Home » Physics » AP Physics 1 & 2 » Refraction & Lenses

Dan Fullerton

Dan Fullerton

Refraction & Lenses

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Table of Contents

Section 1: Introduction
What is Physics?

7m 38s

Intro
0:00
Objectives
0:12
What is Physics?
0:31
What is Matter, Energy, and How to They Interact
0:55
Why?
0:58
Physics Answers the 'Why' Questions.
1:05
Matter
1:23
Matter
1:29
Mass
1:33
Inertial Mass
1:53
Gravitational Mass
2:12
A Spacecraft's Mass
2:58
Energy
3:37
Energy: The Ability or Capacity to Do Work
3:39
Work: The Process of Moving an Object
3:45
The Ability or Capacity to Move an Object
3:54
Mass-Energy Equivalence
4:51
Relationship Between Mass and Energy E=mc2
5:01
The Mass of An Object is Really a Measure of Its Energy
5:05
The Study of Everything
5:42
Introductory Course
6:19
Next Steps
7:15
Math Review

24m 12s

Intro
0:00
Outline
0:10
Objectives
0:28
Why Do We Need Units?
0:52
Need to Set Specific Standards for Our Measurements
1:01
Physicists Have Agreed to Use the Systeme International
1:24
The Systeme International
1:50
Based on Powers of 10
1:52
7 Fundamental Units: Meter, Kilogram, Second, Ampere, Candela, Kelvin, Mole
2:02
The Meter
2:18
Meter is a Measure of Length
2:20
Measurements Smaller than a Meter, Use: Centimeter, Millimeter, Micrometer, Nanometer
2:25
Measurements Larger Than a Meter, Use Kilometer
2:38
The Kilogram
2:46
Roughly Equivalent to 2.2 English Pounds
2:49
Grams, Milligrams
2:53
Megagram
2:59
Seconds
3:10
Base Unit of Time
3:12
Minute, Hour, Day
3:20
Milliseconds, Microseconds
3:33
Derived Units
3:41
Velocity
3:45
Acceleration
3:57
Force
4:04
Prefixes for Powers of 10
4:21
Converting Fundamental Units, Example 1
4:53
Converting Fundamental Units, Example 2
7:18
Two-Step Conversions, Example 1
8:24
Two-Step Conversions, Example 2
10:06
Derived Unit Conversions
11:29
Multi-Step Conversions
13:25
Metric Estimations
15:04
What are Significant Figures?
16:01
Represent a Manner of Showing Which Digits In a Number Are Known to Some Level of Certainty
16:03
Example
16:09
Measuring with Sig Figs
16:36
Rule 1
16:40
Rule 2
16:44
Rule 3
16:52
Reading Significant Figures
16:57
All Non-Zero Digits Are Significant
17:04
All Digits Between Non-Zero Digits Are Significant
17:07
Zeros to the Left of the Significant Digits
17:11
Zeros to the Right of the Significant Digits
17:16
Non-Zero Digits
17:21
Digits Between Non-Zeros Are Significant
17:45
Zeroes to the Right of the Sig Figs Are Significant
18:17
Why Scientific Notation?
18:36
Physical Measurements Vary Tremendously in Magnitude
18:38
Example
18:47
Scientific Notation in Practice
19:23
Example 1
19:28
Example 2
19:44
Using Scientific Notation
20:02
Show Your Value Using Correct Number of Significant Figures
20:05
Move the Decimal Point
20:09
Show Your Number Being Multiplied by 10 Raised to the Appropriate Power
20:14
Accuracy and Precision
20:23
Accuracy
20:36
Precision
20:41
Example 1: Scientific Notation w/ Sig Figs
21:48
Example 2: Scientific Notation - Compress
22:25
Example 3: Scientific Notation - Compress
23:07
Example 4: Scientific Notation - Expand
23:31
Vectors & Scalars

25m 5s

Intro
0:00
Objectives
0:05
Scalars
0:29
Definition of Scalar
0:39
Temperature, Mass, Time
0:45
Vectors
1:12
Vectors are Quantities That Have Magnitude and Direction
1:13
Represented by Arrows
1:31
Vector Representations
1:47
Graphical Vector Addition
2:42
Graphical Vector Subtraction
4:58
Vector Components
6:08
Angle of a Vector
8:22
Vector Notation
9:52
Example 1: Vector Components
14:30
Example 2: Vector Components
16:05
Example 3: Vector Magnitude
17:26
Example 4: Vector Addition
19:38
Example 5: Angle of a Vector
24:06
Section 2: Mechanics
Defining & Graphing Motion

30m 11s

Intro
0:00
Objectives
0:07
Position
0:40
An Object's Position Cab Be Assigned to a Variable on a Number Scale
0:43
Symbol for Position
1:07
Distance
1:13
When Position Changes, An Object Has Traveled Some Distance
1:14
Distance is Scalar and Measured in Meters
1:21
Example 1: Distance
1:34
Displacement
2:17
Displacement is a Vector Which Describes the Straight Line From Start to End Point
2:18
Measured in Meters
2:27
Example 2: Displacement
2:39
Average Speed
3:32
The Distance Traveled Divided by the Time Interval
3:33
Speed is a Scalar
3:47
Example 3: Average Speed
3:57
Average Velocity
4:37
The Displacement Divided by the Time Interval
4:38
Velocity is a Vector
4:53
Example 4: Average Velocity
5:06
Example 5: Chuck the Hungry Squirrel
5:55
Acceleration
8:02
Rate At Which Velocity Changes
8:13
Acceleration is a Vector
8:26
Example 6: Acceleration Problem
8:52
Average vs. Instantaneous
9:44
Average Values Take Into Account an Entire Time Interval
9:50
Instantaneous Value Tells the Rate of Change of a Quantity at a Specific Instant in Time
9:54
Example 7: Average Velocity
10:06
Particle Diagrams
11:57
Similar to the Effect of Oil Leak from a Car on the Pavement
11:59
Accelerating
13:03
Position-Time Graphs
14:17
Shows Position as a Function of Time
14:24
Slope of x-t Graph
15:08
Slope Gives You the Velocity
15:09
Negative Indicates Direction
16:27
Velocity-Time Graphs
16:45
Shows Velocity as a Function of Time
16:49
Area Under v-t Graphs
17:47
Area Under the V-T Graph Gives You Change in Displacement
17:48
Example 8: Slope of a v-t Graph
19:45
Acceleration-Time Graphs
21:44
Slope of the v-t Graph Gives You Acceleration
21:45
Area Under the a-t Graph Gives You an Object's Change in Velocity
22:24
Example 10: Motion Graphing
24:03
Example 11: v-t Graph
27:14
Example 12: Displacement From v-t Graph
28:14
Kinematic Equations

36m 13s

Intro
0:00
Objectives
0:07
Problem-Solving Toolbox
0:42
Graphs Are Not Always the Most Effective
0:47
Kinematic Equations Helps us Solve for Five Key Variables
0:56
Deriving the Kinematic Equations
1:29
Kinematic Equations
7:40
Problem Solving Steps
8:13
Label Your Horizontal or Vertical Motion
8:20
Choose a Direction as Positive
8:24
Create a Motion Analysis Table
8:33
Fill in Your Givens
8:42
Solve for Unknowns
8:45
Example 1: Horizontal Kinematics
8:51
Example 2: Vertical Kinematics
11:13
Example 3: 2 Step Problem
13:25
Example 4: Acceleration Problem
16:44
Example 5: Particle Diagrams
17:56
Example 6: Quadratic Solution
20:13
Free Fall
24:24
When the Only Force Acting on an Object is the Force of Gravity, the Motion is Free Fall
24:27
Air Resistance
24:51
Drop a Ball
24:56
Remove the Air from the Room
25:02
Analyze the Motion of Objects by Neglecting Air Resistance
25:06
Acceleration Due to Gravity
25:22
g = 9.8 m/s2
25:25
Approximate g as 10 m/s2 on the AP Exam
25:37
G is Referred to as the Gravitational Field Strength
25:48
Objects Falling From Rest
26:15
Objects Starting from Rest Have an Initial velocity of 0
26:19
Acceleration is +g
26:34
Example 7: Falling Objects
26:47
Objects Launched Upward
27:59
Acceleration is -g
28:04
At Highest Point, the Object has a Velocity of 0
28:19
Symmetry of Motion
28:27
Example 8: Ball Thrown Upward
28:47
Example 9: Height of a Jump
29:23
Example 10: Ball Thrown Downward
33:08
Example 11: Maximum Height
34:16
Projectiles

20m 32s

Intro
0:00
Objectives
0:06
What is a Projectile?
0:26
An Object That is Acted Upon Only By Gravity
0:29
Typically Launched at an Angle
0:43
Path of a Projectile
1:03
Projectiles Launched at an Angle Move in Parabolic Arcs
1:06
Symmetric and Parabolic
1:32
Horizontal Range and Max Height
1:49
Independence of Motion
2:17
Vertical
2:49
Horizontal
2:52
Example 1: Horizontal Launch
3:49
Example 2: Parabolic Path
7:41
Angled Projectiles
8:30
Must First Break Up the Object's Initial Velocity Into x- and y- Components of Initial Velocity
8:32
An Object Will Travel the Maximum Horizontal Distance with a Launch Angle of 45 Degrees
8:43
Example 3: Human Cannonball
8:55
Example 4: Motion Graphs
12:55
Example 5: Launch From a Height
15:33
Example 6: Acceleration of a Projectile
19:56
Relative Motion

10m 52s

Intro
0:00
Objectives
0:06
Reference Frames
0:18
Motion of an Observer
0:21
No Way to Distinguish Between Motion at Rest and Motion at a Constant Velocity
0:44
Motion is Relative
1:35
Example 1
1:39
Example 2
2:09
Calculating Relative Velocities
2:31
Example 1
2:43
Example 2
2:48
Example 3
2:52
Example 1
4:58
Example 2: Airspeed
6:19
Example 3: 2-D Relative Motion
7:39
Example 4: Relative Velocity with Direction
9:40
Newton's 1st Law of Motion

10m 16s

Intro
0:00
Objective
0:05
Newton's 1st Law of Motion
0:16
An Object At Rest Will Remain At Rest
0:21
An Object In Motion Will Remain in Motion
0:26
Net Force
0:39
Also Known As the Law of Inertia
0:46
Force
1:02
Push or Pull
1:04
Newtons
1:08
Contact and Field Forces
1:31
Contact Forces
1:50
Field Forces
2:11
What is a Net Force?
2:30
Vector Sum of All the Forces Acting on an Object
2:33
Translational Equilibrium
2:37
Unbalanced Force Is a Net Force
2:46
What Does It Mean?
3:49
An Object Will Continue in Its Current State of Motion Unless an Unbalanced Force Acts Upon It
3:50
Example of Newton's First Law
4:20
Objects in Motion
5:05
Will Remain in Motion At Constant Velocity
5:06
Hard to Find a Frictionless Environment on Earth
5:10
Static Equilibrium
5:40
Net Force on an Object is 0
5:44
Inertia
6:21
Tendency of an Object to Resist a Change in Velocity
6:23
Inertial Mass
6:35
Gravitational Mass
6:40
Example 1: Inertia
7:10
Example 2: Inertia
7:37
Example 3: Translational Equilibrium
8:03
Example 4: Net Force
8:40
Newton's 2nd Law of Motion

34m 55s

Intro
0:00
Objective
0:07
Free Body Diagrams
0:37
Tools Used to Analyze Physical Situations
0:40
Show All the Forces Acting on a Single Object
0:45
Drawing FBDs
0:58
Draw Object of Interest as a Dot
1:00
Sketch a Coordinate System
1:10
Example 1: Falling Elephant
1:18
Example 2: Falling Elephant with Air Resistance
2:07
Example 3: Soda on Table
3:00
Example 4: Box in Equilibrium
4:25
Example 5: Block on a Ramp
5:01
Pseudo-FBDs
5:53
Draw When Forces Don't Line Up with Axes
5:56
Break Forces That Don’t Line Up with Axes into Components That Do
6:00
Example 6: Objects on a Ramp
6:32
Example 7: Car on a Banked Turn
10:23
Newton's 2nd Law of Motion
12:56
The Acceleration of an Object is in the Direction of the Directly Proportional to the Net Force Applied
13:06
Newton's 1st Two Laws Compared
13:45
Newton's 1st Law
13:51
Newton's 2nd Law
14:10
Applying Newton's 2nd Law
14:50
Example 8: Applying Newton's 2nd Law
15:23
Example 9: Stopping a Baseball
16:52
Example 10: Block on a Surface
19:51
Example 11: Concurrent Forces
21:16
Mass vs. Weight
22:28
Mass
22:29
Weight
22:47
Example 12: Mass vs. Weight
23:16
Translational Equilibrium
24:47
Occurs When There Is No Net Force on an Object
24:49
Equilibrant
24:57
Example 13: Translational Equilibrium
25:29
Example 14: Translational Equilibrium
26:56
Example 15: Determining Acceleration
28:05
Example 16: Suspended Mass
31:03
Newton's 3rd Law of Motion

5m 58s

Intro
0:00
Objectives
0:06
Newton's 3rd Law of Motion
0:20
All Forces Come in Pairs
0:24
Examples
1:22
Action-Reaction Pairs
2:07
Girl Kicking Soccer Ball
2:11
Rocket Ship in Space
2:29
Gravity on You
2:53
Example 1: Force of Gravity
3:34
Example 2: Sailboat
4:00
Example 3: Hammer and Nail
4:49
Example 4: Net Force
5:06
Friction

17m 49s

Intro
0:00
Objectives
0:06
Examples
0:23
Friction Opposes Motion
0:24
Kinetic Friction
0:27
Static Friction
0:36
Magnitude of Frictional Force Is Determined By Two Things
0:41
Coefficient Friction
2:27
Ratio of the Frictional Force and the Normal Force
2:28
Chart of Different Values of Friction
2:48
Kinetic or Static?
3:31
Example 1: Car Sliding
4:18
Example 2: Block on Incline
5:03
Calculating the Force of Friction
5:48
Depends Only Upon the Nature of the Surfaces in Contact and the Magnitude of the Force
5:50
Terminal Velocity
6:14
Air Resistance
6:18
Terminal Velocity of the Falling Object
6:33
Example 3: Finding the Frictional Force
7:36
Example 4: Box on Wood Surface
9:13
Example 5: Static vs. Kinetic Friction
11:49
Example 6: Drag Force on Airplane
12:15
Example 7: Pulling a Sled
13:21
Dynamics Applications

