Inspirational Quote

On March 9th, 2016, Drakeson looked out the window and saw someone walking in the rain.  He turned to me and asked, "Is he wearing umbraiya uppatoppa her head?"

It was the best question I've been asked in a long time.

Basic Physics

Occasionally, it is necessary to review some basic physics.  After all, you never know when you'll be in your favorite little black dress, waterproof mascara perfectly applied, cosmopolitan in hand, stumbling in your stilettos into the arms of the future love of your life.  You'll need to talk about something.
My source for this post is: http://www.physicsclassroom.com/.  I fully admit to a lot of plagiarism.

Chapter 1: 4 Kinematic Equations

Scalar - quantity described by magnitude/number
Ex: My baby is 15 pounds.

Vector - quantity that requires magnitude and direction
Ex: My baby is travelling due North at the speed of light.

Distance - scalar quantity; how much ground an object covered
Ex: Drakeson nearly drowned swimming to the other side of the pool and back, a total distance of 50 meters.

Displacement - vector quantity; how far out of place an object is
Ex: He cried when I told him his displacement was 0 meters, but he stopped crying when I told him he could choose which direction to apply the 0 meters to.

Speed - scalar quantity; how fast an object is moving
Average Speed - scalar quantity; (change in distance)/(time)
Instantaneous Speed - scalar quantity; speed at any given instant
Ex: The carousel is going an alarming average speed of 70 mph, and at times, it's instantaneous speed is 85 mph.  Needless to say, I'm not signing that permission slip.

Velocity - vector quantity; the rate at which an object changes position
Average Velocity - (displacement)/(time)

Acceleration - vector quantity; the rate at which an object changes velocity; direction is positive or negative
Average Acceleration - vector quantity; (change in velocity)/(time)
Ex: When the gorgeous damsel in distress, Malinda, was spotted on the railroad tracks, the train conductor put on the breaks, and the train's acceleration was negative 20 miles per hour per second.

Constant Acceleration - occurs when velocity changes by a constant amount
1: A free falling object, or an object falling under the sole influence of gravity, has a constant acceleration of -9.8m/s^2.
2: For objects that have a constant acceleration, the distance travelled is directly proportional to the time squared.

Slope - vector quantity; (change in y)/change in x); "rise over run"; direction is positive or negative
1: The slope of a line in a position-time graph is the velocity of an object, and the slope of a line in a velocity-time graph is the acceleration of an object.

Area in a velocity-time graph - area bound by the line and axes represents displacement.
1: To do this, we calculate the areas of rectangles and triangles.

Gravity - acceleration of gravity, g, is -9.8m/s^2, or 9.8 meters per second per second downwards on and near earth's atmosphere
1: All objects free fall at the same rate of acceleration regardless of mass; free falling objects do not encounter air resistance.
2: The velocity of a falling object after t seconds can be expressed: v = g*t.
3: The distance of a falling object after t seconds can be expressed: d = .5 *g*t^2.
4: If an object is forced upwards at x m/s, then it will travel upwards until at some point its velocity is 0 m/s; when it returns to its starting point, its velocity will be -x m/s.

The Kinematic Equations - four equations that describe objects motion; in the following kinematic equations, d = displacement, t = time, a = acceleration, v_i = initial velocity, and v_f = final velocity.
d = v_i*t + (1/2)*a*t^2
d = (v_i + v_f)/2 *t
v_f  = v_i + a*t
(v_f)^2 = (v_i)^2 + 2*a*d

Chapter 2: Newton's 3 Laws

Newton's First Law of Motion/Law of Inertia - an object at rest stays at rest and an object in motion stays in motion with the same speed and direction, unless acted upon by an unbalanced force

Inertia - tendency to resist changes in motion

Force - vector quantity; push or pull on an object from the interaction with another object; forces are either contact forces or distance forces
1: Contact forces: holding hands, air resistance, metal spring force
2: Distance forces: gravitational forces, electrical forces, magnetic forces

Applied Force - applied by a person or another object
Gravitational Force/Weight - earth, moon, or other massively large object attracts another towards itself
1: F_grav = m*g where m = mass and g = -9.8m/s^2
Normal Force - support force in contact with another stable object; always directed perpendicular to surface
Frictional Force - exerted by a surface as an object moves across it; usually opposes motion
Air Resistance Force - frictional force for objects that travel through air; most noticeable for objects that travel at high speeds or objects with large surface areas
Tension Force - transmitted through string, rope, cable, or wire when it is pulled tight
Spring Force - exerted by a compressed or stretched spring

Newton - standard metric unit of force; N = kg*m/s^2

Weight - force of gravity acting upon an object
Mass - amount of matter that is contained by the object
Ex: George's enormous mass remains the same in water, but his weight changes.

Sliding friction - results when an object slides across a surface
Static friction - results when the surfaces of two objects are at rest relative to one another and a force exists on one of the objects to set it into motion relative to the other object
1: F_{sliding friction} = µ_{sliding friction}*F_norm  where µ_{sliding friction} = the coefficient of sliding friction
2: F_{static friction} ≤ µ_{static friction}*F_norm where µ_{static friction} = the coefficient of static friction
Ex: My beautiful Steinway grand piano is on wheels and sitting on a carpet.  It takes a lot of effort to move it at all due to its static friction, and a lot of effort to keep it moving due to its sliding friction.

Newton's Second Law of Motion - the acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object
1: F_net = m*a, where F_net = the vector sum of all forces, m = mass, and a = acceleration

Terminal Velocity - force of air resistance becomes large enough to balance the force of gravity and the object stops accelerating

Newton's Third Law of Motion - for every action, there is an equal and opposite reaction
1: In other words, forces always come in pairs called action-reaction force pairs.

Equilibrium - all forces that act upon an object are balanced; the object will therefore not accelerate
1: If an object at equilibrium is at rest, it will stay at rest; if in motion, it will stay in motion with the same speed and direction.

Chapter 3: Vectors

Arrow - has a head and a tail; can be used to represent a vector

1: As previously discussed, vectors have magnitude and direction.
2: The magnitude is expressed by arrow length, and is also written near the vector.
3: The direction is expressed by an angle which begins with the vector pointing East and rotating counterclockwise.  Thus, the direction N has an angle of 90, and the direction NW has an angle of 135.

Vector Addition - vectors can be added by the "head to tail" method in which the vectors are placed head to tail; they can also be broken down into horizontal and vertical components through the Pythagorean theorem or an understanding of sine, cosine, and tangent relationships

Resultant Vector - represents the sum, or magnitude and direction, of two or more vectors

Pythagorean Theorem - in a right triangle where c = the length of the hypotenuse and a and b are the lengths of the other two sides, a^2 + b^2 = c^2

SOH CAH TOA - for an acute angle in a right triangle where o = length of opposite side, h = length of hypotenuse, and a = length of adjacent side, the sine of the angle = o/h, the cosine of the angle = a/h, and the tangent of the angle = o/a

Projectile - any object, that once projected, continues in motion by its own inertia and has no force other than gravity acting upon it; travels in a parabolic trajectory

1: For a projectile, there is no horizontal acceleration, and the vertical acceleration is caused by gravity.

2: The horizontal velocity is constant and independent of the object's vertical motion, and the vertical velocity changes by 9.8 m/s each second.

3: It is very important to remember that perpendicular components of motion are independent of each other.

Displacement equations - to understand where a projectile will be after t seconds, there are separate equations for the vertical displacement, y, and the horizontal displacement, x

1: For a horizontally launched projectile, y = .5 *g*t^2

2: For an angled-launched projectile, y = v_y*t + .5*g*t^2, where v_y = the vertical component of the initial velocity

3: For any projectile, x =  v_x*t, where v_x = the horizontal component of the initial velocity

Horizontal and Vertical Kinematic Equations - review of the displacement equations where d = displacement, t = time, a = acceleration, v_i = initial velocity, and v_f = final velocity:

d = v_i*t + (1/2)*a*t^2

v_f  = v_i + a*t

(v_f)^2 = (v_i)^2 + 2*a*d

1: These equations can be used for horizontal motion, where d = horizontal displacement, t = time, a = horizontal acceleration, v_i = initial horizontal velocity, and v_f = final horizontal velocity. These are horizontal kinematic equations.

2: They can also be used for vertical motion, where d = vertical displacement, t = time, a = vertical acceleration, v_i = initial vertical velocity, and v_f = final vertical velocity.  Note that in this case, a = g.  These are vertical kinematic equations.

Chapter 4: Momentum

Momentum - vector quantity; how hard it is to stop something

1: Momentum = mass*velocity, or p = m*v, measured in kg*m/s.

Impulse - vector quantity; force*time

Change in Momentum - mass*(change in velocity)

Impulse Momentum Change Theorem - F*t = m*(change in v), where F = force, t = time, m = mass, and v = velocity

Momentum Conservation - total momentum of two objects before a collision is equal to the total momentum of the objects after the collision

1: If one object collides with another, the forces will be equal in magnitude and opposite in direction.

2: The time the objects will be in contact will be the same.

3: Because we know that impulse = force*time, this means the impulses will be equal in magnitude and opposite in direction.

4: But because impulse = change in momentum, this also means that the momentum changes will be equal in magnitude and opposite in direction.

5: In other words, the momentum lost by one object in a collision is equal and to the momentum gained by the other object.

System - collection of 2 or more objects

Isolated System - system that is free from the influence of a net external force that alters the momentum of the system

1: Such an external force must originate from a source other than the objects of the system and must not be balanced by other forces.

2: If a system is not isolated, the total system momentum is not conserved.

3: Total system momentum is conserved in an explosion occurring in an isolated system.

Chapter 5: Work, Energy, & Power

Work - result of a force causing a displacement on an object

1: W = F*d*cos(a), where F = force, d = displacement, and a = the angle between the force and the displacement.
2: When work is negative, the force hinders the displacement instead of causing it.

Joule - unit of work; 1 Joule = 1 Newton of force causing a displacement of 1 meter, or J = N*m = kg*m^2/s^2

Potential Energy - stored energy of  position possessed by an object
1: Gravitational potential energy is energy stored as the result of its height, and it = m*g*h, where m = mass,  g = -9.8m/s^2, and h - height.
2: Elastic potential energy is energy stored in elastic materials as the result of their stretching or compressing.
3: The potential energy of a spring = .5*k*x^2, where k = the spring constant, and x = the amount of compression relative to the spring's equilibrium position.

Kinetic Energy - energy of motion
1: KE = .5*m*v^2, where KE = kinetic energy, m = mass, and v = velocity
2:  Kinetic Energy is a scalar quantity measured in Joules.

Mechanical Energy - energy acquired by objects upon which work is done
1:  Mechanical energy is possessed by an object due to its motion or position; it can be kinetic or potential.
2:  An object that possesses mechanical energy is able to do work.
3:  The total mechanical energy is the sum of the potential energy and the kinetic energy; or the sum of the gravitational potential energy, the spring potential energy, and the kinetic energy.

Power - rate at which work is done; P = W/t, where P = power, W = work, and t = time.
1:  Also, Power = Work/time = Force*displacement/time = Force*velocity; P = F*v

Watt - standard unit of power; 1 Watt = 1 Joule per second
1: 1 horsepower = 750 Watts.

External Force/Nonconservative force - when doing work upon an object, the object's total mechanical energy, kenetic energy + potential energy, is changed
1: External forces: applied force, normal force, tension force, friction force, air resistance force
2: When an external force does positive work on an object, the object will gain energy.  If the work is negative, the object will lose energy.

