• Shuffle
    Toggle On
    Toggle Off
  • Alphabetize
    Toggle On
    Toggle Off
  • Front First
    Toggle On
    Toggle Off
  • Both Sides
    Toggle On
    Toggle Off
  • Read
    Toggle On
    Toggle Off
Reading...
Front

Card Range To Study

through

image

Play button

image

Play button

image

Progress

1/431

Click to flip

Use LEFT and RIGHT arrow keys to navigate between flashcards;

Use UP and DOWN arrow keys to flip the card;

H to show hint;

A reads text to speech;

431 Cards in this Set

  • Front
  • Back
Average Acceleration
ΔV / Δt
Final Velocity
Vi + at
Displacement
ΔX = Vi*t + 1/2(at^2)
Final Velocity
Vf^2 = Vi^2 + 2aΔX
Average Velocity
1/2 (Vi + Vf)
Gravitational Force
F = (G*m1*m2)/r^2
Torque
τ = rFsinθ
Kinetic or Static Friction
F(friction)≤ μ * N
Centripital Acceleration
(velocity)^2 / (radius)
Centripital Force
Mass * Acceleration
or
(mass)(velocity)^2 / (radius)
Work
F d cosθ
Power
Work/time
Kinetic Nrg
KE = 1/2 (mass)(velocity)^2
Potential Nrg
U = mass * gravity * height
momentum
p = mass * velocity
Impulse
Δp = Force * time
or
m*Vf - m*Vi
Celsius
C = K -273
Thermal Expansion
ΔL = α L ΔT
Volume Thermal Expansion
ΔV = β V ΔT
Heat Gained (Q)
Q = m c Δt
Heat Gained (Δphase)
Q = m * L

(L=heat of transformation constant)
1st Law of Thermodynamics
ΔU = Q - W

(Q=heat nrg and W=work)
2nd Law of Thermodynamics
ΔS of closed system will increase or remain unchanged
Density
ρ = mass / volume
Pressure
P = Force / Area
Absolute Pressure
Pabs= Patm + ρgh
Two Pistons
F1/A1 = F2/A2
Boyant Force
FB= ρ g V (where V is the volume of the object and ρ is the density of the liquid)
Velocity in different areas of a pipe (volume flow rate)
A1V1=A2V2
Stress
F/A
Strain
ΔL/L
Y (Young's Modulus)
Y= (F/A) / (ΔL/L)
Coulomb's Law (Force b/n charges)
F = (k*q1*q2) / r^2
Electric Field
E = k*q / r^2
Force of E Field on a charge
F = q * E
Electric potential
V = kq / r
Electric Potential Nrg
U = qV

(charge * voltage)
Force of B Field on charge
q v B sinθ
Current
I = Δq / Δt
Force of Wire with current
F = I L B sinθ

(current*length*Bfield)
B field created by long straight wire
B = (μo*I) / (2πr)
B field created by loop wire
B = (μo * I) / (2r)
Voltage
V = IR
Power in circuits
P = IV
Resistors in series
Rs = R1 + R2 ...
Resistors in Parallel
1 / Rp = 1/R1 + 1/R2 ...
Capacitance
C = Q / V
E field b/n capacitor plates
E = V / d
Capacitors in series
1 / Cs = 1/C1 + 1/C2 ...
Capacitors in Parallel
Cp = C1 + C2 ...
Irms
Imax / sqroot2
Vrms
Vmax / sqroot2
Imax
Irms * sqroot2
Vmax
Vrms * sqroot2
Hookes Law (Force of spring)
F = -k x
angular freq of spring
ω = sq root (k/m)
angular freq of pendulum
ω = sq root (g/L)
Frequency
F = 1 / T

T=period
Period of Spring
T = 2π sqroot(m/k)
Period of Pendulum
T = 2π sqroot (L/g)
***
Velocity of wave
V = fλ
Speed of Light
c = 3x10^8
Intensity
I = Power / area
Object and image formula
1/o + 1/i = 1/f = 2/r
Focal length
F = radius curve / 2
Magnification
m = -image distance / object distance
or
-i / o
Index of Refraction
n = c / v
Snell's law of refraction
n1 sinθ1 = n2 sinθ2
Lens Power
P = 1 / f
Photon Nrg
E = h f
or
E = hc/λ

h= 6.6x10^-34 J*s
h= 4x10^-15 eV
Binding Nrg
E = Δm c^2
Alpha Particle decay
-4
-2
-Beta decay
+0
+1
+Beta decay (positron)
-0
-1
Gamma decay
nothing!!
1/2 life formula
Nf = Ni * e^(λt)
Capacitance
C = k*(perm. free space)* (A/d)