35m 27s

Intro
0:00
Objectives
0:08
Free Body Diagrams
0:49
Drawing FBDs
1:09
Draw Object of Interest as a Dot
1:12
Sketch a Coordinate System
1:18
Example 1: FBD of Block on Ramp
1:39
Pseudo-FBDs
1:59
Draw Object of Interest as a Dot
2:00
Break Up the Forces
2:07
Box on a Ramp
2:12
Example 2: Box at Rest
4:28
Example 3: Box Held by Force
5:00
What is an Atwood Machine?
6:46
Two Objects are Connected by a Light String Over a Mass-less Pulley
6:49
Properties of Atwood Machines
7:13
Ideal Pulleys are Frictionless and Mass-less
7:16
Tension is Constant in a Light String Passing Over an Ideal Pulley
7:23
Solving Atwood Machine Problems
8:02
Alternate Solution
12:07
Analyze the System as a Whole
12:12
Elevators
14:24
Scales Read the Force They Exert on an Object Placed Upon Them
14:42
Can be Used to Analyze Using Newton's 2nd Law and Free body Diagrams
15:23
Example 4: Elevator Accelerates Upward
15:36
Example 5: Truck on a Hill
18:30
Example 6: Force Up a Ramp
19:28
Example 7: Acceleration Down a Ramp
21:56
Example 8: Basic Atwood Machine
24:05
Example 9: Masses and Pulley on a Table
26:47
Example 10: Mass and Pulley on a Ramp
29:15
Example 11: Elevator Accelerating Downward
33:00
Impulse & Momentum

26m 6s

Intro
0:00
Objectives
0:06
Momentum
0:31
Example
0:35
Momentum measures How Hard It Is to Stop a Moving Object
0:47
Vector Quantity
0:58
Example 1: Comparing Momenta
1:48
Example 2: Calculating Momentum
3:08
Example 3: Changing Momentum
3:50
Impulse
5:02
Change In Momentum
5:05
Example 4: Impulse
5:26
Example 5: Impulse-Momentum
6:41
Deriving the Impulse-Momentum Theorem
9:04
Impulse-Momentum Theorem
12:02
Example 6: Impulse-Momentum Theorem
12:15
Non-Constant Forces
13:55
Impulse or Change in Momentum
13:56
Determine the Impulse by Calculating the Area of the Triangle Under the Curve
14:07
Center of Mass
14:56
Real Objects Are More Complex Than Theoretical Particles
14:59
Treat Entire Object as if Its Entire Mass Were Contained at the Object's Center of Mass
15:09
To Calculate the Center of Mass
15:17
Example 7: Force on a Moving Object
15:49
Example 8: Motorcycle Accident
17:49
Example 9: Auto Collision
19:32
Example 10: Center of Mass (1D)
21:29
Example 11: Center of Mass (2D)
23:28
Collisions

21m 59s

Intro
0:00
Objectives
0:09
Conservation of Momentum
0:18
Linear Momentum is Conserved in an Isolated System
0:21
Useful for Analyzing Collisions and Explosions
0:27
Momentum Tables
0:58
Identify Objects in the System
1:05
Determine the Momenta of the Objects Before and After the Event
1:10
Add All the Momenta From Before the Event and Set Them Equal to Momenta After the Event
1:15
Solve Your Resulting Equation for Unknowns
1:20
Types of Collisions
1:31
Elastic Collision
1:36
Inelastic Collision
1:56
Example 1: Conservation of Momentum (1D)
2:02
Example 2: Inelastic Collision
5:12
Example 3: Recoil Velocity
7:16
Example 4: Conservation of Momentum (2D)
9:29
Example 5: Atomic Collision
16:02
Describing Circular Motion

7m 18s

Intro
0:00
Objectives
0:07
Uniform Circular Motion
0:20
Circumference
0:32
Average Speed Formula Still Applies
0:46
Frequency
1:03
Number of Revolutions or Cycles Which Occur Each Second
1:04
Hertz
1:24
Formula for Frequency
1:28
Period
1:36
Time It Takes for One Complete Revolution or Cycle
1:37
Frequency and Period
1:54
Example 1: Car on a Track
2:08
Example 2: Race Car
3:55
Example 3: Toy Train
4:45
Example 4: Round-A-Bout
5:39
Centripetal Acceleration & Force

26m 37s

Intro
0:00
Objectives
0:08
Uniform Circular Motion
0:38
Direction of ac
1:41
Magnitude of ac
3:50
Centripetal Force
4:08
For an Object to Accelerate, There Must Be a Net Force
4:18
Centripetal Force
4:26
Calculating Centripetal Force
6:14
Example 1: Acceleration
7:31
Example 2: Direction of ac
8:53
Example 3: Loss of Centripetal Force
9:19
Example 4: Velocity and Centripetal Force
10:08
Example 5: Demon Drop
10:55
Example 6: Centripetal Acceleration vs. Speed
14:11
Example 7: Calculating ac
15:03
Example 8: Running Back
15:45
Example 9: Car at an Intersection
17:15
Example 10: Bucket in Horizontal Circle
18:40
Example 11: Bucket in Vertical Circle
19:20
Example 12: Frictionless Banked Curve
21:55
Gravitation

32m 56s

Intro
0:00
Objectives
0:08
Universal Gravitation
0:29
The Bigger the Mass the Closer the Attraction
0:48
Formula for Gravitational Force
1:16
Calculating g
2:43
Mass of Earth
2:51
Radius of Earth
2:55
Inverse Square Relationship
4:32
Problem Solving Hints
7:21
Substitute Values in For Variables at the End of the Problem Only
7:26
Estimate the Order of Magnitude of the Answer Before Using Your Calculator
7:38
Make Sure Your Answer Makes Sense
7:55
Example 1: Asteroids
8:20
Example 2: Meteor and the Earth
10:17
Example 3: Satellite
13:13
Gravitational Fields
13:50
Gravity is a Non-Contact Force
13:54
Closer Objects
14:14
Denser Force Vectors
14:19
Gravitational Field Strength
15:09
Example 4: Astronaut
16:19
Gravitational Potential Energy
18:07
Two Masses Separated by Distance Exhibit an Attractive Force
18:11
Formula for Gravitational Field
19:21
How Do Orbits Work?
19:36
Example5: Gravitational Field Strength for Space Shuttle in Orbit
21:35
Example 6: Earth's Orbit
25:13
Example 7: Bowling Balls
27:25
Example 8: Freely Falling Object
28:07
Example 9: Finding g
28:40
Example 10: Space Vehicle on Mars
29:10
Example 11: Fg vs. Mass Graph
30:24
Example 12: Mass on Mars
31:14
Example 13: Two Satellites
31:51
Rotational Kinematics

15m 33s

Intro
0:00
Objectives
0:07
Radians and Degrees
0:26
In Degrees, Once Around a Circle is 360 Degrees
0:29
In Radians, Once Around a Circle is 2π
0:34
Example 1: Degrees to Radians
0:57
Example 2: Radians to Degrees
1:31
Linear vs. Angular Displacement
2:00
Linear Position
2:05
Angular Position
2:10
Linear vs. Angular Velocity
2:35
Linear Speed
2:39
Angular Speed
2:42
Direction of Angular Velocity
3:05
Converting Linear to Angular Velocity
4:22
Example 3: Angular Velocity Example
4:41
Linear vs. Angular Acceleration
5:36
Example 4: Angular Acceleration
6:15
Kinematic Variable Parallels
7:47
Displacement
7:52
Velocity
8:10
Acceleration
8:16
Time
8:22
Kinematic Variable Translations
8:30
Displacement
8:34
Velocity
8:42
Acceleration
8:50
Time
8:58
Kinematic Equation Parallels
9:09
Kinematic Equations
9:12
Delta
9:33
Final Velocity Squared and Angular Velocity Squared
9:54
Example 5: Medieval Flail
10:24
Example 6: CD Player
10:57
Example 7: Carousel
12:13
Example 8: Circular Saw
13:35
Torque

11m 21s

Intro
0:00
Objectives
0:05
Torque
0:18
Force That Causes an Object to Turn
0:22
Must be Perpendicular to the Displacement to Cause a Rotation
0:27
Lever Arm: The Stronger the Force, The More Torque
0:45
Direction of the Torque Vector
1:53
Perpendicular to the Position Vector and the Force Vector
1:54
Right-Hand Rule
2:08
Newton's 2nd Law: Translational vs. Rotational
2:46
Equilibrium
3:58
Static Equilibrium
4:01
Dynamic Equilibrium
4:09
Rotational Equilibrium
4:22
Example 1: Pirate Captain
4:32
Example 2: Auto Mechanic
5:25
Example 3: Sign Post
6:44
Example 4: See-Saw
9:01
Rotational Dynamics

36m 6s

Intro
0:00
Objectives
0:08
Types of Inertia
0:39
Inertial Mass (Translational Inertia)
0:42
Moment of Inertia (Rotational Inertia)
0:53
Moment of Inertia for Common Objects
1:48
Example 1: Calculating Moment of Inertia
2:53
Newton's 2nd Law - Revisited
5:09
Acceleration of an Object
5:15
Angular Acceleration of an Object
5:24
Example 2: Rotating Top
5:47
Example 3: Spinning Disc
7:54
Angular Momentum
9:41
Linear Momentum
9:43
Angular Momentum
10:00
Calculating Angular Momentum
10:51
Direction of the Angular Momentum Vector
11:26
Total Angular Momentum
12:29
Example 4: Angular Momentum of Particles
14:15
Example 5: Rotating Pedestal
16:51
Example 6: Rotating Discs
18:39
Angular Momentum and Heavenly Bodies
20:13
Types of Kinetic Energy
23:41
Objects Traveling with a Translational Velocity
23:45
Objects Traveling with Angular Velocity
24:00
Translational vs. Rotational Variables
24:33
Example 7: Kinetic Energy of a Basketball
25:45
Example 8: Playground Round-A-Bout
28:17
Example 9: The Ice Skater
30:54
Example 10: The Bowler
33:15
Work & Power

31m 20s

Intro
0:00
Objectives
0:09
What Is Work?
0:31
Power Output
0:35
Transfer Energy
0:39
Work is the Process of Moving an Object by Applying a Force
0:46
Examples of Work
0:56
Calculating Work
2:16
Only the Force in the Direction of the Displacement Counts
2:33
Formula for Work
2:48
Example 1: Moving a Refrigerator
3:16
Example 2: Liberating a Car
3:59
Example 3: Crate on a Ramp
5:20
Example 4: Lifting a Box
7:11
Example 5: Pulling a Wagon
8:38
Force vs. Displacement Graphs
9:33
The Area Under a Force vs. Displacement Graph is the Work Done by the Force
9:37
Find the Work Done
9:49
Example 6: Work From a Varying Force
11:00
Hooke's Law
12:42
The More You Stretch or Compress a Spring, The Greater the Force of the Spring
12:46
The Spring's Force is Opposite the Direction of Its Displacement from Equilibrium
13:00
Determining the Spring Constant
14:21
Work Done in Compressing the Spring
15:27
Example 7: Finding Spring Constant
16:21
Example 8: Calculating Spring Constant
17:58
Power
18:43
Work
18:46
Power
18:50
Example 9: Moving a Sofa
19:26
Calculating Power
20:41
Example 10: Motors Delivering Power
21:27
Example 11: Force on a Cyclist
22:40
Example 12: Work on a Spinning Mass
23:52
Example 13: Work Done by Friction
25:05
Example 14: Units of Power
28:38
Example 15: Frictional Force on a Sled
29:43
Energy

20m 15s

Intro
0:00
Objectives
0:07
What is Energy?
0:24
The Ability or Capacity to do Work
0:26
The Ability or Capacity to Move an Object
0:34
Types of Energy
0:39
Energy Transformations
2:07
Transfer Energy by Doing Work
2:12
Work-Energy Theorem
2:20
Units of Energy
2:51
Kinetic Energy
3:08
Energy of Motion
3:13
Ability or Capacity of a Moving Object to Move Another Object
3:17
A Single Object Can Only Have Kinetic Energy
3:46
Example 1: Kinetic Energy of a Motorcycle
5:08
Potential Energy
5:59
Energy An Object Possesses
6:10
Gravitational Potential Energy
7:21
Elastic Potential Energy
9:58
Internal Energy
10:16
Includes the Kinetic Energy of the Objects That Make Up the System and the Potential Energy of the Configuration
10:20
Calculating Gravitational Potential Energy in a Constant Gravitational Field
10:57
Sources of Energy on Earth
12:41
Example 2: Potential Energy
13:41
Example 3: Energy of a System
14:40
Example 4: Kinetic and Potential Energy
15:36
Example 5: Pendulum
16:55
Conservation of Energy

23m 20s

Intro
0:00
Objectives
0:08
Law of Conservation of Energy
0:22
Energy Cannot Be Created or Destroyed.. It Can Only Be Changed
0:27
Mechanical Energy
0:34
Conservation Laws
0:40
Examples
0:49
Kinematics vs. Energy
4:34
Energy Approach
4:56
Kinematics Approach
6:04
The Pendulum
8:07
Example 1: Cart Compressing a Spring
13:09
Example 2
14:23
Example 3: Car Skidding to a Stop
16:15
Example 4: Accelerating an Object
17:27
Example 5: Block on Ramp
18:06
Example 6: Energy Transfers
19:21
Simple Harmonic Motion

58m 30s

Intro
0:00
Objectives
0:08
What Is Simple Harmonic Motion?
0:57
Nature's Typical Reaction to a Disturbance
1:00
A Displacement Which Results in a Linear Restoring Force Results in SHM
1:25
Review of Springs
1:43
When a Force is Applied to a Spring, the Spring Applies a Restoring Force
1:46
When the Spring is in Equilibrium, It Is 'Unstrained'
1:54
Factors Affecting the Force of A Spring
2:00
Oscillations
3:42
Repeated Motions
3:45
Cycle 1
3:52
Period
3:58
Frequency
4:07
Spring-Block Oscillator
4:47
Mass of the Block
4:59
Spring Constant
5:05
Example 1: Spring-Block Oscillator
6:30
Diagrams
8:07
Displacement
8:42
Velocity
8:57
Force
9:36
Acceleration
10:09
U
10:24
K
10:47
Example 2: Harmonic Oscillator Analysis
16:22
Circular Motion vs. SHM
23:26
Graphing SHM
25:52
Example 3: Position of an Oscillator
28:31
Vertical Spring-Block Oscillator
31:13
Example 4: Vertical Spring-Block Oscillator
34:26
Example 5: Bungee
36:39
The Pendulum
43:55
Mass Is Attached to a Light String That Swings Without Friction About the Vertical Equilibrium
44:04
Energy and the Simple Pendulum
44:58
Frequency and Period of a Pendulum
48:25
Period of an Ideal Pendulum
48:31
Assume Theta is Small
48:54
Example 6: The Pendulum
50:15
Example 7: Pendulum Clock
53:38
Example 8: Pendulum on the Moon
55:14
Example 9: Mass on a Spring
56:01
Section 3: Fluids
Density & Buoyancy

