a reactor to use as fuel.
Uranium-233 can be used as a fissile fuel, but can also absorb neutrons to form U234 or U-235:
1
233
235
0
92
92
2 n U  U
96
Lighter elements when combined together release a large amount of energy.
Deuterium fusion:
2
2
4
1
1
2
H  H  He
Calculate the energy lost in this nuclear reaction.
97
The temperatures needed to overcome the electrostatic repulsion of the nuclei
exceed all melting points of objects. Because of this, the main focus of fusion
reactors has been magnetic confinement – containing a plasma, used to produce
fusion, in a strong magnetic field away from material objects.
2
1
H 12H 24He
In this main fusion reaction, calculate the KE needed to overcome this repulsion:
(assume each hydrogen nucleus is a sphere with diameter = 1.6 fm)
Remember that the electric potential energy = kinetic energy of the hydrogen atom
v
H
H
H
e+
H
+
Movie: Fat Man and Little Boy
Assign. HW Ch.22: 12, 19 – 21, 32, 37 - 40
98
n
Protons and electrons were once considered to be the elementary particles that make
up all matter. Protons are now thought to be composed of dimensionless
elementary particles called quarks.
How many different particles do you think have been currently recorded?
+300 different particles have been catalogued; this includes matter, antimatter, and field particles.
Review of the 4 Natural Forces
Mediating
Particle
Strong
Nuclear
Force
Electromagnet
ic Force
Weak
Nuclear
Force
Gravity
Range
~ 1 fm
Relative
Strength
1
Infinite
10-2
~10-2 fm
10-13
Infinite
10-38
According to particle physics, the process of force is mediated by the exchange of
virtual or short lived massive particles. (Quantum Electrodynamics – QED)
 A virtual photon is seen as the force exchanger between charged particles
 An attractive force can be seen as a “boomerang” from particles coming from
infinity
 If given enough energy “virtual” photons can become real – i.e. light
99
Matter
Hadrons Leptons
Baryons
Mesons
Anti-Matter – particles that have the same properties as regular matter but
have opposite spin and charge.
Electron – an elementary dimensionless particle with a negative
charge, it does not interact with the strong nuclear force.
Positron – an anti-electron, it has a positive charge.
 when matter and anti-matter meet they annihilate each other creating high
energy photons
Leptons – considered elementary particles that are influenced only by three of
the natural forces but not the strong nuclear force.
Muons – have the same charge as an electron and significantly more mass,
however are very short lived and will disintegrate.
No measurable size
Leptons
 No internal structure
Electron
Muon
Tau
Electron
neutrino
Muon
neutrino
Tau
neutrino
Note: each particle has a corresponding anti-particle.
100
Hadrons – particles that have an internal structure, composed of a
combination of elementary particles called quarks. They are influenced by all
of the natural forces.
Note: Mesons are composed of two quarks, one of them is an anti-quark – they
are highly unstable and short-lived.
 are not elementary particles
Hadrons
*Protons
u,u,d
Baryons
Mesons
Composed of 3 quarks
Composed of 2 quarks
*Neutrons
u,d,d
Other short lived
particles composed of
quark combinations
Pion
Kaon
u, anti-d
anti-u, s
* common matter is composed of up and down quarks
Quarks – elementary particles that are influenced by all the natural forces,
including the strong nuclear force. They have a charge equivalent to 1/3 or 2/3
of the electron charge.
 considered elementary particles
 each quark has an anti-quark with opposite charge
Quarks
Bottom
Top
Strange
Charm
Down
Up
-1/3e
+2/3e
-1/3e
+2/3e
-1/3e
+2/3e
101
 physicists theorize that quarks cannot be directly observed because the strong
force is so strong that the energy needed to rip apart the quarks is enough to
create a quark/ anti-quark pair. Therefore quarks will always appear in pairs or
triplets maintaining whole numbers of elementary charge.
 Ripping apart a baryon (3 quarks) creates a meson (2 quarks)
Proton
D
U
D
D
U
U
U
High Energy Photon
Pion
U
Neutron
D
D
U
D
* by E=mc2, the energy required to remove a quark (up quark) is greater than twice
the rest energy of a quark. Upon colliding with the high energy photon, the energy
is converted into a quark and its corresponding anti-quark – in this example a
proton is converted into a neutron and pion.
Compare the net-charges of the proton, neutron, and pion using the charges of their
corresponding quarks:
Proton = -1/3e + 2/3e + 2/3e = +1e, Neutron = -1/3e – 1/3e + 2/3e = 0e,
Pion = +1/3e + 2/3 e = +1e
Assign - HW Ch. 22: 25 - 31
102
103
Class Activity:
Draw and Color a picture on white construction paper using only these colors:
Red, Blue, Green,
What happens when the pictures you made are viewed under specific colors of
light? Reds turn black under green light, Greens turn black under red light.
What are the colors that make up white light?
Red orange yellow green blue
indigo violet
cyan blue
When we see something that’s white what do we actually see?
All the colors being reflected
Why do we see color?
Three color frequency sensitive cone cells in our eyes. High freq. – blue, Mid. freq.
– Green, Low freq. – Red
Color by Reflection – the color seen is that color being reflected to our eyes, more
than one color frequency can be reflected and will be combined to produce other
perceived colors
Is Black a color?
No, it is the absorption of color.
What colors make up a color TV set? Why would they be those specific colors?
Red, Green, Blue. They correspond to the color freqs. our eyes are sensitive to.
Red
Green
Blue
Demo: primary light colors on white board
 Observe the combinations of the primary colors using the shadows on the
white board
What colors are made when mixing the Primary Light Colors?
Cyan, Magenta, Yellow
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Magenta
Yellow
Cyan
Magenta = __red__ + __blue__
Yellow = __red___ + ___green___
Cyan = __blue___ + ___green__
White = __red__ + __blue__ + ___green___
Complimentary Colors – 2 colors when combined create white light
Blue + __yellow___ = White
Red + __cyan___ = White
Green + __magenta__ = White
Demo: Color Wheel
105
Make a rainbow by mixing only the 3 colors Yellow, Magenta, and Cyan colored
ink.
Demo: mixing colored paints
Color by Subtraction – color pigments will absorb one specific primary color
frequency and reflect 2 primary light colors
Magenta
Magenta
Absorbs
green
Yellow
Reflects
red and blue
Yellow
blue
red and green
Cyan
red
blue and green
Red
Red
Absorbs
green and blue
Green
Reflects
red
Green
blue and red
green
Blue
red and green
blue
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Cyan
Blue
Color by Transmission – similar to color by subtraction but its color is the
frequencies allowed to shine through the transparent material.
Demo: Colored News Print
Why do we see a Red apple as Red, and Green grass as Green?
It reflects red and absorbs blue and green. It reflects green and absorbs blue and red.
What are the Primary light colors that are reflected from a yellow dandelion?
Red and Green
What are the Primary light colors that are reflected from a deep pink flower?
Red and Blue
What are the Primary light colors that are reflected from a blue car?
Blue
What Primary pigment colors are combined to make the blue paint for the car?
Magenta and Cyan
Assignment Ch. 13: 37, 38, 40-42
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Color by Addition
Color by Subtraction
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