A=area
d=distance b/n plates
Work done by gas expansion
W = P*ΔV
Vector Quantity
Has magnitude and direction; and usually a unit of measure (The symbol is →) A vector can represent displacement, velocity, acceleration
Scalar Quantity
A quantity that is fully specified by giving its magnitude (mass or speed)
Are the following scalar or vector: 1) speed; 2) weight; 3) mass; 4) velocity
1) scalar; 2) vector; 3) scalar; 4) vector
Newton's First Law
A body at rest stays at rest and a body in motion stays in motion at constant velocity if no net force acts on it
Contrast Speed vs. Velocity
Speed has only magnitude. Velocity is a vector having magnitude and direction.
Equation for distance at constant velocity
see equation
Force
A vector quantity which is a push or pull exerted on a body.
Newton's Second Law
Newton's Second Law
Uniformly Accelerated Motion
Uniformly Accelerated Motion
Velocity Equation for Uniform Acceleration
Velocity Equation for Uniform Acceleration
Acceleration Equation
Acceleration Equation
Equation for final velocity with uniform acceleration
Equation for final velocity with uniform acceleration
Equation for average speed with constant acceleration (not starting from rest)
Equation for average speed with constant acceleration (not starting from rest)
Describe a force in terms of its components
A single force may be replaced by two or more forces (its component forces). These are vectors which, by using vector addition, add up to the original force.
Torque
The effectiveness of a force in producing rotation. Also called moment of force.
Newton's Law of Universal Gravitation
Two objects attract each other each other with a force that is proportionate to the product of their masses and inversely proportionate to the square of distance between them.
Center of Gravity
A point in or on the object where all the weight is concentrated. If supported only at this point the object will be in balance.
Equation for average speed with constant acceleration (starting from rest
Equation for average speed with constant acceleration (starting from rest
Inertia
The property by which an object resists being accelerated.
After 6 seconds, how far will a body fall in a vacuum (g=32)
After 6 seconds, how far will a body fall in a vacuum (g=32)
With acceleration constant at 10 m/s2 and an initial velocity of 3 m/s, how far will a body move in 7 s?
With acceleration constant at 10 m/s2 and an initial velocity of 3 m/s, how far will a body move in 7 s?
With an initial velocity of 4 ft/s and a constant aceleration of 7 ft/sec2, what is the velocity after 12 s?
With an initial velocity of 4 ft/s and a constant aceleration of 7 ft/sec2, what is the velocity after 12 s?
Formula for final velocity given the distance s, the acceleration a, and the initial velocity Vi.
Formula for final velocity given the distance s, the acceleration a, and the initial velocity Vi.
Which force is referred to in Newton's second law when there is more than one force on a body
The vector sum of all forces.
Newton's Third Law
When one object exerts a force on a second object, the second object exerts an equal and opposite force on the first (action equals reaction.)
Centripetal Force
The inward force that must be applied to keep a body moving in a circle
Equation for Centripetal Acceleration
Equation for Centripetal Acceleration
For liner motion with constant acceleration, what are the formulas for 1) distance, 2) velocity, 3) average velocity, 4) final velocity independent of time
For liner motion with constant acceleration, what are the formulas for 1) distance, 2) velocity, 3) average velocity, 4) final velocity independent of time
Frame of Reference
any system for specifying the precise location of objects in space. Your frame of reference is where you view the scene from. Ex. From a moving airplane or standing in your living room
Conservation of Momentum
In a closed system where no external forces act, the total momentum of the system is conserved.
Equation for Newton's Law of Gravitation
Equation for Newton's Law of Gravitation
Work; Equation for Work
The product of the force on an object and the distance the object moves in the direction of the force. W = Fd; W=work in joules; F=force in Newtons; d=distance in meters
Potential Energy; Equation for Potential Energy
The energy stored by an object because of its position or its condition. Ex. A skier on top of a mountain has potential energy. PE = wh = mgh; w=weight; h=object height; m=mass; g=constant gravitation; PE=potential energy
Kinetic Energy; Equation for Kinetic Energy
Kinetic Energy; Equation for Kinetic Energy
Equation for coefficient of sliding friction
Equation for coefficient of sliding friction
Equation for work against friction
Equation for work against friction
Power; Equation for Power
The measure of how much work gets done per unit time; measured in watts. 1 watt = 1 joule/sec; P=W/t = Fd/t; P=power (watts); W=work (joules); t=time in seconds; F=force in newtons; d=distance in meters.
Equation for Momentum
P = mv; m=mass; v=velocity; P=momentum
Line of Force
A line drawn so that a tangent to it at any point indicates the direction of an electric or magnetic field.
Normal Force
A force perpendicular to the surface of an object. When you press down on the object, the normal force presses up.
Hooke's Law
F = -(k)x; k=spring constant; x=distortion distance; F=distortion force
Equation for work done in stretching a spring
Equation for work done in stretching a spring
Equation for Change in Length when a solid expands or contracts
Equation for Change in Length when a solid expands or contracts
Archimedes Principle