19m 48s

Intro
0:00
Objectives
0:09
Fluids
0:27
Fluid is Matter That Flows Under Pressure
0:31
Fluid Mechanics is the Study of Fluids
0:44
Density
0:57
Density is the Ratio of an Object's Mass to the Volume It Occupies
0:58
Less Dense Fluids
1:06
Less Dense Solids
1:09
Example 1: Density of Water
1:27
Example 2: Volume of Gold
2:19
Example 3: Floating
3:06
Buoyancy
3:54
Force Exerted by a Fluid on an Object, Opposing the Object's Weight
3:56
Buoyant Force Determined Using Archimedes Principle
4:03
Example 4: Buoyant Force
5:12
Example 5: Shark Tank
5:56
Example 6: Concrete Boat
7:47
Example 7: Apparent Mass
10:08
Example 8: Volume of a Submerged Cube
13:21
Example 9: Determining Density
15:37
Pressure & Pascal's Principle

18m 7s

Intro
0:00
Objectives
0:09
Pressure
0:25
Pressure is the Effect of a Force Acting Upon a Surface
0:27
Formula for Pressure
0:41
Force is Always Perpendicular to the Surface
0:50
Exerting Pressure
1:03
Fluids Exert Outward Pressure in All Directions on the Sides of Any Container Holding the Fluid
1:36
Earth's Atmosphere Exerts Pressure
1:42
Example 1: Pressure on Keyboard
2:17
Example 2: Sleepy Fisherman
3:03
Example 3: Scale on Planet Physica
4:12
Example 4: Ranking Pressures
5:00
Pressure on a Submerged Object
6:45
Pressure a Fluid Exerts on an Object Submerged in That Fluid
6:46
If There Is Atmosphere Above the Fluid
7:03
Example 5: Gauge Pressure Scuba Diving
7:27
Example 6: Absolute Pressure Scuba Diving
8:13
Pascal's Principle
8:51
Force Multiplication Using Pascal's Principle
9:24
Example 7: Barber's Chair
11:38
Example 8: Hydraulic Auto Lift
13:26
Example 9: Pressure on a Penny
14:41
Example 10: Depth in Fresh Water
16:39
Example 11: Absolute vs. Gauge Pressure
17:23
Continuity Equation for Fluids

7m

Intro
0:00
Objectives
0:08
Conservation of Mass for Fluid Flow
0:18
Law of Conservation of Mass for Fluids
0:21
Volume Flow Rate Remains Constant Throughout the Pipe
0:35
Volume Flow Rate
0:59
Quantified In Terms Of Volume Flow Rate
1:01
Area of Pipe x Velocity of Fluid
1:05
Must Be Constant Throughout Pipe
1:10
Example 1: Tapered Pipe
1:44
Example 2: Garden Hose
2:37
Example 3: Oil Pipeline
4:49
Example 4: Roots of Continuity Equation
6:16
Bernoulli's Principle

20m

Intro
0:00
Objectives
0:08
Bernoulli's Principle
0:21
Airplane Wings
0:35
Venturi Pump
1:56
Bernoulli's Equation
3:32
Example 1: Torricelli's Theorem
4:38
Example 2: Gauge Pressure
7:26
Example 3: Shower Pressure
8:16
Example 4: Water Fountain
12:29
Example 5: Elevated Cistern
15:26
Section 4: Thermal Physics
Temperature, Heat, & Thermal Expansion

24m 17s

Intro
0:00
Objectives
0:12
Thermal Physics
0:42
Explores the Internal Energy of Objects Due to the Motion of the Atoms and Molecules Comprising the Objects
0:46
Explores the Transfer of This Energy From Object to Object
0:53
Temperature
1:00
Thermal Energy Is Related to the Kinetic Energy of All the Particles Comprising the Object
1:03
The More Kinetic Energy of the Constituent Particles Have, The Greater the Object's Thermal Energy
1:12
Temperature and Phases of Matter
1:44
Solids
1:48
Liquids
1:56
Gases
2:02
Average Kinetic Energy and Temperature
2:16
Average Kinetic Energy
2:24
Boltzmann's Constant
2:29
Temperature Scales
3:06
Converting Temperatures
4:37
Heat
5:03
Transfer of Thermal Energy
5:06
Accomplished Through Collisions Which is Conduction
5:13
Methods of Heat Transfer
5:52
Conduction
5:59
Convection
6:19
Radiation
6:31
Quantifying Heat Transfer in Conduction
6:37
Rate of Heat Transfer is Measured in Watts
6:42
Thermal Conductivity
7:12
Example 1: Average Kinetic Energy
7:35
Example 2: Body Temperature
8:22
Example 3: Temperature of Space
9:30
Example 4: Temperature of the Sun
10:44
Example 5: Heat Transfer Through Window
11:38
Example 6: Heat Transfer Across a Rod
12:40
Thermal Expansion
14:18
When Objects Are Heated, They Tend to Expand
14:19
At Higher Temperatures, Objects Have Higher Average Kinetic Energies
14:24
At Higher Levels of Vibration, The Particles Are Not Bound As Tightly to Each Other
14:30
Linear Expansion
15:11
Amount a Material Expands is Characterized by the Material's Coefficient of Expansion
15:14
One-Dimensional Expansion -> Linear Coefficient of Expansion
15:20
Volumetric Expansion
15:38
Three-Dimensional Expansion -> Volumetric Coefficient of Expansion
15:45
Volumetric Coefficient of Expansion is Roughly Three Times the Linear Coefficient of Expansion
16:03
Coefficients of Thermal Expansion
16:24
Example 7: Contracting Railroad Tie
16:59
Example 8: Expansion of an Aluminum Rod
18:37
Example 9: Water Spilling Out of a Glass
20:18
Example 10: Average Kinetic Energy vs. Temperature
22:18
Example 11: Expansion of a Ring
23:07
Ideal Gases

24m 15s

Intro
0:00
Objectives
0:10
Ideal Gases
0:25
Gas Is Comprised of Many Particles Moving Randomly in a Container
0:34
Particles Are Far Apart From One Another
0:46
Particles Do Not Exert Forces Upon One Another Unless They Come In Contact in an Elastic Collision
0:53
Ideal Gas Law
1:18
Atoms, Molecules, and Moles
2:56
Protons
2:59
Neutrons
3:15
Electrons
3:18
Examples
3:25
Example 1: Counting Moles
4:58
Example 2: Moles of CO2 in a Bottle
6:00
Example 3: Pressurized CO2
6:54
Example 4: Helium Balloon
8:53
Internal Energy of an Ideal Gas
10:17
The Average Kinetic Energy of the Particles of an Ideal Gas
10:21
Total Internal Energy of the Ideal Gas Can Be Found by Multiplying the Average Kinetic Energy of the Gas's Particles by the Numbers of Particles in the Gas
10:32
Example 5: Internal Energy of Oxygen
12:00
Example 6: Temperature of Argon
12:41
Root-Mean-Square Velocity
13:40
This is the Square Root of the Average Velocity Squared For All the Molecules in the System
13:43
Derived from the Maxwell-Boltzmann Distribution Function
13:56
Calculating vrms
14:56
Example 7: Average Velocity of a Gas
18:32
Example 8: Average Velocity of a Gas
19:44
Example 9: vrms of Molecules in Equilibrium
20:59
Example 10: Moles to Molecules
22:25
Example 11: Relating Temperature and Internal Energy
23:22
Thermodynamics

22m 29s

Intro
0:00
Objectives
0:06
Zeroth Law of Thermodynamics
0:26
First Law of Thermodynamics
1:00
The Change in the Internal Energy of a Closed System is Equal to the Heat Added to the System Plus the Work Done on the System
1:04
It is a Restatement of the Law of Conservation of Energy
1:19
Sign Conventions Are Important
1:25
Work Done on a Gas
1:44
Example 1: Adding Heat to a System
3:25
Example 2: Expanding a Gas
4:07
P-V Diagrams
5:11
Pressure-Volume Diagrams are Useful Tools for Visualizing Thermodynamic Processes of Gases
5:13
Use Ideal Gas Law to Determine Temperature of Gas
5:25
P-V Diagrams II
5:55
Volume Increases, Pressure Decreases
6:00
As Volume Expands, Gas Does Work
6:19
Temperature Rises as You Travel Up and Right on a PV Diagram
6:29
Example 3: PV Diagram Analysis
6:40
Types of PV Processes
7:52
Adiabatic
8:03
Isobaric
8:19
Isochoric
8:28
Isothermal
8:35
Adiabatic Processes
8:47
Heat Is not Transferred Into or Out of The System
8:50
Heat = 0
8:55
Isobaric Processes
9:19
Pressure Remains Constant
9:21
PV Diagram Shows a Horizontal Line
9:27
Isochoric Processes
9:51
Volume Remains Constant
9:52
PV Diagram Shows a Vertical Line
9:58
Work Done on the Gas is Zero
10:01
Isothermal Processes
10:27
Temperature Remains Constant
10:29
Lines on a PV Diagram Are Isotherms
10:31
PV Remains Constant
10:38
Internal Energy of Gas Remains Constant
10:40
Example 4: Adiabatic Expansion
10:46
Example 5: Removing Heat
11:25
Example 6: Ranking Processes
13:08
Second Law of Thermodynamics
13:59
Heat Flows Naturally From a Warmer Object to a Colder Object
14:02
Heat Energy Cannot be Completely Transformed Into Mechanical Work
14:11
All Natural Systems Tend Toward a Higher Level of Disorder
14:19
Heat Engines
14:52
Heat Engines Convert Heat Into Mechanical Work
14:56
Efficiency of a Heat Engine is the Ratio of the Engine You Get Out to the Energy You Put In
14:59
Power in Heat Engines
16:09
Heat Engines and PV Diagrams
17:38
Carnot Engine
17:54
It Is a Theoretical Heat Engine That Operates at Maximum Possible Efficiency
18:02
It Uses Only Isothermal and Adiabatic Processes
18:08
Carnot's Theorem
18:11
Example 7: Carnot Engine
18:49
Example 8: Maximum Efficiency
21:02
Example 9: PV Processes
21:51
Section 5: Electricity & Magnetism
Electric Fields & Forces

38m 24s

Intro
0:00
Objectives
0:10
Electric Charges
0:34
Matter is Made Up of Atoms
0:37
Protons Have a Charge of +1
0:45
Electrons Have a Charge of -1
1:00
Most Atoms Are Neutral
1:04
Ions
1:15
Fundamental Unit of Charge is the Coulomb
1:29
Like Charges Repel, While Opposites Attract
1:50
Example 1: Charge on an Object
2:22
Example 2: Charge of an Alpha Particle
3:36
Conductors and Insulators
4:27
Conductors Allow Electric Charges to Move Freely
4:30
Insulators Do Not Allow Electric Charges to Move Freely
4:39
Resistivity is a Material Property
4:45
Charging by Conduction
5:05
Materials May Be Charged by Contact, Known as Conduction
5:07
Conductors May Be Charged by Contact
5:24
Example 3: Charging by Conduction
5:38
The Electroscope
6:44
Charging by Induction
8:00
Example 4: Electrostatic Attraction
9:23
Coulomb's Law
11:46
Charged Objects Apply a Force Upon Each Other = Coulombic Force
11:52
Force of Attraction or Repulsion is Determined by the Amount of Charge and the Distance Between the Charges
12:04
Example 5: Determine Electrostatic Force
13:09
Example 6: Deflecting an Electron Beam
15:35
Electric Fields
16:28
The Property of Space That Allows a Charged Object to Feel a Force
16:44
Electric Field Strength Vector is the Amount of Electrostatic Force Observed by a Charge Per Unit of Charge
17:01
The Direction of the Electric Field Vector is the Direction a Positive Charge Would Feel a Force
17:24
Example 7: Field Between Metal Plates
17:58
Visualizing the Electric Field
19:27
Electric Field Lines Point Away from Positive Charges and Toward Negative Charges
19:40
Electric Field Lines Intersect Conductors at Right Angles to the Surface
19:50
Field Strength and Line Density Decreases as You Move Away From the Charges
19:58
Electric Field Lines
20:09
E Field Due to a Point Charge
22:32
Electric Fields Are Caused by Charges
22:35
Electric Field Due to a Point Charge Can Be Derived From the Definition of the Electric Field and Coulomb's Law
22:38
To Find the Electric Field Due to Multiple Charges
23:09
Comparing Electricity to Gravity
23:56
Force
24:02
Field Strength
24:16
Constant
24:37
Charge/ Mass Units
25:01
Example 8: E Field From 3 Point Charges
25:07
Example 9: Where is the E Field Zero?
31:43
Example 10: Gravity and Electricity
36:38
Example 11: Field Due to Point Charge
37:34
Electric Potential Difference

35m 58s

Intro
0:00
Objectives
0:09
Electric Potential Energy
0:32
When an Object Was Lifted Against Gravity By Applying a Force for Some Distance, Work Was Done
0:35
When a Charged Object is Moved Against an Electric Field by Applying a Force for Some Distance, Work is Done
0:43
Electric Potential Difference
1:30
Example 1: Charge From Work
2:06
Example 2: Electric Energy
3:09
The Electron-Volt
4:02
Electronvolt (eV)
4:15
1eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt
4:28
Example 3: Energy in eV
5:33
Equipotential Lines
6:32
Topographic Maps Show Lines of Equal Altitude, or Equal Gravitational Potential
6:36
Lines Connecting Points of Equal Electrical Potential are Known as Equipotential Lines
6:57
Drawing Equipotential Lines
8:15
Potential Due to a Point Charge
10:46
Calculate the Electric Field Vector Due to a Point Charge
10:52
Calculate the Potential Difference Due to a Point Charge
11:05
To Find the Potential Difference Due to Multiple Point Charges
11:16
Example 4: Potential Due to a Point Charge
11:52
Example 5: Potential Due to Point Charges
13:04
Parallel Plates
16:34
Configurations in Which Parallel Plates of Opposite Charge are Situated a Fixed Distance From Each Other
16:37
These Can Create a Capacitor
16:45
E Field Due to Parallel Plates
17:14
Electric Field Away From the Edges of Two Oppositely Charged Parallel Plates is Constant
17:15
Magnitude of the Electric Field Strength is Give By the Potential Difference Between the Plates Divided by the Plate Separation
17:47
Capacitors
18:09
Electric Device Used to Store Charge
18:11
Once the Plates Are Charged, They Are Disconnected
18:30
Device's Capacitance
18:46
Capacitors Store Energy
19:28
Charges Located on the Opposite Plates of a Capacitor Exert Forces on Each Other
19:31
Example 6: Capacitance
20:28
Example 7: Charge on a Capacitor
22:03
Designing Capacitors
24:00
Area of the Plates
24:05
Separation of the Plates
24:09
Insulating Material
24:13
Example 8: Designing a Capacitor
25:35
Example 9: Calculating Capacitance
27:39
Example 10: Electron in Space
29:47
Example 11: Proton Energy Transfer
30:35
Example 12: Two Conducting Spheres
32:50
Example 13: Equipotential Lines for a Capacitor
34:48
Current & Resistance