Internal Force/Conservative force - when doing work upon an object, the object's total mechanical energy, kinetic energy + potential energy, remains constant
1: Internal forces: gravity force, magnetic force, electrical force, spring force
2: When an internal force does work on an object, the object's energy changes from kinetic to potential or vice versa.

Work and Energy - KE_i + PE_i + W_ex = KE_f + PE_f, where KE_i = initial kinetic energy, PE_i = initial potential energy, W_ex = work done by external forces, KE_f = final kinetic energy, and PE_f = final potential energy
1: This also means that the initial amount of total mechanical energy plus the work done by external forces is equal to the final amount of total mechanical energy.
2: If the angle between the force and displacement vectors is 180, then the work value will be negative; if it is 0, then the work value will be positive.

Chapter 6: Circular Motion

Uniform Circular Motion - motion of an object in a circle with a constant speed
1: Because average speed = (change in distance)/(time) and distance in circular motion is circumference, which is 2*π*R where R = radius, then circular motion average speed = 2*π*R/T where T = period.
2: An object moving in uniform circular motion has constant speed, but changing velocity.  The velocity, while constant in magnitude, has a changing direction, which is always tangent to the circle.
3: Because the velocity is constantly changing (in direction), an object with uniform circular motion is not only accelerating, but the direction of the acceleration is towards the center of the circle.

Centripetal Force - force seeking the center
1: From Newton's second law of motion, we know that an object experiencing acceleration is also experiencing a net force, and the direction of the force is the same as the direction of the acceleration.
2: For an object in uniform circular motion with an acceleration towards the center of the circle, the force towards the center of the circle is called centripetal force.
3: The feeling of wanting to move outwards in a centrifugal way is not due to an outward force; it can be explained by Newton's first law.  An object experiencing uniform circular motion wants to continue to move (in a straight line).

Circular Acceleration Equation - where A = acceleration of an object moving in a circle, v = speed, R = radius, and T = period,
A = v^2/R
A = 4*π^2*R/T^2

Circular Force Equation - where F = net force of an object moving in a circle, m = mass, v = speed, R = radius, and T = period,
F = m*a
F = m*v^2/R
F = m*4*π^2*R/T^2

Kepler's 3 Laws - describe motion of planets about the sun

Kepler's First Law/The Law of Ellipses - the paths of the planets about the sun are elliptical in shape, with the center of the sun being located at one focus
1: An ellipse is a curve in which the sum of the distances from every point on the curve to two other points (called foci) is a constant.
2: All planets orbit the sun in an elliptical path where the sun is one of the foci.

Kepler's Second Law/The Law of Equal Areas - an imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time
1: A planet moves fastest when it is closest to the sun and slowest when it is furthest from the sun.

Kepler's Third Law/The Law of Harmonies - the ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun
1: This law compares the orbital period and radius of orbit of one planet to those of other planets.

Universal Gravitation - concept that any two masses have gravity between them, necessary for Newton's rationalization for the circular nature of motion for celestial bodies

1: Imagine firing an object with such a tremendous force that the trajectory of the object matched the curvature of the earth.  The object would then fall around the earth instead of into it, and become a satellite orbiting in circular motion.  (This launch speed is 8,000 m/s.)
2: At an even greater launch speed, the object would orbit the earth in an elliptical path.
If T = the period, or time required to complete one orbit around the sun, and R = radius of orbit, or average distance away from the sun, then each planet has the same T^2/R^3 value.
3: Less specifically, as the planets get further away from the sun, their orbits take longer.

Newton's Law of Universal Gravitation - the force of gravity between two objects is proportional to the product of their masses divided by the square of the distance between their centers.
1: Universal Gravitation Constant - G = 6.673 x 10^-11 in N*m^2/kg^2
2: Universal Gravitation Equation - F = G*m₁*m₂/d^2
3: All objects attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the distance between their centers.

g Anywhere - while g = -9.8m/s^2 on or near earth's surface, its value changes depending on location
1: Setting the two force of gravity equations equal to each other, we have m*g = G*mearth*m/d^2, or  g = G*m_earth/d^2.  Increasing the distance from the earth's center weakens the value of g.
2: The same equation can be used to calculate the value of g on any planet, where m = planet mass and d = planet radius.

Satellites - any object orbiting a massive body; can be natural or man-made.
1: All satellites are projectiles, or objects that have no force other than gravity acting upon them.
2: Satellites, like any object in circular motion, has a velocity in the direction tangent to the orbit path, an acceleration towards the center of the orbit, and a net force towards the center of the orbit.

Orbital Speed Equation - where G = 6.673 x 10^-11, M = the mass of the central body, and R = the average radius of orbit,
v = (G*M/R)^(1/2)
1: This can be derived by setting the circular force equation (F = m*v^2/R) equal to the universal gravitation equation (F = G*m1*m2/d^2) and solving for v.

Orbital Acceleration Equation - where G = 6.673 x 10^-11, M = the mass of the central body, and R = the average radius of orbit,
a = G*M/R^2

Orbital Period Equation - where T = time required to complete one orbit, R = average radius of orbit, G = 6.673 x 10^-11, and M = the mass of the central body,
T^2/R^3 = 4*π^2/G*M

Weightlessness - sensation where all contact forces are removed
1: Astronauts experience weightlessness because they are in a constant state of free fall.  The only force acting upon their bodies is gravity, but gravity cannot be felt without any other opposing forces
2: A scale doesn't measure weight, but rather the upward force applied by the scale to balance to downward force of gravity acting upon an object.
3: Gravity is a force that acts between the masses of two objects and is unaffected by air or air pressure.

Mechanical Energy of a Satellite - total mechanical energy of the system is conserved, whether in circular or elliptical motion.
1: KE_i + PE_i = KE_f + PE_f, where KE_i = initial kinetic energy, PE_i = initial potential energy, KE_f = final kinetic energy, and PE_f = final potential energy.
2: In circular motion, both KE and PE remain constant.
3: In elliptical motion, they will not.

Chapter 7: Thermal Physics

Temperature - what a thermometer reads; a measure of the average kinetic energy of the particles within a sample of matter
1: A thermometer works by encasing a liquid such as liquid mercury in a narrow glass column; as the liquid gets hotter, the volume increases.
2: If the cross sections of this column are the same, the increase in the height of the liquid column is proportional to the increase in temperature.
3: Three common forms of kinetic energy are vibrational kinetic energy, rotational kinetic energy, and translational kinetic energy.
4: When the temperature of an object increases, the particles that compose the object move faster.
5: Temperature is a measure of the ability of a substance to transfer heat energy to another physical system.

Temperature Scales - measured in Celsius, Fahrenheit, and Kelvin
1: Celsius  - water freezes at 0° and boils at 100° at an atmospheric pressure of 1 atm.
2: Fahrenheit - °C = (°F-32°)*4/5, and °F = 5°C/4 + 32°.
3: Water freezes at 32° F and boils at 212° F at an atmospheric pressure of 1 atm.
4: Kelvin  - °C = K - 273.15°, and K = °C + 273.15°.
5: The zero point on the Kelvin scale is absolute zero, which is the lowest temperature that can be achieved.

Heat - transfer of energy from a higher temperature object to a lower temperature object
1: An object decreases its temperature by releasing energy in the form of heat to its surroundings and increases temperature by gaining energy in the form of heat from its surroundings.

Thermal Equilibrium - point at which the system and surroundings reach the same temperature and heat transfers cease
1: At thermal equilibrium, there is no net energy transfer resulting from collisions of particles at the perimeter.

Zeroth Law of Thermodynamics -  A temperature difference between two locations will cause a flow of heat along a path between those two locations, and as long as the temperature difference is maintained, a flow of heat will occur.

Conduction - transfer of heat from one location to another without any material flow, but through particle collisions which result in gains and losses of kinetic energy

Convection - transfer of heat from one location to another by the movement of fluids such as air or water
1: Liquids and gases are poor conductors of heat.
2: Liquids and gases expand when heated and become less dense, which leads to circulation currents.
3: Instead of the notion that "heat rises," heated air rises.
4: Convection can be natural convection, in which the driving force of the circulation is natural, or forced convection, in which fluid is forced from one location or another by fans, pumps, or other devices.

Radiation - transfer of heat through electromagnetic waves
1: "To radiate" means to send out from a central location, and electromagnetic radiation emitted from a source carries energy away from the source to surrounding objects.  These objects absorb this energy, causing the average kinetic energy of their particles to increase.
2: All objects radiate energy in the form of electromagnetic waves, and the rate at which this energy is released is proportional to the Kelvin temperature raised to the 4th power.  The hotter the object, the more it radiates.

Thermal Conductivity - number that describes the effect of a material on heat transfer rates
1: Materials with a high thermal conductivity are called thermal conductors, and materials with a low thermal conductivity are called thermal insulators.
2: Metals usually have the highest thermal conductivity, followed by other solids, and then liquids and gases.
3: The rate of heat transfer is directly proportional to the surface area through which the heat is being conducted.
4: The rate of heat transfer is inversely proportional to the thickness or distance through which the heat is being conducted.

Heat Transfer - four variables that affect the rate of heat transfer between two locations are temperature difference, materials, area, and distance
1: For flat borders where k = thermal conductivity value of the border, A = area of the border, T₁ = temperature of one location, T₂ = temperature of the other, and d = thickness of the border,
Rate = k*A*(T₁ - T₂)/d in Watts.
2: Heat can change the temperature of objects, it can change the state of matter.
3: All phase transitions occur at a constant temperature.
4: Heat transfer can also do work upon the system or surroundings.  Devices for this are called heat engines.  For an internal combustion engine, internal energy stored in the chemical (fuel) is converted into thermal energy, which results in work.

Specific Heat Capacity - amount of heat required to cause a unit of mass to change its temperature by 1°C in J/g/°C; specific heat capacity of different materials vary

Quantity of Heat - where Q = quantity of heat transferred, m = object mass, C = specific heat capacity of object material, and T = change of object temperature,
Q = m*C*T
1: When Q is positive, the object gained thermal energy from its surroundings; when Q is negative, the object released thermal energy to its surroundings.

Endothermic - energy must be added to the matter to cause state change
Exothermic - energy is released by the matter when state changes occur
1: Melting, boiling, and sublimation are examples of endothermic changes of state, while freezing, condensation, and deposition are exothermic.
2: Melting - solid to liquid; freezing - liquid to solid; vaporization - liquid to gas; condensation - gas to liquid; sublimation - solid to gas; deposition - gas to solid.
3: For melting and freezing, where Q = quantity of energy gained or released, m = mass, and H = specific heat fusion per gram,
Q = m*H
3: For vaporization and condensation, where Q = quantity of energy gained or released, m = mass, and H = specific heat of vaporization per gram,
Q = m*H

Calorimeter - device used to measure quantity of heat transferred to or from an object
1: In determining the calorie content of food, a bomb calorimeter is often used.  Such a device has a reaction chamber where the sample, oxygen, and fuel are contained.  This reaction chamber is encased in water with some sort of stirring motor.  When the contents of the reaction chamber are ignited, the water is stirred, and the temperature difference is measured to calculate the quantity of energy released.

Chapter 8: Static Electricity

Atom - basic unit from which matter is composed
1: The different types of atoms are called elements.
2: Different elements can combine in different ratios of masses to form compounds.
3: The three main subatomic particles that compose an atom are protons (positive), electrons (negative), and neutrons (neutral).
4: Atoms that are held together by chemical bonds form molecules.