21m 14s

Intro
0:00
Objectives
0:06
Electric Current
0:19
Path Through Current Flows
0:21
Current is the Amount of Charge Passing a Point Per Unit Time
0:25
Conventional Current is the Direction of Positive Charge Flow
0:43
Example 1: Current Through a Resistor
1:19
Example 2: Current Due to Elementary Charges
1:47
Example 3: Charge in a Light Bulb
2:35
Example 4: Flashlights
3:03
Conductivity and Resistivity
4:41
Conductivity is a Material's Ability to Conduct Electric Charge
4:53
Resistivity is a Material's Ability to Resist the Movement of Electric Charge
5:11
Resistance vs. Resistivity vs. Resistors
5:35
Resistivity Is a Material Property
5:40
Resistance Is a Functional Property of an Element in an Electric Circuit
5:57
A Resistor is a Circuit Element
7:23
Resistors
7:45
Example 5: Calculating Resistance
8:17
Example 6: Resistance Dependencies
10:09
Configuration of Resistors
10:50
When Placed in a Circuit, Resistors Can be Organized in Both Serial and Parallel Arrangements
10:53
May Be Useful to Determine an Equivalent Resistance Which Could Be Used to Replace a System or Resistors with a Single Equivalent Resistor
10:58
Resistors in Series
11:15
Resistors in Parallel
12:35
Example 7: Finding Equivalent Resistance
15:01
Example 8: Length and Resistance
17:43
Example 9: Comparing Resistors
18:21
Example 10: Comparing Wires
19:12
Ohm's Law & Power

10m 35s

Intro
0:00
Objectives
0:06
Ohm's Law
0:21
Relates Resistance, Potential Difference, and Current Flow
0:23
Example 1: Resistance of a Wire
1:22
Example 2: Circuit Current
1:58
Example 3: Variable Resistor
2:30
Ohm's 'Law'?
3:22
Very Useful Empirical Relationship
3:31
Test if a Material is 'Ohmic'
3:40
Example 4: Ohmic Material
3:58
Electrical Power
4:24
Current Flowing Through a Circuit Causes a Transfer of Energy Into Different Types
4:26
Example: Light Bulb
4:36
Example: Television
4:58
Calculating Power
5:09
Electrical Energy
5:14
Charge Per Unit Time Is Current
5:29
Expand Using Ohm's Law
5:48
Example 5: Toaster
7:43
Example 6: Electric Iron
8:19
Example 7: Power of a Resistor
9:19
Example 8: Information Required to Determine Power in a Resistor
9:55
Circuits & Electrical Meters

8m 44s

Intro
0:00
Objectives
0:08
Electrical Circuits
0:21
A Closed-Loop Path Through Which Current Can Flow
0:22
Can Be Made Up of Most Any Materials, But Typically Comprised of Electrical Devices
0:27
Circuit Schematics
1:09
Symbols Represent Circuit Elements
1:30
Lines Represent Wires
1:33
Sources for Potential Difference: Voltaic Cells, Batteries, Power Supplies
1:36
Complete Conducting Paths
2:43
Voltmeters
3:20
Measure the Potential Difference Between Two Points in a Circuit
3:21
Connected in Parallel with the Element to be Measured
3:25
Have Very High Resistance
3:59
Ammeters
4:19
Measure the Current Flowing Through an Element of a Circuit
4:20
Connected in Series with the Circuit
4:25
Have Very Low Resistance
4:45
Example 1: Ammeter and Voltmeter Placement
4:56
Example 2: Analyzing R
6:27
Example 3: Voltmeter Placement
7:12
Example 4: Behavior or Electrical Meters
7:31
Circuit Analysis

48m 58s

Intro
0:00
Objectives
0:07
Series Circuits
0:27
Series Circuits Have Only a Single Current Path
0:29
Removal of any Circuit Element Causes an Open Circuit
0:31
Kirchhoff's Laws
1:36
Tools Utilized in Analyzing Circuits
1:42
Kirchhoff's Current Law States
1:47
Junction Rule
2:00
Kirchhoff's Voltage Law States
2:05
Loop Rule
2:18
Example 1: Voltage Across a Resistor
2:23
Example 2: Current at a Node
3:45
Basic Series Circuit Analysis
4:53
Example 3: Current in a Series Circuit
9:21
Example 4: Energy Expenditure in a Series Circuit
10:14
Example 5: Analysis of a Series Circuit
12:07
Example 6: Voltmeter In a Series Circuit
14:57
Parallel Circuits
17:11
Parallel Circuits Have Multiple Current Paths
17:13
Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating
17:15
Basic Parallel Circuit Analysis
18:19
Example 7: Parallel Circuit Analysis
21:05
Example 8: Equivalent Resistance
22:39
Example 9: Four Parallel Resistors
23:16
Example 10: Ammeter in a Parallel Circuit
26:27
Combination Series-Parallel Circuits
28:50
Look For Portions of the Circuit With Parallel Elements
28:56
Work Back to Original Circuit
29:09
Analysis of a Combination Circuit
29:20
Internal Resistance
34:11
In Reality, Voltage Sources Have Some Amount of 'Internal Resistance'
34:16
Terminal Voltage of the Voltage Source is Reduced Slightly
34:25
Example 11: Two Voltage Sources
35:16
Example 12: Internal Resistance
42:46
Example 13: Complex Circuit with Meters
45:22
Example 14: Parallel Equivalent Resistance
48:24
RC Circuits

24m 47s

Intro
0:00
Objectives
0:08
Capacitors in Parallel
0:34
Capacitors Store Charge on Their Plates
0:37
Capacitors In Parallel Can Be Replaced with an Equivalent Capacitor
0:46
Capacitors in Series
2:42
Charge on Capacitors Must Be the Same
2:44
Capacitor In Series Can Be Replaced With an Equivalent Capacitor
2:47
RC Circuits
5:40
Comprised of a Source of Potential Difference, a Resistor Network, and One or More Capacitors
5:42
Uncharged Capacitors Act Like Wires
6:04
Charged Capacitors Act Like Opens
6:12
Charging an RC Circuit
6:23
Discharging an RC Circuit
11:36
Example 1: RC Analysis
14:50
Example 2: More RC Analysis
18:26
Example 3: Equivalent Capacitance
21:19
Example 4: More Equivalent Capacitance
22:48
Magnetic Fields & Properties

19m 48s

Intro
0:00
Objectives
0:07
Magnetism
0:32
A Force Caused by Moving Charges
0:34
Magnetic Domains Are Clusters of Atoms with Electrons Spinning in the Same Direction
0:51
Example 1: Types of Fields
1:23
Magnetic Field Lines
2:25
Make Closed Loops and Run From North to South Outside the Magnet
2:26
Magnetic Flux
2:42
Show the Direction the North Pole of a Magnet Would Tend to Point If Placed in the Field
2:54
Example 2: Lines of Magnetic Force
3:49
Example 3: Forces Between Bar Magnets
4:39
The Compass
5:28
The Earth is a Giant Magnet
5:31
The Earth's Magnetic North pole is Located Near the Geographic South Pole, and Vice Versa
5:33
A Compass Lines Up with the Net Magnetic Field
6:07
Example 3: Compass in Magnetic Field
6:41
Example 4: Compass Near a Bar Magnet
7:14
Magnetic Permeability
7:59
The Ratio of the Magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field
8:02
Free Space
8:13
Highly Magnetic Materials Have Higher Values of Magnetic Permeability
8:34
Magnetic Dipole Moment
8:41
The Force That a Magnet Can Exert on Moving Charges
8:46
Relative Strength of a Magnet
8:54
Forces on Moving Charges
9:10
Moving Charges Create Magnetic Fields
9:11
Magnetic Fields Exert Forces on Moving Charges
9:17
Direction of the Magnetic Force
9:57
Direction is Given by the Right-Hand Rule
10:05
Right-Hand Rule
10:09
Mass Spectrometer
10:52
Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle
10:58
Used to Determine the Mass of an Unknown Particle
11:04
Velocity Selector
12:44
Mass Spectrometer with an Electric Field Added
12:47
Example 5: Force on an Electron
14:13
Example 6: Velocity of a Charged Particle
15:25
Example 7: Direction of the Magnetic Force
16:52
Example 8: Direction of Magnetic Force on Moving Charges
17:43
Example 9: Electron Released From Rest in Magnetic Field
18:53
Current-Carrying Wires

21m 29s

Intro
0:00
Objectives
0:09
Force on a Current-Carrying Wire
0:30
A Current-Carrying Wire in a Magnetic Field May Experience a Magnetic Force
0:33
Direction Given by the Right-Hand Rule
1:11
Example 1: Force on a Current-Carrying Wire
1:38
Example 2: Equilibrium on a Submerged Wire
2:33
Example 3: Torque on a Loop of Wire
5:55
Magnetic Field Due to a Current-Carrying Wire
8:49
Moving Charges Create Magnetic Fields
8:53
Wires Carry Moving Charges
8:56
Direction Given by the Right-Hand Rule
9:21
Example 4: Magnetic Field Due to a Wire
10:56
Magnetic Field Due to a Solenoid
12:12
Solenoid is a Coil of Wire
12:19
Direction Given by the Right-Hand Rule
12:47
Forces on 2 Parallel Wires
13:34
Current Flowing in the Same Direction
14:52
Current Flowing in Opposite Directions
14:57
Example 5: Magnetic Field Due to Wires
15:19
Example 6: Strength of an Electromagnet
18:35
Example 7: Force on a Wire
19:30
Example 8: Force Between Parallel Wires
20:47
Intro to Electromagnetic Induction

17m 26s

Intro
0:00
Objectives
0:09
Induced EMF
0:42
Charges Flowing Through a Wire Create Magnetic Fields
0:45
Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction
0:49
Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field
0:57
Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area
1:17
Finding the Magnetic Flux
1:36
Magnetic Field Strength
1:39
Angle Between the Magnetic Field Strength and the Normal to the Area
1:51
Calculating Induced EMF
3:01
The Magnitude of the Induced EMF is Equal to the Rate of Change of the Magnetic Flux
3:04
Induced EMF in a Rectangular Loop of Wire
4:03
Lenz's Law
5:17
Electric Generators and Motors
9:28
Generate an Induced EMF By Turning a Coil of Wire in a magnetic Field
9:31
Generators Use Mechanical Energy to Turn the Coil of Wire
9:39
Electric Motor Operates Using Same Principle
10:30
Example 1: Finding Magnetic Flux
10:43
Example 2: Finding Induced EMF
11:54
Example 3: Changing Magnetic Field
13:52
Example 4: Current Induced in a Rectangular Loop of Wire
15:23
Section 6: Waves & Optics
Wave Characteristics

26m 41s

Intro
0:00
Objectives
0:09
Waves
0:32
Pulse
1:00
A Pulse is a Single Disturbance Which Carries Energy Through a Medium or Space
1:05
A Wave is a Series of Pulses
1:18
When a Pulse Reaches a Hard Boundary
1:37
When a Pulse Reaches a Soft or Flexible Boundary
2:04
Types of Waves
2:44
Mechanical Waves
2:56
Electromagnetic Waves
3:14
Types of Wave Motion
3:38
Longitudinal Waves
3:39
Transverse Waves
4:18
Anatomy of a Transverse Wave
5:18
Example 1: Waves Requiring a Medium
6:59
Example 2: Direction of Displacement
7:36
Example 3: Bell in a Vacuum Jar
8:47
Anatomy of a Longitudinal Wave
9:22
Example 4: Tuning Fork
9:57
Example 5: Amplitude of a Sound Wave
10:24
Frequency and Period
10:47
Example 6: Period of an EM Wave
11:23
Example 7: Frequency and Period
12:01
The Wave Equation
12:32
Velocity of a Wave is a Function of the Type of Wave and the Medium It Travels Through
12:36
Speed of a Wave is Related to Its Frequency and Wavelength
12:41
Example 8: Wavelength Using the Wave Equation
13:54
Example 9: Period of an EM Wave
14:35
Example 10: Blue Whale Waves
16:03
Sound Waves
17:29
Sound is a Mechanical Wave Observed by Detecting Vibrations in the Inner Ear
17:33
Particles of Sound Wave Vibrate Parallel With the Direction of the Wave's Velocity
17:56
Example 11: Distance from Speakers
18:24
Resonance
19:45
An Object with the Same 'Natural Frequency' May Begin to Vibrate at This Frequency
19:55
Classic Example
20:01
Example 12: Vibrating Car
20:32
Example 13: Sonar Signal
21:28
Example 14: Waves Across Media
24:06
Example 15: Wavelength of Middle C
25:24
Wave Interference

20m 45s

Intro
0:00
Objectives
0:09
Superposition
0:30
When More Than One Wave Travels Through the Same Location in the Same Medium
0:32
The Total Displacement is the Sum of All the Individual Displacements of the Waves
0:46
Example 1: Superposition of Pulses
1:01
Types of Interference
2:02
Constructive Interference
2:05
Destructive Interference
2:18
Example 2: Interference
2:47
Example 3: Shallow Water Waves
3:27
Standing Waves
4:23
When Waves of the Same Frequency and Amplitude Traveling in Opposite Directions Meet in the Same Medium
4:26
A Wave in Which Nodes Appear to be Standing Still and Antinodes Vibrate with Maximum Amplitude Above and Below the Axis
4:35
Standing Waves in String Instruments
5:36
Standing Waves in Open Tubes
8:49
Standing Waves in Closed Tubes
9:57
Interference From Multiple Sources
11:43
Constructive
11:55
Destructive
12:14
Beats
12:49
Two Sound Waves with Almost the Same Frequency Interfere to Create a Beat Pattern
12:52
A Frequency Difference of 1 to 4 Hz is Best for Human Detection of Beat Phenomena
13:05
Example 4
14:13
Example 5
18:03
Example 6
19:14
Example 7: Superposition
20:08
Wave Phenomena

19m 2s

Intro
0:00
Objective
0:08
Doppler Effect
0:36
The Shift In A Wave's Observed Frequency Due to Relative Motion Between the Source of the Wave and Observer
0:39
When Source and/or Observer Move Toward Each Other
0:45
When Source and/or Observer Move Away From Each Other
0:52
Practical Doppler Effect
1:01
Vehicle Traveling Past You
1:05
Applications Are Numerous and Widespread
1:56
Doppler Effect - Astronomy
2:43
Observed Frequencies Are Slightly Lower Than Scientists Would Predict
2:50
More Distant Celestial Objects Are Moving Away from the Earth Faster Than Nearer Objects
3:22
Example 1: Car Horn
3:36
Example 2: Moving Speaker
4:13
Diffraction
5:35
The Bending of Waves Around Obstacles
5:37
Most Apparent When Wavelength Is Same Order of Magnitude as the Obstacle/ Opening
6:10
Single-Slit Diffraction
6:16
Double-Slit Diffraction
8:13
Diffraction Grating
11:07
Sharper and Brighter Maxima
11:46
Useful for Determining Wavelengths Accurately
12:07
Example 3: Double Slit Pattern
12:30
Example 4: Determining Wavelength
16:05
Example 5: Radar Gun
18:04
Example 6: Red Shift
18:29
Light As a Wave

11m 35s

Intro
0:00
Objectives
0:14
Electromagnetic (EM) Waves
0:31
Light is an EM Wave
0:43
EM Waves Are Transverse Due to the Modulation of the Electric and Magnetic Fields Perpendicular to the Wave Velocity
1:00
Electromagnetic Wave Characteristics
1:37
The Product of an EM Wave's Frequency and Wavelength Must be Constant in a Vacuum
1:43
Polarization
3:36
Unpoloarized EM Waves Exhibit Modulation in All Directions
3:47
Polarized Light Consists of Light Vibrating in a Single Direction
4:07
Polarizers
4:29
Materials Which Act Like Filters to Only Allow Specific Polarizations of Light to Pass
4:33
Polarizers Typically Are Sheets of Material in Which Long Molecules Are Lined Up Like a Picket Fence
5:10
Polarizing Sunglasses
5:22
Reduce Reflections
5:26
Polarizing Sunglasses Have Vertical Polarizing Filters
5:48
Liquid Crystal Displays
6:08
LCDs Use Liquid Crystals in a Suspension That Align Themselves in a Specific Orientation When a Voltage is Applied
6:13
Cross-Orienting a Polarizer and a Matrix of Liquid Crystals so Light Can Be Modulated Pixel-by-Pixel
6:26
Example 1: Color of Light
7:30
Example 2: Analyzing an EM Wave
8:49
Example 3: Remote Control
9:45
Example 4: Comparing EM Waves
10:32
Reflection & Mirrors

24m 32s

Intro
0:00
Objectives
0:10
Waves at Boundaries
0:37
Reflected
0:43
Transmitted
0:45
Absorbed
0:48
Law of Reflection
0:58
The Angle of Incidence is Equal to the Angle of Reflection
1:00
They Are Both Measured From a Line Perpendicular, or Normal, to the Reflecting Surface
1:22
Types of Reflection
1:54
Diffuse Reflection
1:57
Specular Reflection
2:08
Example 1: Specular Reflection
2:24
Mirrors
3:20
Light Rays From the Object Reach the Plane Mirror and Are Reflected to the Observer
3:27
Virtual Image
3:33
Magnitude of Image Distance
4:05
Plane Mirror Ray Tracing
4:15
Object Distance
4:26
Image Distance
4:43
Magnification of Image
7:03
Example 2: Plane Mirror Images
7:28
Example 3: Image in a Plane Mirror
7:51
Spherical Mirrors
8:10
Inner Surface of a Spherical Mirror
8:19
Outer Surface of a Spherical Mirror
8:30
Focal Point of a Spherical Mirror
8:40
Converging
8:51
Diverging
9:00
Concave (Converging) Spherical Mirrors
9:09
Light Rays Coming Into a Mirror Parallel to the Principal Axis
9:14
Light Rays Passing Through the Center of Curvature
10:17
Light Rays From the Object Passing Directly Through the Focal Point
10:52
Mirror Equation (Lens Equation)
12:06
Object and Image Distances Are Positive on the Reflecting Side of the Mirror
12:13
Formula
12:19
Concave Mirror with Object Inside f
12:39
Example 4: Concave Spherical Mirror
14:21
Example 5: Image From a Concave Mirror
14:51
Convex (Diverging) Spherical Mirrors
16:29
Light Rays Coming Into a Mirror Parallel to the Principal Axis
16:37
Light Rays Striking the Center of the Mirror
16:50
Light Rays Never Converge on the Reflective Side of a Convex Mirror
16:54
Convex Mirror Ray Tracing
17:07
Example 6: Diverging Rays
19:12
Example 7: Focal Length
19:28
Example 8: Reflected Sonar Wave
19:53
Example 9: Plane Mirror Image Distance
20:20
Example 10: Image From a Concave Mirror
21:23
Example 11: Converging Mirror Image Distance
23:09
Refraction & Lenses

39m 42s

Intro
0:00
Objectives
0:09
Refraction
0:42
When a Wave Reaches a Boundary Between Media, Part of the Wave is Reflected and Part of the Wave Enters the New Medium
0:43
Wavelength Must Change If the Wave's Speed Changes
0:57
Refraction is When This Causes The Wave to Bend as It Enters the New Medium
1:12
Marching Band Analogy
1:22
Index of Refraction
2:37
Measure of How Much Light Slows Down in a Material
2:40
Ratio of the Speed of an EM Wave in a Vacuum to the Speed of an EM Wave in Another Material is Known as Index of Refraction
3:03
Indices of Refraction
3:21
Dispersion
4:01
White Light is Refracted Twice in Prism
4:23
Index of Refraction of the Prism Material Varies Slightly with Respect to Frequency
4:41
Example 1: Determining n
5:14
Example 2: Light in Diamond and Crown Glass
5:55
Snell's Law
6:24
The Amount of a Light Wave Bends As It Enters a New Medium is Given by the Law of Refraction
6:32
Light Bends Toward the Normal as it Enters a Material With a Higher n
7:08
Light Bends Toward the Normal as it Enters a Material With a Lower n
7:14
Example 3: Angle of Refraction
7:42
Example 4: Changes with Refraction
9:31
Total Internal Reflection
10:10
When the Angle of Refraction Reaches 90 Degrees
10:23
Critical Angle
10:34
Total Internal Reflection
10:51
Applications of TIR
12:13
Example 5: Critical Angle of Water
13:17
Thin Lenses
14:15
Convex Lenses
14:22
Concave Lenses
14:31
Convex Lenses
15:24
Rays Parallel to the Principal Axis are Refracted Through the Far Focal Point of the Lens
15:28
A Ray Drawn From the Object Through the Center of the Lens Passes Through the Center of the Lens Unbent
15:53
Example 6: Converging Lens Image
16:46
Example 7: Image Distance of Convex Lens
17:18
Concave Lenses
18:21
Rays From the Object Parallel to the Principal Axis Are Refracted Away from the Principal Axis on a Line from the Near Focal Point Through the Point Where the Ray Intercepts the Center of the Lens
18:25
Concave Lenses Produce Upright, Virtual, Reduced Images
20:30
Example 8: Light Ray Thought a Lens
20:36
Systems of Optical Elements
21:05
Find the Image of the First Optical Elements and Utilize It as the Object of the Second Optical Element
21:16
Example 9: Lens and Mirrors
21:35
Thin Film Interference
27:22
When Light is Incident Upon a Thin Film, Some Light is Reflected and Some is Transmitted Into the Film
27:25
If the Transmitted Light is Again Reflected, It Travels Back Out of the Film and Can Interfere
27:31
Phase Change for Every Reflection from Low-Index to High-Index
28:09
Example 10: Thin Film Interference
28:41
Example 11: Wavelength in Diamond
32:07
Example 12: Light Incident on Crown Glass
33:57
Example 13: Real Image from Convex Lens
34:44
Example 14: Diverging Lens
35:45
Example 15: Creating Enlarged, Real Images
36:22
Example 16: Image from a Converging Lens
36:48
Example 17: Converging Lens System
37:50
Wave-Particle Duality

23m 47s

Intro
0:00
Objectives
0:11
Duality of Light
0:37
Photons
0:47
Dual Nature
0:53
Wave Evidence
1:00
Particle Evidence
1:10
Blackbody Radiation & the UV Catastrophe
1:20
Very Hot Objects Emitted Radiation in a Specific Spectrum of Frequencies and Intensities
1:25
Color Objects Emitted More Intensity at Higher Wavelengths
1:45
Quantization of Emitted Radiation
1:56
Photoelectric Effect
2:38
EM Radiation Striking a Piece of Metal May Emit Electrons
2:41
Not All EM Radiation Created Photoelectrons
2:49
Photons of Light
3:23
Photon Has Zero Mass, Zero Charge
3:32
Energy of a Photon is Quantized
3:36
Energy of a Photon is Related to its Frequency
3:41
Creation of Photoelectrons
4:17
Electrons in Metals Were Held in 'Energy Walls'
4:20
Work Function
4:32
Cutoff Frequency
4:54
Kinetic Energy of Photoelectrons
5:14
Electron in a Metal Absorbs a Photon with Energy Greater Than the Metal's Work Function
5:16
Electron is Emitted as a Photoelectron
5:24
Any Absorbed Energy Beyond That Required to Free the Electron is the KE of the Photoelectron
5:28
Photoelectric Effect in a Circuit
6:37
Compton Effect
8:28
Less of Energy and Momentum
8:49
Lost by X-Ray Equals Energy and Gained by Photoelectron
8:52
Compton Wavelength
9:09
Major Conclusions
9:36
De Broglie Wavelength
10:44
Smaller the Particle, the More Apparent the Wave Properties
11:03
Wavelength of a Moving Particle is Known as Its de Broglie Wavelength
11:07
Davisson-Germer Experiment
11:29
Verifies Wave Nature of Moving Particles
11:30
Shoot Electrons at Double Slit
11:34
Example 1
11:46
Example 2
13:07
Example 3
13:48
Example 4A
15:33
Example 4B
18:47
Example 5: Wave Nature of Light
19:54
Example 6: Moving Electrons
20:43
Example 7: Wavelength of an Electron
21:11
Example 8: Wrecking Ball
22:50
Section 7: Modern Physics
Atomic Energy Levels

14m 21s

Intro
0:00
Objectives
0:09
Rutherford's Gold Foil Experiment
0:35
Most of the Particles Go Through Undeflected
1:12
Some Alpha Particles Are Deflected Large Amounts
1:15
Atoms Have a Small, Massive, Positive Nucleus
1:20
Electrons Orbit the Nucleus
1:23
Most of the Atom is Empty Space
1:26
Problems with Rutherford's Model
1:31
Charges Moving in a Circle Accelerate, Therefore Classical Physics Predicts They Should Release Photons
1:39
Lose Energy When They Release Photons
1:46
Orbits Should Decay and They Should Be Unstable
1:50
Bohr Model of the Atom
2:09
Electrons Don't Lose Energy as They Accelerate
2:20
Each Atom Allows Only a Limited Number of Specific Orbits at Each Energy Level
2:35
Electrons Must Absorb or Emit a Photon of Energy to Change Energy Levels
2:40
Energy Level Diagrams
3:29
n=1 is the Lowest Energy State
3:34
Negative Energy Levels Indicate Electron is Bound to Nucleus of the Atom
4:03
When Electron Reaches 0 eV It Is No Longer Bound
4:20
Electron Cloud Model (Probability Model)
4:46
Electron Only Has A Probability of Being Located in Certain Regions Surrounding the Nucleus
4:53
Electron Orbitals Are Probability Regions
4:58
Atomic Spectra
5:16
Atoms Can Only Emit Certain Frequencies of Photons
5:19
Electrons Can Only Absorb Photons With Energy Equal to the Difference in Energy Levels
5:34
This Leads to Unique Atomic Spectra of Emitted and Absorbed Radiation for Each Element
5:37
Incandescence Emits a Continuous Energy
5:43
If All Colors of Light Are Incident Upon a Cold Gas, The Gas Only Absorbs Frequencies Corresponding to Photon Energies Equal to the Difference Between the Gas's Atomic Energy Levels
6:16
Continuous Spectrum
6:42
Absorption Spectrum
6:50
Emission Spectrum
7:08
X-Rays
7:36
The Photoelectric Effect in Reverse
7:38
Electrons Are Accelerated Through a Large Potential Difference and Collide with a Molybdenum or Platinum Plate
7:53
Example 1: Electron in Hydrogen Atom
8:24
Example 2: EM Emission in Hydrogen
10:05
Example 3: Photon Frequencies
11:30
Example 4: Bright-Line Spectrum
12:24
Example 5: Gas Analysis
13:08
Nuclear Physics

15m 47s

Intro
0:00
Objectives
0:08
The Nucleus
0:33
Protons Have a Charge or +1 e
0:39
Neutrons Are Neutral (0 Charge)
0:42
Held Together by the Strong Nuclear Force
0:43
Example 1: Deconstructing an Atom
1:20
Mass-Energy Equivalence
2:06
Mass is a Measure of How Much Energy an Object Contains
2:16
Universal Conservation of Laws
2:31
Nuclear Binding Energy
2:53
A Strong Nuclear Force Holds Nucleons Together
3:04
Mass of the Individual Constituents is Greater Than the Mass of the Combined Nucleus
3:19
Binding Energy of the Nucleus
3:32
Mass Defect
3:37
Nuclear Decay
4:30
Alpha Decay
4:42
Beta Decay
5:09
Gamma Decay
5:46
Fission
6:40
The Splitting of a Nucleus Into Two or More Nuclei
6:42
For Larger Nuclei, the Mass of Original Nucleus is Greater Than the Sum of the Mass of the Products When Split
6:47
Fusion
8:14
The Process of Combining Two Or More Smaller Nuclei Into a Larger Nucleus
8:15
This Fuels Our Sun and Stars
8:28
Basis of Hydrogen Bomb
8:31
Forces in the Universe
9:00
Strong Nuclear Force
9:06
Electromagnetic Force
9:13
Weak Nuclear Force
9:22
Gravitational Force
9:27
Example 2: Deuterium Nucleus
9:39
Example 3: Particle Accelerator
10:24
Example 4: Tritium Formation
12:03
Example 5: Beta Decay
13:02
Example 6: Gamma Decay
14:15
Example 7: Annihilation
14:39
Section 8: Sample AP Exams
AP Practice Exam: Multiple Choice, Part 1