Nucleus - densely packed core of the atom, composed of protons and neutrons
1: Protons and neutrons are much larger than electrons.
2: The nucleus is very small compared to the size of the entire atom, and the area outside the nucleus is spacious and vast.
3: Protons and neutrons are not removable from the nucleus through usual methods, and they will remain in the nucleus for the discussion of electrostatic phenomenon.

Electron Shells - concentric spherical regions outside the nucleus, hold electrons
1: Outer electron shells have higher energy levels are are lower in stability.
2: Electrons in higher energy shells can move down to lower energy shells with the release of energy.
3: Electrons in lower energy shells can move up to higher energy outer shells by adding energy to the atom.
4: With enough energy, an electron can be removed from an atom and freed from its attraction to the nucleus.

Charge - determined by number of electrons that surround a nucleus
1: A proton and an electron have have equal and opposite charges.
2: An atom with equal numbers of protons and electrons are electrically neutral.
3: An atom that contains fewer electrons than protons is positively charged.
4: An atom that contains more electrons than protons is negatively charged.

Coulomb - unit to express the charge of an object
1: The charge of an electron is (-1.6)*10^(-19) C.
2: The charge of a proton is (1.6)*10^(-19) C.

Electric Force - non-contact force exerted by any charged object
1: Objects with like charge repel each other, and objects with opposite charge attract each other.
2: Positively or negatively charged objects attract neutral objects.
3: By Newton's third law, this means that neutral objects attract positively or negatively charged objects as well.

Conductor - material that permit electrons to flow freely from particle to particle
1: A charged object will always distribute its charge until the overall repulsive forces between excess electrons is minimized.
2: If a charged conductor touches another object, the conductor can transfer its charge to that object.
3: Although there are varying degrees of conducting ability, examples of conductors include metals, ionic compounds dissolved in water, graphite, and the human body.
4: Because electrons repel each other, in conducting materials, they will try to get as far away from one another as possible, which leads to an even distribution of electrons.
5: Electrons behave in a way to best serve the entire system involved.

Insulator - material that impede the free flow of electrons from atom to atom and molecule to molecule
1: If charge is transferred to an insulator at a given location, the excess charge will remain in that location.
2: In experiments, conductive objects are often mounted on top of insulating objects.
3: Although there are varying degrees of insulating ability, examples of insulators include plastics, styrofoam, paper, rubber, glass, and dry air.

Polarization - process of separating opposite charges within an object; polarization is not the same as charging
1: For a conductor to become polarized, electrons redistribute themselves across the surface of the conductor.
2: For an insulator to become polarized, electrons redistribute themselves within the atom only.
3: Electrons are located in regions of space called electron clouds.
4: Electron clouds vary in density and are highly distortable.
5: When an atom is polarized, the centers of positive and negative charge are no longer in the same location.

Polar Bond - bond between different types of atoms; electrons are not equally shared
1:  Atoms are bonded when protons in one atom attract electrons in the electron clouds of another to form molecules.
2: If these atoms are of different types, then the electrons within these clouds are not equally shared.
3: In this case, the electron cloud becomes distorted, and the distribution of electrons within the cloud is shifted more towards one atom.

Electron Affinity - how much a given material wants to take electrons
1. A triboelectric series is an ordering of materials by their electron affinity.

Law of Conservation of Charge - The net charge in the system remains constant before and after a charging process.

Charging by Friction - two materials of different electron affinity are rubbed together
1. Materials with a large electron affinity will have the greatest tendency to acquire a negative charge.

Charging by Induction - a charged object is placed near a neutral object to polarize it, and one side is of the neutral object is then grounded.
1. The charged object always creates an opposite charge in the neutral object.
2. A ground is any large object that serves as a nearly infinite source to supply or receive electrons.

Charging by Conduction/Charging by Contact - a charged object contacts a neutral object
1. The charged object always creates the same charge in the neutral object.
2. Both objects involved must be conductors.

Charging by Lightning - a charged insulating object charges a conductor
1. Charging by lightning can happen with or without contact.
2. The two objects do not act together to share the charge, but electrons burst through air between the objects.
3. Like charging by conduction, both objects will result in the same charge.

Grounding - process of removing excess charge on an object by transferring it to a ground
1. The extent an object is willing to share charge is proportional to its size, so an effective ground is one with enough size to share the overwhelming majority of excess charge.
2. Grounding requires a conducting pathway.

Coulomb's Law Equation - where F = electric force between two charged objects, k = Coulomb's law constant, Q₁ = quantity of charge in object 1, Q₂ = quantity of charge in object 2, and d = distance of separation from the centers of the two objects,
F = k*Q_1*Q₂/d^2
1. The value of k is dependent upon the medium the charged objects are in.  When in air, k = 9*10^9 in N*m2/C^2.
2. Electric forces, like all forces, follow Newton's laws of motion.
3. Electrical forces result from mutual interactions between two charges, so in situations involving three or more charges, the electrical force on a single charge is the result of the combined effects of that charge with all the other charges.

Field Force - concept to help explain distance forces like gravitational forces, electrical forces, magnetic forces
1. An electric charge creates an electric field; it alters the nature of the space surrounding the charge
2. Both conductors and insulators of positive or negative charge create electric fields.

Electric Field Strength - vector quantity; where F = electric force experienced by test charge, and q = test charge quantity,
E = F/q in N/C.
1. A source charge and a test charge are necessary because two charges are required to encounter a force.
2. By substituting Coulomb's law for F, we get
E = k*Q/d^2, where Q = source charge quantity.
3. The direction of E is either towards the source charge or away from it.  Scientists have agreed to define the direction this way: the direction of E is the direction that a positive test charge is pushed or pulled when in the electric field.

Electric Field Lines - force vectors used to visually represent the nature of an electric field surrounding a charged object
1. These lines are most dense around objects with the greatest amount of charge.
2. Where they meet the surface of an object, they are perpendicular to that surface.
3. They always extend from a positively charged object to a negatively charged object, from a positively charged object to infinity, or from infinity to a negatively charged object.
4. They never cross each other.  In the case of diagrams involving two or more charges, the vectors can be added to determine a new direction, and in these cases, electric field lines curve.

Electrostatic Equilibrium - condition established by charged conductors in which the excess charge has optimally distanced itself
1. For a conductor at electrostatic equilibrium, the electric field anywhere beneath the surface is zero.  Excess charge on a conductor exists only on its outer surface.
2. For a conductor at electrostatic equilibrium, the direction of the electric field upon the surface of the conductor is perpendicular to the surface.
3. For a conductor at electrostatic equilibrium, the electric fields are strongest along the most curved areas of the surface.  This is this concept behind the design of a lightning rod.

Lightning - result of static charge build up in clouds
1. Storm clouds contain millions of moving water droplets and ice particles.  As additional water from the ground evaporates, there are many water droplet collisions within the clouds, and electrons are exchanged.
2. Rising moisture encounters cooler temperature at higher altitudes, and water begins to freeze.  The frozen particles tend to move towards the central regions of water clusters, and become negatively charged while the outer regions become positively charged.  Air currents rip the outer regions of the clusters upwards, and the frozen centers gravitate towards the bottom of the clouds.
3. Thus, storm clouds become polarized.  The tops of the cloud acquire an excess of positive charge, and the bottoms acquire an excess of negative charge.
4. The cloud's electric field extends to the earth's surface, repelling electrons.  This results in a positive charge in the earth's surface, including the buildings, trees, and people there.
5. Normally, the air surrounding a cloud acts as an insulator, but when strong electric fields are present, they can ionize the air and transform it into a conductive plasma made of positively charged atoms and molecules and free electrons.
6. Excess electrons from the bottom of the cloud begin moving through the conducting air, creating a step leader.  As the step leader approaches the earth's surface, the positive charge increases and migrates upwards, becoming a streamer.
7. The streamer meets the step leader in the air, and a complete conducting pathway is formed.  The contact point between the ground charge and cloud charge ascends upwards as fast as 50,000 miles per second, and as many as a billion trillion electrons can travel this path in less than a millisecond.
8. The initial lightning strike is followed by several more strikes in rapid succession, and the flow of charge heats the surrounding air, causing extreme expansion.  The shockwave of this expansion is thunder.

Lightning Rod - provide a conductive pathway of cloud charge to the earth
1. Lightning rods should be blunt tipped, elevated above the building it is protecting, and connected by a low resistance wire to a buried grounding rod.

Chapter 9: Current Electricity

Electric Potential - amount of potential energy per unit of charge, property of the location within an electric field
1. Electric potential energy is dependent on the electric charge of the object in the electric field and the location within the electric field.
2. Electric potential, on the other hand, is a quantity per charge, dependent only on location, or distance from the source.
3. Moving a positive test charge against the electric field requires work and results in a gain of potential energy, while moving a positive test charge in the direction of the field requires no work and results in a loss of potential energy.

Battery Circuits - have locations of high and low potential
1. There is an electric field directed from the positive terminal towards the negative terminal.
2. Because electric fields are based on the direction of movement of positive test charges, the positive terminal is the high potential terminal, and the negative terminal is the low potential terminal.
3. An electric circuit is an energy conversion system where chemical energy is used to do work on a positive test charge in order to move it from the low potential terminal to the high potential terminal.
4. Within the battery/internal circuit, chemical energy is transformed into electric potential energy.  After a positive test charge moves to the high potential terminal, it moves through the external circuit to do work, transforming its electric potential energy into useful forms.  Finally, the positive test charge returns to the negative terminal at low energy and low potential, ready to repeat the circuit.
5. The movement of a charge through an external circuit is natural because it is in the direction of the electric field.

Electric Potential Difference - difference in electric potential between the final location and the initial location when work is done upon a charge to change its potential energy
1. The difference in electric potential is work divided by charge or change in potential energy divided by charge.

Volt - standard metric unit for electric potential difference; I Volt = 1 Joule per Coulomb
1. If the electric potential difference between two locations is 1 Volt, 1 Coulomb of charge will gain 1 Joule of potential energy when moved between those two locations.
2. Electric potential difference is sometimes called voltage.
3. If a 12 Volt battery is used in a circuit, every Coulomb of charge gains 12 Joules of potential energy as it moves through the battery and loses 12 Joules of electric potential energy as it passes through the external circuit.
4. The loss of electric potential energy in external circuits results in light energy, thermal energy, and other forms of non-electrical energy.

Internal Circuit - energy is supplied to the charge
External Circuit - electrical energy is lost by the charge as it does work on circuit elements (like a light bulb)
1. Two high potential locations are the positive battery terminal and the end of its wire where it meets the circuit element.
2. Two low potential locations are the negative battery terminal and the end of its wire where it meets the circuit element.

Voltage Drop - loss in electric potential while passing through a circuit element
1. The positive terminal of the battery has an electric potential equal to the voltage of the battery, and the negative terminal has 0 Volts.
2. The total voltage drop across the external circuit equals the battery voltage as the charge moves from the positive terminal back to 0 Volts at the negative terminal.

Electric Circuit - closed loop through which charges can continuously move
1. The electric circuit can be divided into two parts: the internal circuit (battery) and the external circuit (wires and light bulb).
2. For an electric circuit to work, there must be a closed conducting path that extends from the high potential positive terminal to the low potential negative terminal.
3. There must also be a source of energy, like a battery, capable of increasing electric potential energy.  In household circuits, the energy is supplied by a utility company, who ensure that the plates within the circuit panel box have an electric potential difference of 110-120 Volts.