38m 1s

Intro
0:00
Problem 1
1:33
Problem 2
1:57
Problem 3
2:50
Problem 4
3:46
Problem 5
4:13
Problem 6
4:41
Problem 7
6:12
Problem 8
6:49
Problem 9
7:49
Problem 10
9:31
Problem 11
10:08
Problem 12
11:03
Problem 13
11:30
Problem 14
12:28
Problem 15
14:04
Problem 16
15:05
Problem 17
15:55
Problem 18
17:06
Problem 19
18:43
Problem 20
19:58
Problem 21
22:03
Problem 22
22:49
Problem 23
23:28
Problem 24
24:04
Problem 25
25:07
Problem 26
26:46
Problem 27
28:03
Problem 28
28:49
Problem 29
30:20
Problem 30
31:10
Problem 31
33:03
Problem 32
33:46
Problem 33
34:47
Problem 34
36:07
Problem 35
36:44
AP Practice Exam: Multiple Choice, Part 2

37m 49s

Intro
0:00
Problem 36
0:18
Problem 37
0:42
Problem 38
2:13
Problem 39
4:10
Problem 40
4:47
Problem 41
5:52
Problem 42
7:22
Problem 43
8:16
Problem 44
9:11
Problem 45
9:42
Problem 46
10:56
Problem 47
12:03
Problem 48
13:58
Problem 49
14:49
Problem 50
15:36
Problem 51
15:51
Problem 52
17:18
Problem 53
17:59
Problem 54
19:10
Problem 55
21:27
Problem 56
22:40
Problem 57
23:19
Problem 58
23:50
Problem 59
25:35
Problem 60
26:45
Problem 61
27:57
Problem 62
28:32
Problem 63
29:52
Problem 64
30:27
Problem 65
31:27
Problem 66
32:22
Problem 67
33:18
Problem 68
35:21
Problem 69
36:27
Problem 70
36:46
AP Practice Exam: Free Response, Part 1

16m 53s

Intro
0:00
Question 1
0:23
Question 2
8:55
AP Practice Exam: Free Response, Part 2

9m 20s

Intro
0:00
Question 3
0:14
Question 4
4:34
AP Practice Exam: Free Response, Part 3

18m 12s

Intro
0:00
Question 5
0:15
Question 6
3:29
Question 7
6:18
Question 8
12:53
Section 9: Additional Examples
Metric Estimation

3m 53s

Intro
0:00
Question 1
0:38
Question 2
0:51
Question 3
1:09
Question 4
1:24
Question 5
1:49
Question 6
2:11
Question 7
2:27
Question 8
2:49
Question 9
3:03
Question 10
3:23
Defining Motion

7m 6s

Intro
0:00
Question 1
0:13
Question 2
0:50
Question 3
1:56
Question 4
2:24
Question 5
3:32
Question 6
4:01
Question 7
5:36
Question 8
6:36
Motion Graphs

6m 48s

Intro
0:00
Question 1
0:13
Question 2
2:01
Question 3
3:06
Question 4
3:41
Question 5
4:30
Question 6
5:52
Horizontal Kinematics

8m 16s

Intro
0:00
Question 1
0:19
Question 2
2:19
Question 3
3:16
Question 4
4:36
Question 5
6:43
Free Fall

7m 56s

Intro
0:00
Question 1-4
0:12
Question 5
2:36
Question 6
3:11
Question 7
4:44
Question 8
6:16
Projectile Motion

4m 17s

Intro
0:00
Question 1
0:13
Question 2
0:45
Question 3
1:25
Question 4
2:00
Question 5
2:32
Question 6
3:38
Newton's 1st Law

4m 34s

Intro
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0:15
Question 2
1:02
Question 3
1:50
Question 4
2:04
Question 5
2:26
Question 6
2:54
Question 7
3:11
Question 8
3:29
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3:47
Question 10
4:02
Newton's 2nd Law

5m 40s

Intro
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0:16
Question 2
0:55
Question 3
1:50
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2:40
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3:33
Question 6
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Question 7
4:29
Newton's 3rd Law

3m 44s

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0:17
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0:44
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1:14
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1:51
Question 5
2:11
Question 6
2:29
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Friction

6m 37s

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0:47
Question 3
1:25
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2:26
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3:43
Question 6
4:41
Question 7
5:13
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5:50
Ramps and Inclines

6m 13s

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0:18
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1:01
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2:50
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3:11
Question 5
5:08
Circular Motion

5m 17s

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0:21
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1:01
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2:33
Question 5
3:10
Question 6
3:31
Question 7
3:56
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4:33
Gravity

6m 33s

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0:19
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1:05
Question 3
2:09
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2:53
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3:17
Question 6
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4:41
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5:20
Momentum & Impulse

9m 29s

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7:47
Conservation of Momentum

9m 33s

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2:08
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4:03
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4:10
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8:26
Work & Power

6m 2s

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0:29
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0:55
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1:36
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3:22
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4:18
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Springs

7m 59s

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2:26
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3:37
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4:39
Question 7
5:28
Question 8
5:51
Energy & Energy Conservation

8m 47s

Intro
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1:27
Question 3
1:44
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2:33
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2:44
Question 6
3:33
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Question 8
5:19
Question 9
5:37
Question 10
7:12
Question 11
7:40
Electric Charge

7m 6s

Intro
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Question 1
0:10
Question 2
1:03
Question 3
1:32
Question 4
2:12
Question 5
3:01
Question 6
3:49
Question 7
4:24
Question 8
4:50
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5:32
Question 10
5:55
Question 11
6:26
Coulomb's Law

4m 13s

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0:14
Question 2
0:47
Question 3
1:25
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2:25
Question 5
3:01
Electric Fields & Forces

4m 11s

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0:51
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1:30
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2:19
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3:12
Electric Potential

5m 12s

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0:14
Question 2
0:42
Question 3
1:08
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1:43
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2:22
Question 6
2:49
Question 7
3:14
Question 8
4:02
Electrical Current

6m 54s

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0:42
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2:01
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3:02
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3:52
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4:15
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4:37
Question 8
4:59
Question 9
5:50
Resistance

5m 15s

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0:12
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0:53
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1:44
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2:31
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3:21
Question 6
4:06
Ohm's Law

4m 27s

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0:12
Question 2
0:33
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0:59
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1:32
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1:56
Question 6
2:50
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3:19
Question 8
3:50
Circuit Analysis

6m 36s

Intro
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0:12
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2:16
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2:33
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2:42
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3:18
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5:51
Question 7
6:00
Magnetism

3m 43s

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0:16
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0:31
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0:56
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1:19
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1:35
Question 6
2:36
Question 7
3:03
Wave Basics

4m 21s

Intro
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0:13
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0:36
Question 3
0:47
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1:13
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1:27
Question 6
1:39
Question 7
1:54
Question 8
2:22
Question 9
2:51
Question 10
3:32
Wave Characteristics

5m 33s

Intro
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0:23
Question 2
1:04
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2:01
Question 4
2:50
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3:12
Question 6
3:57
Question 7
4:16
Question 8
4:42
Question 9
4:56
Wave Behaviors

3m 52s

Intro
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0:13
Question 2
0:40
Question 3
1:04
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1:17
Question 5
1:39
Question 6
2:07
Question 7
2:41
Question 8
3:09
Reflection

3m 48s

Intro
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0:12
Question 2
0:50
Question 3
1:29
Question 4
1:46
Question 5
3:08
Refraction

2m 49s

Intro
0:00
Question 1
0:29
Question 5
1:03
Question 6
1:24
Question 7
2:01
Diffraction

2m 34s

Intro
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0:16
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0:31
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0:50
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1:05
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1:37
Question 6
2:04
Electromagnetic Spectrum

7m 6s

Intro
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Question 1
0:24
Question 2
0:39
Question 3
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Question 4
1:51
Question 5
2:03
Question 6
2:58
Question 7
3:14
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3:52
Question 9
4:30
Question 10
5:04
Question 11
6:01
Question 12
6:16
Wave-Particle Duality

5m 30s

Intro
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Question 1
0:15
Question 2
0:34
Question 3
0:53
Question 4
1:54
Question 5
2:16
Question 6
2:27
Question 7
2:42
Question 8
2:59
Question 9
3:45
Question 10
4:13
Question 11
4:33
Energy Levels

8m 13s

Intro
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Question 1
0:25
Question 2
1:18
Question 3
1:43
Question 4
2:08
Question 5
3:17
Question 6
3:54
Question 7
4:40
Question 8
5:15
Question 9
5:54
Question 10
6:41
Question 11
7:14
Mass-Energy Equivalence

8m 15s

Intro
0:00
Question 1
0:19
Question 2
1:02
Question 3
1:37
Question 4
2:17
Question 5
2:55
Question 6
3:32
Question 7
4:13
Question 8
5:04
Question 9
5:29
Question 10
5:58
Question 11
6:48
Question 12
7:39
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Lecture Comments (17)

1 answer

Last reply by: Professor Dan Fullerton
Mon Feb 12, 2024 5:48 AM

Post by Rajesh Iyer on February 11 at 10:37:12 PM

Why does the wave not fully go through the medium crossssing?

2 answers

Last reply by: Peter Ke
Thu Jul 7, 2016 4:34 PM

Post by Peter Ke on July 6, 2016

For example 10 at 30:22, you said c/f is constant thus n_1(lamda) = n_2(lamda).
I understand that f, frequency, is always constant but why c, the speed of light is also constant? Because the velocity for light changes as it enters a new medium so how c is constant?

1 answer

Last reply by: Professor Dan Fullerton
Fri Apr 1, 2016 1:19 PM

Post by Sarmad Khokhar on April 1, 2016

How did you decide on the direction of the arrow in 16:20 when new real image formed ?

1 answer

Last reply by: Professor Dan Fullerton
Fri May 1, 2015 2:11 PM

Post by BRAD POOLE on May 1, 2015

Isn't n1 lambda1 = n2 lambda2 just the thin film interference equation?  And also when you have 1 phase change that is m=1/2, 2 phase changes is m=1, 3 phase changes is m=3/2, 4 phase changes is m=2 and so on?

1 answer

Last reply by: Professor Dan Fullerton
Wed Jul 2, 2014 1:21 PM

Post by Lalit Shorey on July 1, 2014

On example 8, why didn't you choose D?

1 answer

Last reply by: Professor Dan Fullerton
Sun Mar 16, 2014 7:10 AM

Post by Emmil Zarrugh on March 16, 2014

At 27:12, you describe the image by saying it's upright, real, and reduced. However, wouldn't it be virtual, since it is the image of a concave lens?

1 answer

Last reply by: Professor Dan Fullerton
Sat Nov 30, 2013 7:45 PM

Post by Rob Escalera on November 30, 2013

At about 7:10 you said that if you go from a lower to higher index the light ray will bend toward the normal. The you said if you go from a lower to a higher index, it will bend away from the normal. That is the same thing with two contradictory results.

1 answer

Last reply by: Professor Dan Fullerton
Sat Aug 10, 2013 6:26 AM

Post by Ikze Cho on August 10, 2013

If colour doesn't change when entering a new medium, how does a prism change white light into the colours of the rainbow?

Refraction & Lenses

  • As a wave enters a new medium, the speed and wavelength of the wave may change, but the frequency remains constant.
  • The bending of a wave as it enters a new medium due to its change of speed is known as refraction.
  • The index of refraction is a measure of how much an EM wave slows down in a material. n=c/v
  • Snell's Law states that n1sinθ1=n2sinθ2, where all angles are measured to the normal.
  • Index of refraction varies with frequency. This effect is known as dispersion and is responsible for the separation of light through prisms.
  • Total Internal Reflection occurs when the angle of refraction reaches 90 degrees. The incident angle at which this occurs is known as the critical angle. TIR only occurs when light moves from a high-index to a low-index medium.
  • Lens equation states that 1/f = 1/d0 + 1/di
  • Ray tracing is a method of analyzing the effect of optical systems. Rays parallel to the principal axis are refracted/reflected through the focal point. A ray drawn through the center of a lens passes through the lens unbent. A ray drawn to the center of a spherical mirror on the principal axis is reflected at the same angle as its incidence.
  • In optical systems with more than one element, find the image of the first object, and use that as the object for the next element, and so on.
  • Light incident upon a thin film may interfere with itself. For maximum interference, 2t=mλ, where the wavelength is the wavelength in the film. Phase changes occur at every point of reflection from low-index to high-index materials. For maximum constructive interference, m=1,2,3,… for an even number of phase changes, and m=1/2, 3/2, 5/2, … for an odd number of phase changes.

Refraction & Lenses

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  1. Intro
    • Objectives
      • Refraction
      • Marching Band Analogy
        • Index of Refraction
        • Indices of Refraction
          • Dispersion
          • Example 1: Determining n
            • Example 2: Light in Diamond and Crown Glass
              • Snell's Law
              • Example 3: Angle of Refraction
                • Example 4: Changes with Refraction
                  • Total Internal Reflection
                  • Applications of TIR
                    • Example 5: Critical Angle of Water
                      • Thin Lenses
                      • Convex Lenses
                      • Example 6: Converging Lens Image
                        • Example 7: Image Distance of Convex Lens
                          • Concave Lenses
                          • Example 8: Light Ray Thought a Lens
                            • Systems of Optical Elements
                            • Example 9: Lens and Mirrors
                              • Thin Film Interference
                              • Example 10: Thin Film Interference
                                • Example 11: Wavelength in Diamond
                                  • Example 12: Light Incident on Crown Glass
                                    • Example 13: Real Image from Convex Lens
                                      • Example 14: Diverging Lens
                                        • Example 15: Creating Enlarged, Real Images
                                          • Example 16: Image from a Converging Lens
                                            • Example 17: Converging Lens System
                                              • Intro 0:00
                                              • Objectives 0:09
                                              • Refraction 0:42
                                                • When a Wave Reaches a Boundary Between Media, Part of the Wave is Reflected and Part of the Wave Enters the New Medium
                                                • Wavelength Must Change If the Wave's Speed Changes
                                                • Refraction is When This Causes The Wave to Bend as It Enters the New Medium
                                              • Marching Band Analogy 1:22
                                              • Index of Refraction 2:37
                                                • Measure of How Much Light Slows Down in a Material
                                                • Ratio of the Speed of an EM Wave in a Vacuum to the Speed of an EM Wave in Another Material is Known as Index of Refraction
                                              • Indices of Refraction 3:21
                                              • Dispersion 4:01
                                                • White Light is Refracted Twice in Prism
                                                • Index of Refraction of the Prism Material Varies Slightly with Respect to Frequency
                                              • Example 1: Determining n 5:14
                                              • Example 2: Light in Diamond and Crown Glass 5:55
                                              • Snell's Law 6:24
                                                • The Amount of a Light Wave Bends As It Enters a New Medium is Given by the Law of Refraction
                                                • Light Bends Toward the Normal as it Enters a Material With a Higher n
                                                • Light Bends Toward the Normal as it Enters a Material With a Lower n
                                              • Example 3: Angle of Refraction 7:42
                                              • Example 4: Changes with Refraction 9:31
                                              • Total Internal Reflection 10:10
                                                • When the Angle of Refraction Reaches 90 Degrees
                                                • Critical Angle
                                                • Total Internal Reflection
                                              • Applications of TIR 12:13
                                              • Example 5: Critical Angle of Water 13:17
                                              • Thin Lenses 14:15
                                                • Convex Lenses
                                                • Concave Lenses
                                              • Convex Lenses 15:24
                                                • Rays Parallel to the Principal Axis are Refracted Through the Far Focal Point of the Lens
                                                • A Ray Drawn From the Object Through the Center of the Lens Passes Through the Center of the Lens Unbent
                                              • Example 6: Converging Lens Image 16:46
                                              • Example 7: Image Distance of Convex Lens 17:18
                                              • Concave Lenses 18:21
                                                • Rays From the Object Parallel to the Principal Axis Are Refracted Away from the Principal Axis on a Line from the Near Focal Point Through the Point Where the Ray Intercepts the Center of the Lens
                                                • Concave Lenses Produce Upright, Virtual, Reduced Images
                                              • Example 8: Light Ray Thought a Lens 20:36
                                              • Systems of Optical Elements 21:05
                                                • Find the Image of the First Optical Elements and Utilize It as the Object of the Second Optical Element
                                              • Example 9: Lens and Mirrors 21:35
                                              • Thin Film Interference 27:22
                                                • When Light is Incident Upon a Thin Film, Some Light is Reflected and Some is Transmitted Into the Film
                                                • If the Transmitted Light is Again Reflected, It Travels Back Out of the Film and Can Interfere
                                                • Phase Change for Every Reflection from Low-Index to High-Index
                                              • Example 10: Thin Film Interference 28:41
                                              • Example 11: Wavelength in Diamond 32:07
                                              • Example 12: Light Incident on Crown Glass 33:57
                                              • Example 13: Real Image from Convex Lens 34:44
                                              • Example 14: Diverging Lens 35:45
                                              • Example 15: Creating Enlarged, Real Images 36:22
                                              • Example 16: Image from a Converging Lens 36:48
                                              • Example 17: Converging Lens System 37:50

                                              Transcription: Refraction & Lenses

                                              Hi everyone and welcome back to Educator.com.0000

                                              I am Dan Fullerton and today we are going to be talking about refraction and lenses as we continue our study of optics.0003

                                              Our goals for this lesson are going to be to calculate the wavelength and velocity of an electromagnetic wave in a medium with a specific index of refraction, to utilize Snell's Law to determine the angle of refraction of an incident ray, determine the critical angle for a ray moving from a high-index material to a lower-index material...0009

                                              ...analyzing system of lenses and mirrors with respect to object and image distances, heights, magnification and image type; and analyzing the behavior of light incident upon thin, optically transparent films.0027

                                              Refraction -- When a wave reaches a boundary between media, part of the wave is reflected and part enters the new medium.0042

                                              As the wave enters the new medium the speed of the wave can change but frequency, again, remains constant.0049

                                              If the speed is changing and frequency is constant, the wavelength must also change.0055

                                              Now the front of a wave has some actual width, so if the wave enters the new medium at an angle other than 90 degrees, not all of that wave front enters the new medium at the same time.0062

                                              When that happens, you actually get some bending of the wave as it enters the new medium, and that is known as 'refraction'.0072

                                              I like to use a marching band analogy to help understand why waves bend when they enter a new medium where their speed is changing.0083

                                              Imagine you are in a line in a marching band connected by all your bandmates by a short string or maybe your arms are linked.0090

                                              You march down the field in unison until you arrive at a mud pit, so here is the line of your band, you are moving down the field, and then you are going to find this mud pit.0098

                                              Now the band members who reach the mud pit first, they have to slow down before the band members who reach it later, but you are all tied together.0113

                                              As this happens, the folks on this side of the line gets slowed down first, the rest of the line keeps moving at the same speed until they hit the mud pit, and you are actually going to get a shifting because this side slows down before this side.0121

                                              Well now the direction of the band is shifted until you come back out of it again, and then maybe it shifts a little bit more depending on who comes out first and speeds up first.0136

                                              You get this overall shifting in direction due to the speed changing at different points on the wave front, all at slightly different times.0148

                                              Now the index of refraction is a measure of how much light slows down in a material.0158

                                              Bigger indices of refraction (n) indicates slower velocities.0163

                                              In vacuum and air, all electromagnetic waves travel at the same speed (c) 3 × 108 m/s, which corresponds to an index of refraction of 1.0167

                                              In other materials, the electromagnetic waves slow down by some amount.0178

                                              Now the ratio of the speed of an electromagnetic wave in a vacuum to the speed in another material is the index of refraction or the index of refraction is the speed in the vacuum divided by that speed in the new material; and typically, you would look up the index of refraction for some material.0182

                                              Here we have a table of indices of refraction and they are given at a specific frequency 5.09 × 1014 Hz, because to a small extent index of refraction is a little bit of a function of frequency of the electromagnetic radiation.0201

                                              Air and vacuum are 1, corn oil (1.47) and light slows down a little more, diamond (2.42) is a very high index of refraction -- the light slows down a lot in diamond -- and you can see a bunch of other materials here, too.0217

                                              From air (1.0) the smallest index of refraction, and the highest on the table -- the slowest material -- is diamond here.0232

                                              Now not only this index of refraction depend upon the medium, it also has a slight variation with frequency.0242

                                              That frequency dependence is typically relatively small but it can be very useful.0247

                                              Dispersion is the effect that you get because you have a slightly different index of refraction based on frequency.0252

                                              This is what is responsible for the behavior of prisms.0260

                                              If you have white light that is coming upon a prism -- well when it comes in there and you have white light that is all the colors of the rainbow, all the frequencies of visible light, it is bent once upon entering and it is bent again upon leaving.0263

                                              It has two areas where it is going to be refracted -- incoming and exiting point of the prism.0275

                                              Now at each of those points you have a slightly different index of refraction, a slightly different speed in that material for the different colors, therefore they are going to be bent slightly different amounts.0281

                                              As the light enters you get a slight shift in the paths based on color and as it leaves you get another shift in the paths due to color.0291

                                              Therefore, because of that change in index of refraction, you actually can see the light spreading out into the spectrum.0301

                                              You have that red, orange, yellow, green, blue, indigo, violet.0308

                                              How do you determine index of refraction -- our first example.0314

                                              Let us say a light ray traveling in air enters a second medium and its speed slows down to 1.71 × 108 m/s.0318

                                              Find the index of refraction of this second medium.0325

                                              Well index of refraction is the ratio of the speed of light in a vacuum to the speed of light in that new medium, so that is going to be 3 × 108 m/s over 1.71 × 108 m/s.0329

                                              So our index of refraction in this problem would be right about 1.75.0344

                                              Let us move on to another one. We have light in diamond and crown glass.0353

                                              In which way does blue light change as it travels from diamond -- and from our table index of refraction of diamond is 2.42 -- into crown class where n = 1.52.0357

                                              Well you are going from a higher index to a lower index.0370

                                              Lower indexes imply faster media, so its speed must be increasing.0374

                                              Let us talk a little bit more about the bending of light.0385

                                              We can analyze that analytically using Snell's Law in the quantifiable sense.0387

                                              The amount a light wave bends as it enters a new medium is given by the Law of Refraction which we call Snell's Law, and what it says is that the first index of medium 1 times the sine of the incident angle θ1 is equal to the index of refraction of the second medium times the refracted angle sin(θ2).0392

                                              Always measuring these angles to the normal, we have θ1 (incident angle), θ2 (refracted angle), medium 1 has some index 1, medium 2 has some index 2.0416

                                              Now if you are going from a low to a higher index material, the light ray is going to bend toward the normal.0427

                                              And if you go from a low index to a high index, then it is going to bend away from the normal as it enters that faster medium.0433

                                              The key here is to always measure angles in optics to the normal.0441

                                              What you do not want to do is take this angle to the interface, or this angle; it is always measured to the normal to that interface.0452

                                              All right. An example with the angle of refraction.0463

                                              A ray of light in air is incident at an angle of 40 degrees on an air crown glass interface as shown.0466

                                              What is the angle of refraction for this light ray?0473

                                              Well over here, we are at air so the index is 1; we know that the incident angle is 40 degrees and we are going to a higher index material -- crown glass where n2 is 1.52 -- so it is going to bend toward the normal as it enter the new medium.0476

                                              We are going from a lower index to a higher index, and this angle we will call θ2.0496

                                              We can use Snell's Law to figure out what is going on -- n1 sin(θ1) = n2 sin(θ2), and we want the angle of refraction or θ2 so I would say then that sin(θ2) = n1/n2 sin(θ1).0504

                                              If the sin(θ2) is equal to this, to get just θ2, θ2 will be the inverse sine of n1/n2 sin(θ1).0527

                                              Or as I substitute in my variables, sin(θ2) equals the inverse sine of n1 (1) over n2 -- 1.52 sin(θ1) (40 degrees), therefore θ2 equals right around 25 degrees.0541

                                              So that angle must be 25 degrees -- an application of Snell's Law.0564

                                              When a light wave enters a new medium and is refracted, there must be a change in the light wave's what?0572

                                              And we are going to choose everything that applies here.0576

                                              Color? -- No, that is a function of frequency and frequency does not change when you enter the new medium.0579

                                              Frequency? -- We know that is not it as it does not change when you enter a new medium.0586

                                              Period? -- No, not so much. It is 1/frequency and frequency is constant.0590

                                              Speed? -- Yes, speed can change and if V = F(λ), if F is constant, and speed is changing, then λ has to change as well -- wavelength.0594

                                              So D and E must be our correct answers here.0605

                                              All right. Let us talk about total internal reflection.0612

                                              When light passes from a high index or a slower material to a low index or faster material, the light bends away from the normal, but when that angle of refraction reaches 90 degrees, that cannot get into that new interface anymore.0615

                                              The refracted way would travel right on the boundary between the surfaces -- that does not make any sense.0628

                                              That is going to occur at an angle of incidence that we are going to call the critical angle θc.0634

                                              When that happens for all angles of incidence greater than that, what you are going to have is instead of refraction into the new media, you are going to get that light by reflecting back into the original media.0640

                                              We call that total internal reflection (TIR), and if we want to analyze that by the Law of Reflection, then n1 sin(θ1) = n2 sin(θ2), but this occurs when θ2 is 90 degrees.0651

                                              That is when you are going to get our critical angle, so if I rewrite this as n2 sin(90 degrees), I can solve to find the θ1 -- n1 sin(θ1) = n2 sin(90 degrees).0672

                                              If I want sin(θ1), that is going to be n2/n1 sin(90 degrees), but the sin(90 degrees) is 1, therefore θ1 is going to be the inverse sine of just n2/n1.0691

                                              That is the angle, the incoming angle, at which you are going to start to see total internal reflection, so that is why that is called the critical angle (θc), which is where that formula comes from.0707

                                              The critical angle is the inverse sine of n2/n1, and it only occurs when you are going from a higher index or a slower material to a lower index or faster material.0720

                                              Some applications of total internal reflection are fiber-optics -- light bending through a transparent media and it keeps reflecting down that media and not going out, a great way to transfer signals.0733

                                              Sparkly diamonds -- diamonds are actually cut in such a manner where they want to enhance total internal reflection or something like that...0748

                                              ...so that what happens is when the light ray comes in, hopefully as it comes in, it keeps reflecting internally until it comes out the top where you see that nice, bright sparkle -- that is where that sparkle comes from.0757

                                              It is useful in binoculars, and you can even see it as the mirror effect when you are looking up from underwater from a shallow angle.0771

                                              As you see in this image here -- you are at a very shallow angle -- the turtles here -- you see the image of the turtle in the water as you are going from a higher index of water (1.33) to air (1) -- you are getting total internal reflection; you cannot see out of the water, so all you see is the reflection there.0777

                                              So that is total internal reflection.0793

                                              Let us take a look at the critical angle of water.0798

                                              Determine that critical angle for a light ray exiting from water into air.0801

                                              Well, the critical angle occurs when n1 sin(θ1) = n2 sin(90 degrees), where the sin(90 degrees) we know is going to be 1, or 1.33 sine of our critical angle (θc) is going to be equal to our n2...0804

                                              ...which is air times sin(90), which is 1, so n1 × 1 or 1 × 1 = 1.0823

                                              Therefore our critical angle is going to be the inverse sine of 1/1.33 or an angle of about 48 degrees; it is the critical angle for a light ray exiting from water into air.0830

                                              Any angles greater than 48 degrees, you are going to get total internal reflection.0848

                                              Let us talk about thin lenses for a couple of minutes.0856

                                              Thin lenses function based on the principle of refraction, whether we have convex lenses, or converging lenses, or concave lenses which are diverging lenses.0859

                                              The convex lenses kind of look like that and diverging lenses typically have that rough shape.0868

                                              Now they can have some variations there but that is the general idea.0874

                                              You can also make lenses with mirrors, though they are typically a lot larger, more complex and a lot more expensive.0877

                                              The advantage they have is you do not have any dispersion effects; you do not have what is known as chromatic aberration, which is where you get a shift in the focal point based on the frequency of the light going through the lens because mirrors operate on reflection...0885

                                              ...so you do not have to worry about the index of refraction varying as a function of frequency.0901

                                              Now similar rules for ray tracing applies what we had when we were talking about mirrors, and the lens equation is still applicable.0908

                                              1/F = 1/object distance (do) + 1/image distance (di), or 'If I do, I die'.0915

                                              All right, let us take a look at a basic convex lens.0924

                                              Rays parallel to the principal axis are refracted through the far focal point of the lens, so if I draw a ray that is parallel to the principal axis -- something like that -- it gets refracted through the far focal point.0927

                                              A ray drawn from the object through the center of the lens passes through the center of the lens unbent, so we could draw that one as well.0952