Light Bulb - has two wires and a filament, all of which are conducting materials
1. One wire is connected to the sides of the bulb and the other is connected to the base, and the side and base are separated by an insulating material.
2. Charge can enter either the wire on the side, go through the filament, and exit out the base, or enter the base, go through the filament, and exit the side.
3. Although electrons are the charge carriers in metal wires, the charge carriers in other circuits can be positive, negative, or both.  Charge carriers in fluorescent lamps are both positive and negative charges, traveling in opposite directions.

Current - flow of charge within a circuit
1. Current is the rate at which charge flows past a point on a circuit.
2. The standard metric unit for current is an Ampere.  1 Amp = 1 Coulomb/1 second.

Drift Speed - average distance traveled by a charge carrier per unit of time
1. The path of a typical electron moving through a wire is full of collisions with fixed atoms and direction changes, and a typical drift speed is 1 meter per hour.
2. While this is very slow, there are many, many charge carriers moving once through the circuit at once.  If the charge carriers are densely packed, a high current is achieved regardless of drift speed.
3. Once an electric circuit is established, the electric field signal travels at nearly the speed of light to all mobile electrons within the circuit, and they all begin moving.  The current, or rate of charge flow, is the same everywhere.

Electrical Power - rate at which electrical energy is added or removed from a circuit by a battery or load
1. A load is an electrical device like a light bulb.
2. The unit of electrical power is the Watt, which is 1 Joule of energy per second.

Kilowatt-Hour - unit of energy
1. A kilowatt is a unit of power, and an hour is a unit of time.  Power*time = change in energy.
2. Utility companies charge by kilowatt-hours; they provide the energy that causes the motion of charge carriers that are already present within household circuits.

Rechargeable Batteries - batteries are not rechargeable; they are not the source of charge in the first place.

1. Electric circuits are about energy, not charge.  When a battery no longer works, it is out of energy.

2. A battery has reactive chemicals that undergo an oxidation reduction reaction that produces energy, which pumps charge through the battery from the negative terminal to the positive terminal.

3. When the chemicals have been consumed, the battery no longer works.

4. In "rechargeable" batteries, the reaction can be reversed by turning the chemical products back into chemical reactants.

5. The machines that supply the energy are re-energizing the battery rather than recharging it.

Electrical Resistance - hindrance to the flow of charge

1. The rate at which charge flows from terminal to terminal is the result of electric potential difference and resistance.

2. Greater length of wire increases resistance, and greater cross-sectional area of wire decreases resistance.

3. Different materials have different conducting ability; this quantity is called resistivity.

For most materials, higher temperature increases resistivity.

4. The standard metric unit for resistance is the Ohm.

Electricity Equations - electric potential difference/voltage, current, power, resistance, energy
1. Electric Potential Difference (Voltage) - where PE = potential energy, Q = quantity of charge, I = current, and R = resistance,
(change in V) = (change in PE)/Q
(change in V) = I*R
Measured in Volts
2. Current - where Q = quantity of charge, t = time, (change in V) = voltage, and R = resistance,
I = Q/t
I = (change in V)/R
Measured in Amperes
3. Power - where PE = potential energy, t = time, (change in V) = voltage, I = current, and R = resistance,
P = (change in PE)/t
P = (change in V)*I
P = I^2*R
P = (change in V) ^2/R
Measured in Watts

4. Resistance of a cylindrical conductor - where p = resistivity of material, L = length of wire, A = cross sectional area of wire, (change in V) = voltage, and I = current,

R = p*L/A

R = (change in V)/I

Measured in Ohms

5. Energy - where (change in V) = voltage, Q = quantity of charge,  P = power, and t = time,

(change in PE) = (change in V)*Q

(change in PE) = P*t

Measured in Joules

Ohm's Law - electric potential difference between two points on a circuit equals the product of the current between those two points and the total resistance of all electrical devices between those two points
1. (change in V) = I*R

Series Circuit - an individual charge passes through each of the resistors consecutively on its way back to the negative terminal

1. As the number of resistors increases, the overall resistance increases, and the overall current decreases.

2. If current is cut from any of the resistors, it is cut from all of them.
3. In a series circuit, the equivalent resistance, or amount of resistance a single resistor would need to equal the overall effect of all resistors in the circuit, is simply the sum of the resistance values for these resistors.
4. In a series circuit, the current is the same everywhere.
5. In a series circuit, there is a voltage drop at each resistor, and the sum of these drops is equal to the voltage rating of the power supply.  The greater the resistance of the resistor, the greater the voltage drop.

Parallel Circuit - an individual charge passes through one resistor on one of several branches on its way back to the negative terminal; each device is placed in its own branch

1. As the number of resistors increases, the overall resistance decreases, and the overall current increases.

2. If current is cut from any of the resistors, there is still current in the overall circuit and current in other branches.
3. In a parallel circuit, the equivalent resistance, or amount of resistance a single resistor would need to equal the overall effect of all resistors in the circuit, can be determined with the following equation:
1/R_eq = 1/R₁ + 1/R₂ + 1/R₃ + ...
4. In a parallel circuit, the current outside the branches is the same as the sum of the current in the branches.
5. In a parallel circuit, the voltage drop across the single resistor matches the battery voltage.  The resistor with the greatest resistance experiences the lowest current, and the resistor with the least resistance experiences the greatest current.  A charge chooses the path of least resistance.

Compound/Combination Circuit - circuit with both series and parallel connections
1. In working with a combination circuit, transform each parallel section with a single resistor of equal resistance, and analyze the circuit like a series circuit.

Chapter 10: Waves

Vibrational Motion - type of motion in which an object moves about a its equilibrium position
1. Pendula, inverted pendula, and masses suspended by springs are examples of vibrational motion.
2. Resting Position/Equilibrium Position - state in which all forces are balanced
3. Forced Vibration - force that sets an otherwise resting object into motion
4. Damping - tendency of a vibrating object to lose energy over time
5. Restoring Force - force that causes a vibrating object to slow down as it moves away from its equilibrium position and speed up as it approaches its equilibrium position

Periodic Motion - motion that is regular and repeating; most objects that vibrate have periodic vibrations.
1. A position vs time plot for periodic motion is sinusoidal, or in the shape of a sine wave.
2. Period - The time for a mass to complete its cycle; the period of a wave is the time for a particle on a medium to make one complete vibrational cycle
3. Amplitude - maximum displacement of an object from its resting position
4. Frequency - number of cycles occurring per second
5. Hertz - unit for frequency, where 1 Hz = 1 cycle/second
6. Where f = frequency and T = period,
T = 1/f and f = 1/T.

Pendulum Motion - relatively massive object is hung by a string from a fixed support
1. There are three forces acting upon a pendulum bob at all times during the course of its motion: the downward and constant force of gravity, the changing tension force directed towards the pivot point, and the negligible air resistance force.
2. The kinetic energy, dependent on mass and speed, increases as the bob approaches its equilibrium position and decreases as it moves further away.
3. The gravitational potential energy, dependent on mass and height, decreases as the bob approaches its equilibrium position and increases as it moves further away.
4. The total mechanical energy, or sum of kinetic energy and gravitational potential energy, remains conserved.
5. Where L = length of string and g = acceleration of gravity, the period for a pendulum is
T = 2*π*(L/g)^(1/2)

Motion of Mass on a Spring - can be suspended from a support or supported by a low friction track
Hooke's Law: Where F_spring = force exerted upon the spring, k = spring constant, and x = amount the spring stretches relative to its relaxed position,
F_spring = -k*x
1. There are four forces acting upon a mass on a spring during the course of its motion: the downward and constant force of gravity, the support force that balances the force of gravity, the force of the spring, and the negligible friction force.
2. The kinetic energy, dependent on mass and speed, increases as the mass approaches its equilibrium position and decreases as it moves further away.
3. The elastic potential energy, dependent on the spring constant and distance the spring is stretched or compressed, decreases as the mass approaches its equilibrium position and increases as it moves further away.  Where k = spring constant, and x = amount the spring stretches relative to its relaxed position,
PE_spring = 1/2*k*x^2
4. The total mechanical energy, or sum of kinetic energy and gravitational potential energy, remains conserved.
5. Where m = mass of object and k = spring constant, the period for a mass on a spring is
T = 2*π*(m/k)^(5)

Wave - repeating periodic disturbance that travels through a medium from one location to another

1. Pulse - single disturbance moving through a medium from one location to another

2. Medium - collection of interacting particles

3. A wave transports energy, not matter.  They are an energy transport phenomenon.

4. The particles of the medium are only temporarily displaced, and a force acting upon the particles restores them to their rest position.

Transverse Wave - particles of the medium move in a perpendicular direction to the direction of the wave

Longitudinal Wave - particles of the medium move in a parallel direction to the direction of the wave

Surface Wave - particle of the medium undergo a circular motion

1. Waves travelling through a solid medium can be transverse or longitudinal, but waves travelling through liquids or gasses are always longitudinal.

Electromagnetic Wave - capable of transmitting energy through a vacuum, like a light wave

Mechanical Wave - incapable of transmitting energy through a vacuum; requires a medium, like a sound wave

Crest - point on the medium that exhibits the maximum amount of positive or upward displacement from the rest of the position
Trough - point on the medium that exhibits the maximum amount of negative or downward displacement from the rest of the position
Amplitude - maximum amount of displacement of a particle on the medium from its rest position; distance from rest to crest or rest to trough
Wavelength - length of one complete wave cycle
Compression - point on a medium through which a longitudinal wave is travelling with maximum density
Rarefaction - point on a medium through which a longitudinal wave is travelling with minimum density
1. While a transverse wave has an alternating pattern of crests and troughs, a longitudinal wave has an alternating pattern of compressions and rarefactions.
2. For a transverse wave, the wavelength is determined by measuring from crest to crest.  For a longitudinal wave, the wavelength is determined by measuring the distance between any two corresponding points on adjacent waves, such as one compression to the next or one rarefaction to the next.

Energy - The higher energy the wave, the higher its amplitude
1. Amplitude is dependent upon the amount of initial force and the elasticity of the medium.
2. The energy transported by a wave is directly proportional to the square of the amplitude of the wave; doubling the amplitude quadruples the energy transported by the wave.

Speed - distance traveled by a given point on a wave, such as a crest, in a given interval of time
1. Wave speed is entirely dependent upon the medium.
2. Where W = wavelength, f = frequency, and T = period,
v = W/T, or v = W *f

Boundary - where one medium ends and another begins
Incident Pulse - pulse approaching boundary
1. When an incident pulse reaches the boundary, part of the energy is reflected and returns in the opposite direction, and part of the energy is transmitted to the boundary.
2. When a pulse reflects off a fixed end, the reflected pulse is inverted, and when a pulse reflects off a free end, the reflected pulse is not inverted.
3. The speed of a reflected pulse is the same as the speed of the incident pulse.
4. The wavelength of the reflected pulse is the same as the wavelength of the incident pulse.
5. The amplitude of the reflected pulse is less than the amplitude of the incident pulse.

Reflected Pulse - the returning pulse after a pulse reaches a boundary
Transmitted Pulse - the continued pulse after a pulse reaches a boundary
1. A reflected pulse going from a less dense medium to a more dense medium is inverted.
2. A reflected pulse going from a more dense medium to a less dense medium is not inverted.
3. Transmitted pulses are never inverted.
4. A transmitted pulse in a more dense medium travels more slowly than the reflected pulse in a less dense medium.
5. A transmitted pulse in a less dense medium travels faster than the reflected pulse in a more dense medium.
6. A transmitted pulse in a more dense medium has a smaller wavelength than the reflected pulse in a less dense medium.
7. A transmitted pulse in a less dense medium has a larger wavelength than the reflected pulse in a more dense medium.
8. The speed and the wavelength of a reflected pulse are the same as the incident pulse.

Reflection - change in direction of waves when they bounce off a barrier
Law of Reflection - Waves will always reflect in such a way that the angle at which they approach a barrier equals the angle at which they reflect off the barrier.
Reflection of waves off parabolic barriers results in the convergence of the waves at a focal point.

Refraction - change in direction of waves as they pass from one medium to another, bending of the path of waves
1. Refraction of waves involves a change in direction as they pass from one medium to another.
2. Refraction always involves a wavelength and speed change.
3. Water waves travel fastest when the medium is deepest.
4. As water waves are transmitted from deep water to shallow water, the speed decreases, the wavelength decreases, and the direction changes.

Diffraction - change in direction of waves as they pass through an opening or around a barrier in their path
1. The amount of diffraction, or sharpness of the bending, increases as the wavelength increases and decreases as the wavelength decreases.
2. When the wavelength of a wave is smaller than an obstacle, no noticeable diffraction occurs.

Wave Interference - when two waves meet while traveling along the same medium
Constructive Interference - type of interference that occurs at any location along the medium where two interfering waves have a displacement in the same direction
Destructive Interference - type of interference that occurs at any location along the medium where two interfering waves have a displacement in the opposite direction

Principle of Superposition - when two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.
1. When two waves meet, they produce a net resulting shape of the medium, and then continue what they were doing before the interference.

Doppler Effect - effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers for whom the source is receding.
1. The movement of the wave source does not actually change the frequency; this is just an effect.
2. If the source and the observer are approaching, then the distance is decreasing, and if the source and the observer are receding, then the distance is increasing. Because the source always emits the same frequency, in the same period of time, the same number of waves must fit between the source and the observer.
3. For sound, this means that as the source moves away, the sound waves reach the observer at a lower frequency, which creates the perception of a lower pitch.

Traveling Wave - has a sine pattern that moves in an uninterrupted fashion until it encounters another wave or a boundary
1. Traveling waves are observed when a wave is not confined to a given space.

Standing Wave - pattern resulting from the presence of two or more waves of the same frequency with different directions of travel within the same medium; has specific points along the medium that appear to be standing still from the interference of the incident wave and the reflected wave
1. Standing waves are only created at specific frequencies of vibration called harmonic frequencies.
2. Still points are called nodes, and the largest points of displacement are called antinodes.
3. Nodes are produced when the crests and troughs of the incident wave are met with the troughs and crests of the reflected wave; they are a result of destructive interference.
4. Antinodes are produced where constructive interference occurs.
5. A standing wave pattern is an interference phenomenon, formed by the perfectly timed interference of two waves passing through the same medium.
6. Crests and troughs are points of disturbance, while nodes and antinodes are points on the medium.  Unlike crests or troughs, antinodes vibrate back and forth between upward and downward displacements.  Nodes and antinodes are not part of a wave.

Harmonic - frequency and its associated wave pattern
1. The lowest frequency produced by any instrument is called the fundamental frequency or first harmonic of the instrument.
2. The nth harmonic has (n + 1) nodes and n antinodes.
3. The length of string for the nth harmonic is equal to n/2 times the wavelength.

Chapter 11: Sound Waves

Sound - wave created by vibrating objects
1. Because sound waves are disturbances transported a medium (usually air) through particle to particle interaction, they are mechanical waves.
2. Because sound waves cause a motion of the particles that is parallel to the direction of the energy transport, they are longitudinal waves.
3. As a vibrating string moves in one direction, it pushes the surrounding air molecules towards their nearest neighbor, and they become compressed into a small region of space.  As the string moves in the opposite direction, it lowers the pressure of the air.
4. The regions of high air pressure are called compressions, and the regions of low air pressure are called rarefactions.
5. The wavelength for a longitudinal wave is the distance from one compression to the next or one rarefaction to the next.
6. Because sound waves consist of a repeating pattern of high and low pressure regions, it is a pressure wave.

Frequency - how often the particles of medium vibrate when a wave passes through, measured in Hertz; 1 Hertz = 1 vibration/second
1. As a sound wave moves through a medium, each particle of the medium vibrates at the same frequency of the original vibrating object.
2. The higher the frequency, the shorter the period.

Frequency Perception - the higher the frequency, the higher the pitch
1. The human ear can detect frequencies from 20 Hz to 20,000 Hz
2. Sound below the audible range of hearing is infrasound, and sound above the audible range of hearing is ultrasound.
3. When played simultaneously, certain sound waves will produce a pleasant sensation, or consonance.
4. Any two sounds whose frequencies make a 2:1 ratio are separated by an octave.  Similarly,
Fifth 3:2
Fourth 4:3
Third 5:4

Intensity - amount of energy transported past a given area of the medium per unit of time
1. As the amplitude of the vibration of particles is increased, the amount of energy being carried by the particles increases.
2. Intensity = Energy/Time*Area, or Energy = Power/Area in Watts/meter^2.
3. As a sound wave carries energy, the intensity of the sound wave decreases as the distance from the source increases.
4. This is because as the wave spreads out over a circular or spherical surface, the energy of the sound wave is distributed over a greater surface area.
5. The intensity and distance has an inverse square relationship.  If the distance from the source is doubled, the intensity is quartered.

Intensity Perception - the greater the intensity, the louder the sound
Threshold of hearing - the faintest sound a human can detect has an intensity of 1*10^(-12) W/m^2.

Decibel Scale - scale for measuring intensity
1. The threshold of hearing is 0 decibels.  A sound 10 times more intense, (1*10^(-11) W/m^2), is 10 dB.  A sound 100 times more intense, (1*10^(-10) W/m^2), is 20 dB.
2. A whisper is 20dB, a normal conversation is 60dB, an orchestra performance is 98 dB, a rock concert is 110 dB, and an instant perforation of the eardrum occurs at 160 dB.

Speed of Sound - distance the disturbance travels per unit of time
1. The faster a sound wave travels, the more distance it will cover in the same period of time.
2. The speed of a sound wave is dependent upon both the inertia of the vibration and the elasticity of the material, but elasticity has a stronger influence.
3. In general, solids have the strongest elasticity (or elastic modulus), followed by liquids and then gasses.
4. Longitudinal sound waves travel fastest in solids, followed by liquids, and then gasses.
5. Within the same phase of matter, however, sound waves travel faster in less dense materials.

Speed of Sound in Air - at normal atmospheric pressure, where T = temperature in Celsius, the temperature dependence of the speed of a sound wave through dry air is
v = 331 m/s + (.6 m/s/C)*T
1. Air temperature affects the speed of sound more than humidity does.
2. Temperature affects the strength of the particle interactions, which is an elastic property.
3. Humidity affects the density of the air, which is an inertial property.
At normal atmospheric pressure and a temperature of 20 Celsius, a sound wave travels at 343 m/s.  Light travels about 300,000,000 m/s.
4. The equation for speed of sound in air can help to determine how far away lightning is, assuming that light is traveling at instantaneous speed.
5. The equation for speed of sound in air can also help to determine how far away a barrier is when echos are possible.
6. In the equation speed = wavelength*frequency, speed is not dependent upon either quantity.  An alteration in wavelength affects the frequency instead.

Human Ear - consists of the outer ear, the middle ear, and the inner ear

Outer Ear - collects and channels sound to the middle ear
1. The ear canal is capable of amplifying sounds with frequencies of 3,000 Hz.
2. As sound travels through the outer ear, it is a pressure wave.

Middle Ear - transforms energy of a sound wave into internal vibrations of the bone structure of the middle ear, and transform these vibrations into a compressional wave in the inner ear
1. The middle ear is an air-filled cavity that has an eardrum and three small interconnected bones called the hammer, anvil, and stirrup.  The stirrup is connected to the inner ear.
2. The eardrum is a tightly stretched membrane that vibrates with the same frequency as the incoming pressure waves from the soundwave reach it.
3. The movements of the eardrum set the three bones into motion at that same frequency.

Inner Ear - transforms energy of a compressional wave within the inner ear fluid into nerve impulses that can be transmitted to the brain
1. The vibrations of the stirrup are transmitted to the fluid of the inner ear and create a compression wave.
2. The force of the vibrating stirrup is nearly 15 times larger than the force of the eardrum.
3. The inner ear has a cochlea, semicircular canals, and the auditory nerve.
4. Both the cochlea and semicircular canals are filled with fluid.
5. The inner surface of the cochlea is lined with over 20,000 hair-like nerve cells which differ in length and have different degrees of resiliency to the fluid.
6. Each hair cell has a sensitivity to a particular frequency of vibration, and when the frequency of the compressional wave matches the frequency of the nerve cell, that nerve cell will resonate with a larger amplitude of vibration.
7. This increased amplitude induces the cell to release an electrical impulse that passes along the auditory nerve towards the brain, which can interpret these electric nerve impulses.

Sound Wave Interference - sound waves can either reinforce each other or diminish each other
1. If two sound waves interfere in such a way that a location in the medium repeatedly experiences the interference of two compressions followed by the interference of two rarefactions, then the sound waves will continually reinforce each other and produce a loud sound.
2. The particles at that location undergo oscillations from very high pressures to very low pressures.
3. If two sound waves interfere in such a way that a location in the medium repeatedly experiences the interference of a compression and a rarefaction followed by the interference of a rarefaction and a compression, then the sound waves will cancel each other and produce no sound.
4. The particles at that location remain at rest.

Noise - consists of a mixture of frequencies whose mathematical relationship to one another is not readily discernible
Music - consists of a mixture of frequencies that have a clear mathematical relationship

Beat Frequency - rate at which the volume is heard to be oscillating from high to low
1. The beat frequency is equal to the difference in the frequencies of two notes that interfere.
2. The human ear can detect beats of 7 Hz and below.

Shock Wave - effect where the circular or spherical edges of sound waves cluster together
1. The Doppler effect occurs when the speed of the source moves more slowly than the sound wave.
2. If the moving source travels at the same speed as the sound, then the source will be at the leading edge of the sound waves, causing a cluster at its front end.
3. If the moving source travels faster than the sound, the source will be ahead of the sound waves it produces, causing a cone-like cluster behind it.

Sonic Boom - result of the piling up of compressional wavefronts along the conical edge of the wave pattern
1. If the observer is on the ground when a supersonic aircraft passes overhead, the compressed wavefronts that pile up behind it will interfere to produce high pressure regions in the shape of a cone.
2. These regions create a high pressure zone that do not reach the observer consecutively, but all at once.
3. Because every compression is followed by a rarefaction, the high pressure zone will immediately be followed by a low pressure zone, which creates a very loud noise
4. Sonic booms are observed when any aircraft that is travelling faster than the speed of sound passes overhead.

Sound Waves and Boundary Behavior - there are four behaviors a wave can exhibit at a boundary
Reflection - bouncing off of the boundary
Diffraction - bending around obstacle without crossing over the boundary
Transmission - crossing of boundary into obstacle or new material
Refraction - occurs with transmission, characterized by subsequent change in speed and direction.
1. When a wave reaches the boundary between one medium and another, a portion of the wave undergoes reflection and a portion of the wave undergoes transmission across the boundary.
2. The amount of reflection is dependent upon the dissimilarity of the two media.
3. An acoustically pleasing room is built from materials that are soft, which is more like air than hard materials.  Thus, they can absorb sound better and reflect sound waves less.