                                              And finally, a ray that travels from the object through the focal point, through the near focal point gets refracted parallel to the principal axis.0969

                                              Notice again they all meet at the same point which is where you must have your image -- something like that -- and in this case, this would be a real image; it is reduced in size and it is inverted.0986

                                              In the example below, the diagram shows an arrow placed in front of a converging lens.1007

                                              Determine whether the image is real or virtual, erect or inverted.1012

                                              Well we are going to draw the image over here where we see the light rays converging, so it would look something like that, and based on that it is pretty easy to see that that is going to be a real image because we have the image where the light rays are actually converging and it is inverted.1016

                                              Another example -- An object is located .15 m from a convex lens that has a focal length of .1 m.1039

                                              How far from the lens is the image formed?1046

                                              Well our object distance is .15 m, our focal length is .1 m, and we do not know our image distance.1049

                                              So I will use our lens equation, 1/F = 1/do + 1/di or rearrange this to find that 1/di is 1/focal length - 1/do, which is going to be 1/.1 m - 1/.15 m...1060

                                              ...therefore 1/di is going to be equal to 3.33 or the image distance is 1/3.33 or about 0.3 m.1080

                                              All right. How about a concave lens or a diverging lens?1100

                                              Well in this case, rays from the object parallel to the principal axis are refracted away from the principal axis on a line from the near focal point through the point where the ray intercepts the center of the lens.1104

                                              Let us draw that right away and we will do that in blue.1115

                                              So a ray from the object parallel to the principal axis -- we will start there.1119

                                              What happens here is it is going to be refracted but it is going to diverge, therefore in order to figure out where it is going, we have to draw a virtual line from our focal point in order to figure out the rest of the ray's path.1129

                                              It is going to diverge; it is going to go up to that direction following the line from the focal point through there.1147

                                              Any ray from the object through a focal point is refracted parallel to the principal axis, so if we have one that is going through the focal point, we could have through the focal point and it will get refracted back as if it were going through the principal axis.1155

                                              In the concave lenses, any ray from the object that goes right through the center of the lens also is going to go through unfettered.1169

                                              Let us draw the one through the center of the lens too, that is probably our easiest ray to draw here to give us our second one to figure out where they are going to converge and where we will get our image.1177

                                              So a ray right through the center of the lens continues, and notice here that these two diverge; they are never going to meet, which means we are going to have to come back here to figure out our virtual image.1190

                                              They are crossing right here, therefore that is where we are going to get our image.1204

                                              It is going to be reduced, it is going to be at an image distance (di) about like that, so there is our image.1210

                                              Concave lenses -- you usually have to draw some of those virtual lines to figure out where you are going to get your image.1222

                                              It is upright, virtual and reduced.1229

                                              Which ray best represents the path of light ray (R) after it passes through the lens?1237

                                              Well this is a diverging lens, so as it comes through here, which way is it going to go?1242

                                              If we follow this back, we draw the line that would go through the near focal point, so our correct answer must be A.1250

                                              Now when you have systems of optical elements, you will oftentimes have more than one lens or maybe lenses and mirrors and so on.1266

                                              In those situations, all you do is you do it piece-wise -- find the image of the first optical element first and utilize it as the object of the second optical element.1273

                                              Use the image of the second optical element as the object for the third optical element, and so on.1282

                                              Continue to analyze all these until you have transversed the entire optical path.1289

                                              How does that look in practice?1295

                                              Well we will do an example with it. This may get a little bit complex to draw, but we will see what we can do here.1297

                                              An object sits 50 cm from a convex lens of focal length (F1 = 20 cm) and a concave mirror of focal length (F2 = 14 cm) sits 60 m behind the lens.1302

                                              Determine the position, type and size of the image.1314

                                              The first thing I think I am going to do is I am going to ray trace this just to get an idea of what I am looking at.1318

                                              For our convex lens, I am going to start by drawing our ray parallel to the principal axis and that should be refracted through the far focal point -- something like that.1324

                                              Now I can draw my second ray -- I will draw that right through the center of the lens just because that is a really easy one to do.1344

                                              That is just a straight line right through the center of the lens, and it looks like I am going to get my image right where those two meet, so I do not need the rest of that there.1350

                                              I will draw my image right there. There is my image from my convex or converging lens.1360

                                              That is going to be the object for the concave mirror.1370

                                              So now to do the concave mirror, I will switch colors here, but I know that a ray going through the focal point is going to be reflected back parallel to the principal axis, so I will try drawing that next.1374

                                              So we have something like that, and then it should come back parallel to the axis.1390

                                              Now the other one we could draw is if we go directly through the center of the lens, we will come back off at the exact same angle.1399

                                              I will do my second ray like that and it should come off at the same angle which will be -- if I draw that correctly, maybe right about there.1407

                                              That should be at least reasonably close.1427

                                              Now I have these two rays that cross over here so I can draw my image from the mirror right there.1429

                                              I used the image of the first lens as the object for the second.1440

                                              When I do this -- as I go through the math, I should predict that I am probably going to get an upright and real image.1445

                                              All right, let us analyze this with some numbers.1451

                                              For the convex lens, we know 1/F = 1/do + 1/di, therefore our focal length is .2 m so 1/.2 = 1/.5 m = 50 cm + 1/di...1456

                                              ...and if I solve for that I get that di = .333 m, so my image distance here must be .333 m.1478

                                              That is going to be my object distance -- well 60 cm minus that will be my object distance for the mirror.1495

                                              That is going to be .267, so as I analyze the mirror now I have 1/F = 1/do + 1/di...1504

                                              ...where my focal length now is 1/.14 = 1/60 cm - [33.3] m (.267) + 1/di...1518

                                              ...therefore my image distance is going to be .295 m for my mirror.1535

                                              That means that for my mirror -- let us see -- that distance there must be our .295 m.1544

                                              We have now located our image specifically, so let us see about magnification.1554

                                              Magnification due to our convex lens, well that is -di/do which is going to be -.333 over our object distance, which was .5 or -.666.1559

                                              And magnification for our mirror (m2), also -di/do, but now we need to use the mirror's image and object distances, which is -.295 m for our image distance minus the object distance, which was .267 or -1.1.1575

                                              My total magnification is going to be the magnification of the first element times the magnification of the second element.1599

                                              That is going to be m1 × m2, which will be -.666 × -1.1 = .7326.1606

                                              Again we have a positive number; it is an upright image; it is real and it is slightly reduced, which we expected based on our ray tracing exercise.1627

                                              All right. Let us talk a little bit about thin film interference.1642

                                              When light is incident upon a thin film, some light is reflected and some is transmitted into the film.1645

                                              If the transmitted light is again reflected, it travels back out of the film and it can interfere with itself.1650

                                              If we have light coming here into an interface, part is reflected, part is refracted or transmitted into the film, it travels some distance down and back up, and it can then interfere with itself.1656

                                              How far has it traveled? It has traveled twice the thickness of the film, down and then back.1667

                                              If we want to find out where we have this interference, the total distance it travels, then (2T) is going to be equal to the order (m) times the wavelength of that ray in the film -- not the original wavelength, but the wavelength in the film.1674

                                              Now the only thing that we have to keep in mind here is that there is a little trick to these.1689

                                              As we get a phase change, things switch -- every reflection from low index to high index materials.1693

                                              If you have an even number of phase changes, count all your phase changes and if you have an even number you use m = 1, 2, 3, and so on.1701

                                              If you have an odd number of phase changes, you use 1/2, 3/2, 5/2 and so on.1709

                                              Again it sounds kind of complicated, but it is a lot easier to deal with when you actually see it in practice with an example, so let us do that.1715

                                              Light is incident in air perpendicular to a thin film of glycerol on top of water.1723

                                              What minimum thickness of glycerol gives the reflected light a green, 532 nanometer green color?1728

                                              As we do this, we realize we have an incident light ray, part is going to be reflected, part is going to be transmitted and then it is going to come back out traveling this distance of 2 × T.1736

                                              So first thing I am going to do is count the phase changes. Where do we go from low to high index?1748

                                              And I see one spot right there where we go from 1 to 1.47, the only place where we are talking about having a phase change.1755

                                              We have one of those, therefore when we use our (m), we are going to have to use m = 1/2.1764

                                              Next up is let us see if we can figure out what the wavelength is going to be in the film.1774

                                              We know the wavelength up here is 532 nanometers, but we want to know the wavelength in the glycerol.1779

                                              To do that I am going to go back to my wave equation V = F(λ), but we are talking about light where N = C/V, so I could write that V = C/N and replace velocity with C/N = F(λ).1785

                                              Now I am just going to rearrange this to get all the constants on the same side.1803

                                              Frequency is a constant and so is C, so I will write this as C/F = N(λ).1807

                                              All that is a constant so anywhere in this, these different materials, N(λ) must be the same.1817

                                              So I am going to write that N1(λ)1 = N2(λ)2, where this is medium1 and that is medium2.1822

                                              If I then solve for λ2, the wavelength in the glycerol, that implies that λ2 = N1(λ)1/N2 or λ2 = N1 (1) × λ1 (532 nanometers)/N2 (1.47)...1832

                                              ...or I will get 362 nanometers as the wavelength in the glycerol.1857

                                              Well now finally, let us go figure out what that thickness has to be for the interference that will give us that green color.1864

                                              All right. To do that, 2T = m(λ).1872

                                              In this case we know m = 1/2, because we are looking for the minimum thickness and we have an odd number of phase changes (1), so m = 1/2 and the λ in the film, the wavelength, is 362 nanometers.1878

                                              Therefore, T = m (1/2) × wavelength (362 nanometers) and I have to divide by 2 to get the 2 out of there, or 1/4 of 362 nanometers which is about 90.5 nanometers.1895

                                              So what minimum thickness of glycerol gives the reflected light a green color? 90.5 nanometers of glycerol.1916

                                              Let us take a look at a problem where we are looking for the wavelength of light in diamond.1928

                                              A beam of monochromatic light has a wavelength of 5.89 × 10 -7 m in there. Find its wavelength in diamond.1932

                                              Let us start by talking about the index of the first material in air, which is 1, and the wavelength in air is 5.89 × 10-7 m.1941

                                              The index of diamond (N2) -- to look up on a table, that is 2.42 and we are trying to find what it's new wavelength is.1954

                                              We know that N = C/V and if V = F(λ), we could write this as N = C/F(λ) and again, what I am going to do is I am going to arrange these so I get all the constants on the same side for C/F = N(λ).1966

                                              If those are constant then N(λ) must be the same anywhere in the problem and at any medium.1985

                                              So I could write then that N1(λ)1 = N2(λ)2.1990

                                              Let us just solve for λ2 then and our wavelength in diamond is N1/N2(λ)1.1997

                                              N1 = 1, N2 = 2.42 and λ1 = 5.89 × 10-7 m, which gives me an answer of about 2.43 × 10-7 m, or 243 nanometers.2007

                                              The wavelength has gotten considerably shorter in the diamond, which we would expect because it is going slower.2029

                                              All right. Which diagram best represents the behavior of a ray of monochromatic light in air incident on a block of crown glass?2038

                                              As we look at this one, we know that when light strikes a surface we are going to have part of the ray reflected and part refracted.2048

                                              Here it is all refracted, here it looks like it is all reflected and at a goofy angle -- that is just off -- and here it is being refracted in two different directions in the wrong way, so the correct answer here must be Number 4.2056

                                              We have reflection following the Law of Reflection and we are also bending toward the normal as we go into a higher index material, parts refracted and parts reflected, so 4 is our best answer.2071

                                              A convex lens forms a real image that is four times larger than the object. If the image is located .16 m from the lens, what is the object distance?2085

                                              Well we know that the magnification must be 4 and the image is located .16 m from the lens.2095

                                              It is a real image; it is a convex lens and that is going to tell us that the image distance is going to have to be less than 0 -- there is the trick there.2103

                                              So if it is located .16 m from the lens that means di = -.16 m and the magnification equation: m = -di/do...2111

                                              ...therefore do = -di/m which will be -.16/4 or 0.04 m.2127

                                              All right, an example with a diverging lens.2145

                                              In the diagram below, parallel light rays in air diverge as a result of interacting with an optical device. 2154 What could that device be?2148

                                              Well a convex glass lens is converging -- that is not it.2156

                                              Rectangular glass block -- that is not going to do much of anything.2161

                                              A plain mirror -- that is not going to give us diverging on the opposite side.2165

                                              It has to be a concave glass lens, something sort of that shape; diverging lens is another name for a concave lens.2169

                                              Let us take a look at which glass lens in air can produce an enlarged, real image of an object.2183

                                              Well if we want an enlarged, real image of an object, we need to have a convex lens.2190

                                              Notice that these three are all diverging lenses, the only answer that will do that is 4.2196

                                              Convex lenses can produce enlarged, real images.2201

                                              The diagram here shows an object placed between 1 and 2 focal lengths from a converging lens.2209

                                              The image of the object produced by the lenses -- well to figure this out let us do a little bit of ray tracing -- if we have an object through a converging lens we know that the ray that is coming in parallel to the principal axis right there, is going to be refracted through the far focal point.2215

                                              We can also do the other easy one and draw the line right through the center of the lens.2236

                                              It looks like if I extend these just a touch further, we are going to get an image somewhere way out here, so there is our image.2244

                                              What do we know about it? Well, we are actually having the light rays converge where our image is, therefore it must be real and it has got to be inverted.2257

                                              What is the answer? A.2266

                                              All right, one last problem.2269

                                              A convex lens has a focal length of 0.8 m and a light ray travels from the object to the lens parallel to the principal axis.2271

                                              Which line best represents the path of the ray after it leaves the lens?2282

                                              If the light ray is coming in parallel, which one is going to show its shape after it leaves the lens?2287

                                              That has to be number 3 there -- coming in parallel you get retracted through the far focal point.2293

                                              How far from the lens is the image formed?2302

                                              To do that, we are going to use our lens equation (1/F = 1/do + 1/di), and that is going to imply then that 1/di = 1/F - 1/do...2305

                                              ...which our image distance is 1/.08 - 1/.1, therefore 1/di = 2.5...2322

                                              ... which gives us an image distance of 1/2.5 or 0.4 m.2340

                                              Which one of these best explains the path of the light through the lens: diffraction, dispersion, reflection or refraction?2349

                                              Well the path of the light through the lens is governed by refraction, the bending of the light and that is why lenses work, so our best answer there is C, refraction.2361

                                              Hopefully that gets you started with refraction and lenses.2373

                                              Next up, we will start talking about modern and nuclear physics.2375

                                              Thanks so much for your time everyone and make it a great day.2379

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