Reverberation - reflected sound waves create a prolonging of the sound
Echo -reflected sound waves reach the ear more than .1 seconds after the original sound wave was heard
1. The human brain keeps a sound in memory for up to .1 seconds, and if a reflected sound wave reaches the ear within this time period, the sound seems to be prolonged.
2. Due to the speed of sound, reverberations occurs in a small room with height, width, and length dimensions of 17 meters or less.
3. Reverberations sometimes lead to a displeasing garbling of sounds, but sometimes reflected sound waves can enhance the listening experience.
4. Rough walls diffuse sound, reflecting it in a variety of directions and allowing an observer to perceive sounds from all parts of the room, which makes the room seem full and lively.

Timbre - quality of sound, dependent upon the natural frequencies of the sound waves of produced by the vibrating object
1. Objects that vibrate at a single frequency produce a pure tone.
2. Objects that vibrate and produce complex waves with frequencies that have whole number mathematical relationships have a rich sound.
3. Objects that vibrate at a set of frequencies that have no simple mathematical relationship between them make noise.
4. The natural frequency or set of frequencies of an object is dependent upon the material of the object and the length of the object.
5. Each natural frequency an object produces has its own characteristic standing wave pattern.

Forced Vibration - tendency of one object to force another adjoining object into vibrational motion
1. One example is a piano soundboard.  Because the surface area of the soundboard is greater than the surface area of the string, more surrounding air particles will be forced into vibration, and the sound is amplified.

Resonance -when one object vibrating at the same natural frequency of another object forces that object into vibrational motion
1. This works because the objects are connected by the surrounding air particles.
2. An instrument can be forced into vibrating at one of its harmonics if another interconnected object pushes it with one of those frequencies.
3. When a seashell resonates, it is amplifying one of the many background frequencies nearby.

Open-end Air Column Instruments - Like a recorder
1. In brass instruments, resonance occurs when the vibration of the lips pressed against the mouthpiece matches the natural frequencies of the air column inside the instrument.
2. In woodwind instruments, resonance occurs when the vibration of the reed matches the natural frequencies of the air column inside the instrument.
3. The length of the air column is controlled by opening and closing holes within the tube.
4. Both ends for an open-end air column instrument have antinodes.
5. For the nth harmonic of an open-end air column instrument, there are n nodes and (n + 1) antinodes.
6. There are n/2 waves in the air column.
7. The Wavelength = (2/n)*Length of the column.

Closed-end Air Column Instruments - Like a bottle
1. A closed end in a column of air is analogous to the fixed end on a vibrating string; air at the closed end of the column is still.
2. The open end of a closed-end air column instrument has an antinode, and the closed end has a node.
3. Because of this constraint, closed-end air column instruments can only produce odd numbered harmonics.
4. For the nth harmonic of a closed-end air column instrument, n is always an odd number, and there are (n + 1)/2 nodes and the same number of antinodes.
5. There are n/4 waves in the air column.
6. The Wavelength = (4/n)*Length of the column.

Chapter 12: Light Waves & Color

Light Behavior - characteristic of both waves and particles
1. Light undergoes interference, exhibits the Doppler effect, reflects, refracts, and diffracts the way waves do.

Light Reflection - light reflects
1. Like water waves and sound waves, the angle at which a light wave approaches a flat reflecting surface is equal to the angle at which the wave leaves the surface.
2. The reflection of light waves off a mirror results in the formation of an image.

Light Refraction - like any wave, light refracts as it passes from one medium to another
1. When a wave crosses the boundary between two media, the path of travel gets bent.
2. The direction of this bending is dependent upon how fast the wave travels in the two media.
3. The amount of bending follows distinct mathematical equations.

Light Diffraction - involves a change in direction as waves pass through an opening or around an obstacle
1. When light encounters an obstacle in its path, the obstacle blocks the light and causes the formation of a shadow in the region behind the obstacle, but light does diffract around obstacles.
2. Due to interference effects, the edges of shadows are fuzzy.

Two-Point Source Interference Patterns - the interference of two sets of periodic concentric waves with the same frequency
1. These interferences result in linear patterns of antinodes and nodes called antinodal lines and nodal lines.
2. A two-point source interference pattern always has an alternating pattern of nodal and antinodal lines.
3. An increase in the frequency results in more lines that are closer together.
4. A decrease in the frequency results in fewer lines that are spaced further apart.
5. When the two sources are moved further apart, more lines are produced, and the lines are closer together.

Color - each wavelength is characterized by its own color.

Thin Film Interference - light interference that produces streaks of color on thin films like bubbles
1. When a wave reaches the boundary between two media, part of the wave reflects off the boundary, and part of the wave is transmitted across the boundary.
2. In the case of thin film interference, part of the light wave reflects back into the air, and the other part transmits into the thin film.
3. The transmitted wave reflects and transmits on the other side of the film, and part of this wave transmits back out of the film in very close to the original reflected wave.
4. If these waves are so close that their crests and troughs can meet, and if if the thickness of the film is such that the waves are in phase with each other, these two waves can interfere constructively.
5. Depending on the thickness of the film at different locations, the film may allow different wavelengths to emerge in phase.
6. This means that different colors will appear to be brighter in different locations.

Light Wave - electromagnetic wave that travels through the vacuum of outer space
1. Light waves are produced by vibrating electric charges.
2. An electromagnetic wave is a transverse wave that has both an electric and a magnetic component.

Unpolarized Light - light wave that is vibrating in more than one plane
1. Examples of unpolarized light are sunlight, lamp light, and fire.
2. The electric and magnetic vibrations of an electromagnetic wave occur in numerous planes.

Polarized Light - light waves in which the vibrations occur in a single plane
1. Polarization can reduce glare in glasses, perform stress tests on transparent plastics, and create 3D movies.
2. 3D movies are 2 movies that were filmed from 2 slightly different camera locations, and they are shown from 2 projectors.  The movies are projected through polarizing filters that are perpendicular to one another.  The audience wears glasses with polarizing filters such that the left eye sees the movie from the right projector while the right eye sees the movie from the left projector.  This creates depth perception.

Polarization - process of transforming unpolarized light into polarized light

Polarization by Transmission - light is absorbed into a new material called a Polaroid Filter
1. Polaroid Filters are made of materials that can block one of the two planes of vibration of an electromagnetic wave.
2. The filter can be thought of as having long chain molecules aligned in the same direction, so that the waves vibrating in this direction are absorbed by the filter.
3. The polarization axis is perpendicular to the direction the molecules are aligned.
4. When two Polaroid filters are aligned perpendicularly, no light can pass through.
5. When unpolarized light is transmitted through a Polaroid filter, the vibrations are in a single plane, and the light has half the intensity.

Polarization by Reflection - extent of polarization is dependent upon the angle of light and material of nonmetallic surface
1. Metallic surfaces reflect light with a variety of vibrational directions, but nonmetallic surfaces reflect light so that there is a large concentration of vibrations in a plane parallel to the reflecting surface.

Polarization by Refraction - when a beam of light passes from one material to another
1. At the surface of the two materials, the path of the beam changes direction, and the refracted beam acquires some degree of polarization.
2. The polarization usually occurs in a plane perpendicular to the surface.

Polarization by Scattering - light can be scattered while travelling through a medium
1. When light strikes the atoms of a material, it can set the electrons of those atoms into vibration.
2. These vibrating electrons produce their own electromagnetic wave directed outwards in all directions.
3. This wave strikes neighboring atoms, forcing their electrons to vibrate at the same frequency.
4. These vibrating electrons produce another electromagnetic wave that is also directed outwards in all directions.
5. This absorption and reemission of light waves causes the light to be scattered and partially polarized.
6. This scattered light often produces a glare in the sky; photographers can eliminate this glare with a Polaroid filter.

Electromagnetic Spectrum - continuous range of frequencies for electromagnetic waves
1. Electromagnetic waves have an electric and a magnetic component.
2. Electromagnetic waves are capable of transporting energy through a vacuum, and are produced by a vibrating electric charge.
3. From low frequencies with longer wavelengths to high frequencies with shorter wavelengths, the regions of the electromagnetic spectrum are: radio waves, microwaves, infrared waves, visible light waves, ultraviolet waves, x-ray waves, and gamma waves.
4. The visible light and x-ray regions on the spectrum are very small.

Visible Light Spectrum - narrow band of wavelengths that humans can see known as ROYGBIV
1. Each wavelength within the spectrum of visible light wavelengths represents a color.
2. Dispersion is the process in which light shines through a prism and separates into different wavelengths.
3. Indigo is not observed in the spectrum, and is only added so there is a vowel in the acronym.
4. The red wavelengths are the longest and the violet wavelengths are the shortest.
5. When all the wavelengths strike the eye simultaneously, we see white.
6. When no wavelengths strike the eye, we see black.
Visible light consists of wavelengths ranging from 780 - 390 nanometer.

Color - psychological and physiological response to light waves of a specific frequency or a specific set of frequencies
1. Light enters the eye through the pupil and strikes the surface of the retina, which is lined with light sensing cells known as rods and cones.
2. The rods are sensitive to the intensity of light and the cones sense the different wavelengths.
3. The three kinds of cones are red cones, green cones, and blue cones, because they are sensitive to wavelengths of light associated with those colors.

Visible Light Absorption, Reflection, Transmission - when visible light of many frequencies strikes surfaces, the surfaces have a tendency to selectively absorb, reflect, or transmit certain frequencies; what happens is dependent on the frequencies and the nature of the atoms of the object.
1. Atoms and molecules contain electrons that have a tendency to vibrate at specific frequencies.
2. When a light wave with the same frequency as the electron's natural frequency strikes the atom, the electrons absorb the energy of the light wave and transform it into vibrational motion.
3. The electrons interact with neighboring atoms to convert the vibrational energy into thermal energy.
4. Because different atoms have different natural frequencies of vibration, they selectively absorb different frequencies of visible light.
5. When the frequencies of light waves do not match the natural frequencies of the atoms they strike, reflection and transmission occur.
6. Instead, these light waves strike the atoms and the electrons begin vibrating for brief periods of time with small amplitudes, and the energy is reemitted as a light wave.
7. For transparent objects, the vibrations of electrons are passed to neighboring atoms and reemitted on the opposite side of the object; these frequencies of light waves are transmitted.
8. For opaque objects, the energy is reemitted as a reflected light wave.

Color - color in an object is not contained within the object, but is the result of the way the object interacts with light and reflects or transmits it to our eyes.
1. If an object absorbs all of the frequencies of visible light except for the frequency associated with red light, the object appears green when struck with ROYGBIV.
2. Transparent materials allow one or more of the frequencies of visible light to be transmitted through them.  The colors that are not transmitted are absorbed.

Color Combining - addition and subtraction of light waves
1. White is the presence of all frequencies of visible light, but it can also be produced by combining 3 distinct frequencies of light.
2. Any 3 frequencies of light that produce white light when combined with the correct intensity are called primary colors of light.
3. The most common 3 primary colors of light are red, green, and blue.
4. Where Y = yellow, M = magenta, and C = cyan, Y, M, and C are secondary colors, and can be created by combining equal parts of primary colors R, G, and B.
R + G = Y, R + B = M, and G + B = C.
5. Any two colors of light that produce white when combined in equal intensities are complementary colors.
6. Pigments absorb light.  Pure pigments absorb a single frequency, and the color of light absorbed by a pigment is the complementary color of the pigment.  Red pigments absorb cyan light and vice versa, etc.
7. Transparent objects or filters selectively absorb one or more frequencies of light and transmit what is not absorbed.
8. Y, M, and C are the primary colors of paint, which is why printer cartridges are those colors.

Sky Colors - blue skies and red sunsets
1. The sun emits light waves with a range of frequencies, some of which fall within the visible light spectrum.  Sunlight appears white.
2. The frequencies of visible light are either absorbed, transmitted by transparent materials, or reflected by opaque materials.  The colors we perceive are dependent on reflected and transmitted light.
3. The atmosphere contains many types of particles, and the two most common are nitrogen and oxygen.
4. These particles are most effective in scattering the high frequency/short wavelengths; they scatter violet most easily, followed by blue, etc.
5. As white light passes through the atmosphere, high frequencies become scattered and the low frequencies pass through.
6. We see blue instead of violet because our eyes are more sensitive to light with blue frequencies.
7. The light is not scattered and passes through the atmosphere has lower frequencies, and appears yellow.
8. As the sun approaches the horizon line, sunlight must travel a greater distance through the atmosphere compared to mid-day, and goes through more scattering.
9. Through encountering more atmospheric particles, the light is concentrated with red and orange frequencies.

Anatomy of a Two-Point Source Interference Pattern (in which the wave sources have the same frequency) - names of nodal lines and antinodal lines; these are not perfectly linear
1. The central antinodal line extends outward from the sources in the exact center of the pattern.
2. The closest antinodal lines to this are called the first antinodal lines, and so on.
3. The nodal lines that separate the antinodal lines are named the first nodal lines, and so on.
4. Each line is assigned a number called the order number.
5. The central antinodal line has an order number of 0, and the other antinodal lines have increasing natural number values.
6. The first nodal lines have an order number of .5, and all the other nodal lines end in .5 as well.
7. The order number begins at 0 for the central antinodal line, and increases by .5 as the lines move outwards.

Path Difference - difference in distance traveled from two coherent waves
1. Coherent Waves - waves that maintain a constant phase difference with each other
2. The path difference of any antinode or node is equal to the order number multiplied by the wavelength.
3. Two waves traveling along two different paths to the same point will interfere constructively if the path difference is a natural number.  This also means the point is on an antinodal line.
4. Two waves traveling along two different paths to the same point will interfere destructively if the path difference is a natural number plus .5.  This also means the point is on a nodal line.

Young's Equation - determines wavelength of light based on two-point interference pattern for point P on a nodal or antinodal line
1. Where y = the perpendicular distance from the point P to a point on the central antinodal line, d = the distance between the two light wave sources, m = the order value of the nodal line or antinodal line, and L = the distance from point P to the light wave sources,
Wavelength = (y*d) /(m*L)
2. In order to produce a stable interference pattern, the two light sources must be coherent.

Chapter 13: Light Reflection

Luminous Objects - generate their own light
Illuminated Objects - reflect light to our eyes
1. Without light, there is no sight.
2. The sun is luminous, and the moon is illuminated.
3. Objects emit or reflect light in a variety of directions.  The eye only sees the very small diverging cone of rays coming towards it.

Line of Sight - directing our sight in a specific direction
Incident Ray - light ray approaching a mirror
Reflected Ray - light ray reflected off the mirror
1. To view the image of an object in a mirror, sight along a line at the image.  One of the many rays of light from the object will approach the mirror and reflect along your line of sight.
2. For plane mirrors, the distance from the mirror to the object equals the distance from the mirror to the image.

Law of Reflection - when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection.
1. Light rays approaching a flat mirror follow the Law of Reflection.
2. Normal Line - perpendicular line to the surface of a mirror originating at the point of incidence
3. Angle of Incidence - angle between incident ray and normal line
4. Angle of Reflection - angle between reflected ray and normal line
5. Image Point of an Object - point behind a mirror in which the lines of sight of a reflected object converge.  This point is along the normal line behind the mirror, and the same distance from the mirror as the object is in front of the mirror.

Specular Reflection - reflection off smooth surfaces
Diffuse Reflection - reflection off rough surfaces, which have normal lines pointing in many directions

Image Location - one location in space where all reflected light appears to diverge from
1. The perpendicular distance from this image location to the mirror is equal to the perpendicular distance from the object location to the mirror; the image location and object location are directly across each other with the mirror in the middle.

Plane Mirror - image formation
1. Light emanates from an object in a variety of directions.
2. Some of this light reaches the mirror and reflects off the mirror.
3. Each of these rays can be extended backwards behind the mirror where they intersect at the image point.
4. A person who is positioned along the line of one of these rays can sight along the line and view the image.
5. In the case of plane mirrors, the image formed is a virtual image.
6. A virtual image is an image that is formed in a location where light does not actually reach.
7. A plane mirror image has left-right reversal.
8. A plane mirror image maintains actual dimensions, and is said to have a magnification of 1.
9. A person needs a plane mirror that is half their height to view their entire image.

Right Angle Mirrors - when two plane mirrors are joined at a right angle, they produce three images.
1. The outer two images exhibit left-right reversal.
2. The center image, which is a double reflection, has no left-right reversal.
3. As the angle decreases from 90 to 0 degrees, the number of images approaches infinity.

Spherical Mirrors - mirrors that have a spherical shape
1. Concave mirrors curve around the reflected object.
2. Convex mirrors curve away from the reflected object.
3. The center of curvature is the origin of the sphere.
4. The radius of curvature is the radius of the sphere.
5. The vertex is the center of the mirror.
6. The principal axis is the line from the center of curvature to the vertex.
7. The focal point is the midpoint on the principal axis.
8. The focal length is the distance from the mirror to the focal point, or R/2.
9. The focal point is the point in space that light rays meet after reflection.

Concave Mirror Reflection - light still follows law of reflection
1. If a light bulb is placed in front of a concave mirror behind the center of curvature, each ray of light that strikes the mirror will reflect according to the law of reflection.
2. After reflecting, the light will converge at a point where an image of the object is created.
3. Once the reflected light rays reach the image point, they diverge.
4. Any incident ray traveling parallel to the principal axis on the way to the mirror will pass through the focal point upon reflection.
5. Any incident ray passing through the focal point on the way to the mirror will travel parallel to the principal axis upon reflection.
6. When an object is more than one focal length from a concave mirror, a real image is formed; when an object is located less than one focal length from a concave mirror, a virtual image is formed; when an object is located at the focal point, no image is formed.
7. A real image can be projected onto a piece of paper.

Image Characteristics for Concave Mirrors - 5 cases
1. When an object is located beyond the center of curvature, the image will be between the center of curvature and the focal point; the image will be inverted, reduced in size, and real.
2. When an object is located at the center of curvature, the image will be located at the center of curvature as well; the image will be inverted, of equal size, and real.
3. When an object is located in front of the center of curvature, the image will be located beyond the center of curvature; the image will be inverted, magnified, and real.
4. When an object is located at the focal point, no image is formed.
5. When an object is located beyond the focal point, the image will be located on the opposite side of the mirror; the image will be upright, magnified, and virtual.

Mirror and Magnification Equations - provides numbers describing distance and object size
1. Where f = focal length, d₀ = object distance, and d_i = image distance,
1/f = 1/d₀ + 1/d_i
2. Where M = magnification, h_i = image height, and h₀ = object height,
M = h_i/h₀ = -(d_i/d₀)

Spherical Aberration - a problem with spherical mirrors
1. A spherical mirror cannot focus all the incident light from the same location on an object to a precise point, which results in blurry images.
2. Parabolic mirrors correct this problem.

Convex Mirror Reflection - an outer portion of a sphere that can reflect light
1. The centers of curvature and focal points are located behind convex mirrors.
2. Therefore, the focal length value is negative.
3. Convex mirrors are called diverging mirrors because light originating from the same point will reflect off the mirror and diverge.
4. Convex mirrors produce virtual images that are located behind the mirror.
5. Any incident ray traveling parallel to the principal axis towards a convex mirror will reflect in such a way that its extension will pass through the focal point.
6. Any incident ray traveling towards a convex mirror such that its extension passes through the focal point will reflect and travel parallel to the principal axis.
7. Convex mirrors always produce virtual images that are upright and reduced in size.

Chapter 14: Light Refraction

What happens when a light wave meets a boundary - similar to other wave refractions
1. Some of the wave will reflect off the boundary, and some of the wave will be transmitted into the new medium.
2. Both speed and wavelength will decrease.
3. The light is observed to change directions, and the bending of the path of light is called refraction.
4. Once the wave has passed across a boundary, it travels in a straight line.
5. Refraction is called a boundary behavior.
6. Light rays with arrowheads are drawn in a perpendicular direction to the wavefronts of the light wave.
7. The brain judges image location to be the location light rays appear to originate from.
8. The brain cannot account for the refraction of light.
9. Because light refraction occurs as light crosses a boundary and changes medium as it travels from the object to our eyes, visual distortions can occur.
10. In order for the direction of a light wave to change when crossing a boundary, the speed must change and the wave must approach the boundary at an angle.

Mechanism of energy transport by electromagnetic wave - how light waves are transported
1. An electromagnetic wave is produced by a vibrating charge.
2. As the wave moves through the vacuum of empty space, it travels at the speed of 3*10^8 m/s.
3. When the wave strikes a particle of matter, the energy is absorbed and sets electrons in the atoms into vibrational motion.
4. If the frequency of the electromagnetic wave does not match the frequency of the vibration of the electron, the energy is released in a new electromagnetic wave.
5. This wave has the same frequency of the original save and also travels at the speed of 3*10^8 m/s.
6. This phenomenon repeats, and the cycle of absorption and reemission continues as the energy is transported from particle to particle through the medium.
7. Because the process of being absorbed and reemitted by atoms takes time, the net speed of an electromagnetic wave in any medium is somewhat less than its speed in a vacuum.

Optical Density - the more optically dense a material is, the slower the wave will move through it
Index of Refraction - numerical index values expressed relative to the speed of light in a vacuum

Normal Line - line drawn perpendicular to the boundary at the point of incidence
1. If a ray of light passes across a boundary from a material in which it travels faster into a material in which it travels slower, the light ray will bend towards the normal line.
2. If a ray of light passes across a boundary from a material in which it travels slowly into a material in which it travels faster, the light ray will bend away from the normal line.

Least Time Principle - of all the possible paths that light might take to get from one point to another, it always takes the path that requires the least amount of time

Incident Ray - shows the direction light travels as it approaches the boundary
Refracted Ray - shows direction light travels after it has crossed over the boundary
Angle of Refraction - angle refracted ray makes with the normal line
1. Wherever the light speed changes most, the refraction is greatest.
2. For any given angle of incidence, the angle of refraction is dependent upon the speeds of light in each of the two materials.
3. These speeds are dependent upon the optical density and index of refraction values of the two materials.

Snell's Law - relates angles that the light rays make with the normal line on each side of a boundary
1. Where n_i = index of refraction of the incident medium, A_i = angle of incidence,
n_r = index of refraction of the refraction medium, and A_r = angle of refraction,
n_i*sine(A_i) =  n_r*sine(A_r)

Reflection - bouncing of a light wave off the boundary
Refraction - bending of the path of a light wave upon crossing a boundary
1. When a light wave reaches the end of a medium, it undergoes behaviors including reflection, transmission/refraction, and diffraction.

Point of Incidence - point where incident ray strikes the boundary
Angle of Incidence - angle between the incident ray and the normal line
Angle of Reflection - angle between the reflected ray and the normal line
Angle of Refraction - angle between the refracted ray and the normal line
Law of Reflection - When a light ray reflects off a surface, the angle of incidence is equal to the angle of reflection

Total Internal Reflection/TIR - reflection of the total amount of incident light at the boundary
1. There are two conditions necessary for TIR to take place.
2. The light must be in a more optically dense medium and approaching a less optically dense medium.
3. The angle of incidence must be greater than the critical angle.

Critical Angle - angle of incidence that provides an angle of refraction of 90 degrees
1. Where Ac = critical angle,  n_r = index of refraction of the refraction medium, and n_i = index of refraction of the incident medium,
Ac =  inverse-sine (n_r/n_i)

Dispersion - the separation of visible light into its different colors
1. Each color is characteristic of a distinct wave frequency.
2. The optical density of a material is the result of the tendency of the material's atoms to maintain the absorbed energy of a light wave in the form of vibrating electrons before reemitting that energy as a new electromagnetic disturbance.
3. Materials with higher index of refraction values hold onto the absorbed light energy for greater lengths of time.
4. The more closely the frequency of a light wave matches the resonant frequency of the electrons of the atoms of a material, the greater the optical density and the greater the index of refraction.
5. Index of refraction values are dependent on the frequency of light.

Angle of Deviation - amount of refraction caused by the passage of a light ray through a prism
1. The angle of deviation is the angle made between the incident ray of light entering the first face of the prism and the refracted ray that emerges from the second face of the prism.
2. The angle of deviation varies with wavelength.
3. Colors of the visible light spectrum with shorter wavelengths such as blue, indigo, and violet, will have deviated more from their original paths than colors with longer wavelengths such as red, orange, and yellow.

Rainbow - display of dispersion of light
1. To view a rainbow, your back must be to the sun, and you must look at a 40 degree angle above the ground into a region of the atmosphere with suspended droplets of water.
2. Each individual droplet acts as a tiny prism that disperses light and reflects it back to the eye.
3. Wavelengths of light associated with a specific color arrive at the eye from a collection of droplets.

Suspended Water Droplets - a refractor of light
1. Light waves decrease in speed upon entry into a water droplet, bending the path of light towards the normal line.
2. Upon exiting the droplet, the light speeds up and bends away from the normal.
3. Thus, the droplet causes a deviation in the path of light as it enters and exits.
4. There are countless paths by which light rays from the sun can pass through a drop.
5. One of these is the path in which light refracts into the droplet, internally reflects, and then refracts out of the droplet.
6. A light ray from the sun enters the droplet with a slight downward trajectory, and upon refracting twice and reflecting once, the light ray is dispersed and bent downward towards the earth's surface.
7. As with prisms with nonparallel sides, the refraction of light at two boundaries of the droplet results in the dispersion of light into a spectrum of colors.
8. The angle of deviation between the incoming light rays from the sun and the refracted rays directed to an observer's eyes is about 42° for red light and 40° for blue light.

Formation of the Rainbow - circle or half circle
1. The collection of suspended droplets in the atmosphere that are capable of concentrating the dispersed light at angles of deviation of 40-42° relative to the original path of light from the sun form a circular arc.
2. Every droplet in the arc is refracting and dispersing the entire visible light spectrum.
3. The red light is refracted out of a droplet at steeper angles towards the ground than the blue light.
4. When an observer sights at steeper angles with respect to the ground, droplets of water are refracting the red light to the observer's eye.
5. Bright sunlight, suspended droplets of water, and the proper angle of sighting are the three necessary components to seeing a rainbow.

Mirage - optical phenomenon that creates the illusion of water
1. On hot days, the illusion of a puddle of water can appear in the distance.
2. Mirages result from the refraction of light through a non-uniform medium.
3. Mirages occur on sunny days; the sun heats a roadway to high temperatures.
4. The roadway heats the surrounding air, keeping the air just above the roadway at higher temperatures.
5. Hot air is less optically dense than cooler air, and thus, a non-uniform medium has been created.
6. Light travels in a straight line through a uniform medium, but refracts when traveling through a non-uniform medium.
7. When a driver looks at the roadway at a low angle, or a position nearly one hundred yards away, light from objects above the roadway will follow a curved path to the driver's eye.
8. The light that is traveling downward into less optically dense air speeds up and changes direction.
9. The driver sighting downward at the roadway sees an object located above the roadway.
10. In order to make sense of this, the brain concludes that there is either a mirror on the road, there is a glass window on the road, or there is water on the road.

Lens - piece of transparent material that is shaped to form images
1. They are shaped in such a way that parallel incident rays converge to a point or diverge from a point.
2. A lens can be thought of as a series of tiny refracting prisms, each of which refracts light to produce their own image.
3. When these prisms act together, they produce a bright image.

Principal Axis - horizontal axis for lenses that are symmetrical across this line
Vertical Axis - vertical axis for lenses that are symmetrical across this line
Focal Point - point that light rays converge to or diverge from
2F Point - point on the principal axis twice as far from the vertical axis as the focal point is

Converging Lens - lens that converges rays of light that are traveling parallel to its principal axis
1. Converging lenses are thick across their middle and thin at their upper and lower edges.

Diverging Lens - lens that diverges rays of light that are traveling parallel to its principal axis
1. Diverging lenses are thin across their middle and thick at their upper and lower edges.

Double Convex Lens - lens that is symmetrical across both its horizontal and vertical axis
1. Each of the lens' two faces are shaped as part of a sphere.
2. A double convex lens is thicker across its middle and will converge rays of light that travel parallel to its principal axis.

Double Concave Lens - also symmetrical across both its horizontal and vertical axis
1. Each of the lens' two faces are shaped as if a sphere cut into them.
2. A double concave lens is thinner across its middle and will diverge rays of light that travel parallel to its principal axis.

Refraction Rules for a Converging Lens
1. Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
2. Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
3. An incident ray that passes through the center of the lens will continue in the same direction that it had when it entered the lens.

Refraction Rules for a Diverging Lens
1. Any incident ray traveling parallel to the principal axis of a diverging lens will refract through the lens and travel in line with the focal point.
2. Any incident ray traveling towards the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
3. Like with converging lenses, an incident ray that passes through the center of a diverging lens will continue in the same direction that it had when it entered the lens.

Converging and Diverging Lens Image Formation
1. Converging lenses can produce real and virtual images, while diverging lenses can only produce virtual images.
2. When a real image is formed, it appears to the observer as though light is diverging from the image location.
3. When the path of several light rays through a lens is traced, each will intersect at a point through the lens, and each observer must sight in the direction of this point to view the image of the object.
4. Diverging lenses created virtual images only because the refracted rays do not converge to a point; the image location is on the object's side of the lens where the refracted rays would intersect if extended backwards.
5. Objects that cannot be represented by a single point still form images as an observer sights at the object through a lens.

Converging Lenses and Object-Image Relations
1. When an object is placed in front of a double convex lens, let f represent the distance from the lens to the focal point.

2. If the object is located beyond 2f, the image will be between f and 2f on the other side of the lens.

    It will be inverted.

    It will be reduced in size.

    It will be a real image, meaning that light rays converge at the image location.

    Real images of can be projected on a piece of paper.

3. If the object is located at 2f, the image will be at 2f on the other side of the lens.

    It will be inverted.

    It will be exactly the same size.

    It will also be a real image.

4. If the object is located at the focal point, no image is formed because the light rays are travelling parallel to one another. 

5. If the object is located in between the lens and f, the image will be located on the same side as the object and further from the lens than the object.

    It will be upright.

    It will be enlarged.

    It will not be a real image, meaning that light rays do not pass through the image location.

    The image cannot be projected onto a piece of paper.

Diverging Lenses and Object-Image Relations

1. When an object is placed near a double concave lens, no matter where the object is placed, the image will be located on the same side as the object, upright, reduced in size, and not a real image. 

The Mathematics of Lenses

1. The relationship of the focal length (f), the object distance (d_o), and the image distance (d_i) is:

1/f = 1/d_o + 1/d_i

2. The magnification with image height (h_i) and object height (h_o) can be computed by

M = h_i/h_o = -(d_i/d_o)

3. If the lens is double convex (converging), f is +.

    If the lens is double concave (diverging), f is -.

    If the image is real and on the other side of the lens, di is +.

    If the image is virtual and located on the object's side of the lens, di is -.

    If the image is upright, and therefore virtual, hi is +.

    If the image is inverted, and therefore real, hi is -.

The Anatomy of the Eye

1. Like a camera, the eye can refract light and produce a focused image.

2. The eye is an opaque ball filled with water-like fluid.

3. The cornea is a thin transparent membrane that has an index of refraction of about 1.38.

4. After light passes through the cornea, some of it passes through the pupil.  The light that the pupil allows to enter is absorbed and doesn't exit the eye, so it appears black.

5. The size of the pupil opening can be adjusted by the dilation of the iris - the colored part of the eye.

6. Light that passes through the pupil opening will enter the crystalline lens.  The crystalline lens is made up of fibrous material and has an index of refraction of about 1.40.  It is attached to the ciliary muscles, which change the shape of the lens.

7. The inner surface of the eye is the retina, which contains the rods and cones that detect the intensity and frequency of incoming light.

8. An adult eye has up to 120 million rods and 6 million cones.  These rods and cones send nerve impulses to the brain, which travel through a network of nerve cells.  There are as many as one million neural pathways from the rods and cones to the brain.  This network of nerve cells forms the optic nerve at the back of the eyeball.

Image Formation and Detection

1. Most of the refraction of incoming light rays takes place at the cornea, not the lens.  The index of refraction of the cornea (1.38) is significantly greater than the index of refraction of surrounding air.  The cornea has the shape of a converging lens.  The bulging shape of the cornea causes it to refract light like a double convex lens.

2. The focal length of the cornea-lens system varies with the contractions of the ciliary muscles.  In general, the focal length is about 1.8 cm.  Because the object is typically located more than 2f from the lens, the image will be located between f and 2f, inverted, reduced in size, and real.

3. The cornea-lens system produces and image of an object on the retinal surface.  The reduction allows the image to fit on the retina.  The brain automatically makes the image right side up!

The Wonder of Accommodation

1. The ability of the eye to adjust its focal length is accommodation.

2. Because the nearby object is focused at a further distance, the eye assumes a lens shape with a short focal length.

3. For nearby objects, the ciliary muscles contract and squeeze the lens into a more convex shape, and for distant objects, the ciliary muscles relax and the lens returns to a flatter shape.

4. The power of a lens is measured in diopters.

    diopters = 1/focal length

5. A healthy eye is able to assume both a small and large focal length.  The maximum variation in the power of the eye is power of accommodation.  So if an eye can assume focal length of 1.80 cm to view objects many miles away and 1.68cm to view an object .25 meters away, its power of accommodation is 4 diopters.  The healthy eye of a young adult has a power of accommodation of about 4 diopters.

Farsightedness and its Correction

1. Farsightedness or hyperopia is the inability of the eye to focus on nearby objects.  This happens most frequently in older people because of the weakening of the ciliary muscles or the decreased flexibility of the lens.  This can also happen in young people if the eyeball is shortened.  On the retinal surface, where light-detecting nerve cells are located, the image is not focused.

2. The cure for farsightedness is the assistance of a converging lens.

Nearsightedness and its Correction

1. Nearsightedness or myopia is the inability of the eye to focus on distant objects.  This happens most frequently in young people because of a bulging cornea or elongated eyeball.  On the retinal surface, where light-detecting nerve cells are located, the image is not focused.

2. The cure for farsightedness is the assistance of a diverging lens.