The apparent loss in weight of an object immersed in a fluid equals the weight of the displaced fluid.
Bernoulli's Principle
The greater the velocity of a fluid, the smaller its pressure.
Equation for liquid pressure in a beaker
P=hdg; h=height of the liquid level; d=liquid density; g=gravitational constant; P=pressure
Two insoluble objects lose the same weight in a fluid, the objects must have the same…
Volume. Using Archimedes Principle: the apparent loss in weight is equal to weight of the displaced fluid. They displace the same volume.
Crest
A region of upward displacement in a transverse wave.
Trough
A region of downward displacement in a transverse wave.
Amplitude
The maximum displacement of a vibrating particle from its equilibrium position. The height of the wave.
Wavelength
In a periodic wave, the distance between two adjacent troughs or two crests (λ)
Transverse Wave
A wave in which the vibration are at right angles to the direction of propagation of the wave. Ex, electromagnetic waves.
Periodic Wave
A wave repeated in each of a succession of equal time intervals.
Longitudinal Wave
A wave in which the vibrations are parallel to the direction of propagation of the wave. Ex. Sound waves.
Hertz
The frequency of sound waves. 1 hz = 1 cycle per second.
Decibel
A unit of sound intensity level
Compression
The region of a longitudinal wave in which the vibrating particles are closer than their equilibrium distance.
Rarefaction
The region in a longitudinal wave where vibrating particles are farther apart than the equilibrium distance.
Beats
When two notes of slightly different frequencies reach the ear at the same time. A burst of sound followed by silence
Constructive Interference
When two waves make the medium vibrate in the same direction they reinforce and make a bigger disturbance
Destructive Interference
When two waves make a medium vibrate in opposite directions, they tend to cancel each other. This will result in a smaller wave or one that disappears completely.
Doppler Effect
When there is relative motion between a source of a wave and an observer, the frequency of vibrations received by the observer increases if the source and observer approach each other and decreases when the source and observer distance is increasing. Ex, the pitch of a siren changes as it approaches and passes you.
Law of Reflection
When a wave is reflected, the angle of incidence equals the angle of reflection.
Regular Reflection
from smooth flat surfaces, incident waves in the same plane are reflected in the same plane. Ex. A plane mirror
Diffuse Reflection
from rough and irregular surfaces, reflected light waves go in many directions. Ex. A piece of paper.
Concave Mirror
Reflecting surface is the inside of a spherical shell
Convex Mirror
Reflecting surface is the outside of a spherical shell
Equation for focal length of a spherical mirror
f=R/2; R=radius of the spherical shell; f=focal length
Angle of Incidence
Angle between the incident light and the normal to the reflecting surface
Angle of Reflection
Angle between the reflected light ray and the normal to the reflecting surface
Refraction
The bending of a wave on going into a second medium; eg, a light wave bends when going from air to water
Critical Angle
The limiting angle of incidence in the optically denser medium that results in an angle of refraction of 90 degrees
Snell's Law
Snell's Law
Convex Lens
A convex lens is thicker in the middle than at the edges; it is also called a converging lens
Concave Lens
A concave lens is thinner in the middle than at the edges; it is also called a diverging lens.
Focal Length
The distance from the principal focus to the lens or mirror
Index of Refraction
A measure of the angle or degree an electromagnetic wave bends when travelling from one substance to another. Ex. Put a pencil in a bowl of water, the pencil will appear bent because the light waves bend when going from water to air.
Lens Equation
1/p + 1/q = 1/r; p=object distance; f=focal length; q=image distance
Equation relating object and image sizes for lens.
Equation relating object and image sizes for lens.
Equation for telescopic magnification
Equation for telescopic magnification
Huygen's Principle
Each point on a wave front may be regarded as a new source of disturbance
Diffraction
the bending of a wave around obstacles
Polarized Light
Light whose direction of vibration has been restricted into one plane of vibration
Virtual Image
A mirror or lens image formed by the eye and brain which can not be projected on a screen. Ex, the image you see of yourself in the mirror
Equation for the Focal Length of a spherical mirror of radius R
F=R/2; F=focal length; R=radius
Formula for the Index of Refraction
Formula for the Index of Refraction
Formula for Coulomb's Law
Formula for Coulomb's Law
Equation for Electric Field Intensity
E = F/Q; E=electric field intensity; F= force exerted; Q=charge
Equation for Potential Difference between two points
V=W/Q; V=voltage (volts); Q=charge (coulombs); W=work (joules)
Parallel Circuit
Where resistors in a circuit are connected independent of each other. Circuit is in the form of several loops.
Series Circuit
Where resistors are connected so that the current flows from the tip of one to the tail of another
Formula for Current in a series circuit (Ohm's Law applied)
Formula for Current in a series circuit (Ohm's Law applied)
Formula for current in a parallel circuit (Ohm's Law applied)
Formula for current in a parallel circuit (Ohm's Law applied)
Formula for Resistance in a series circuit (Ohm's Law applied)
Formula for Resistance in a series circuit (Ohm's Law applied)
Formula for Resistance in a parallel circuit (Ohm's Law applied)
Formula for Resistance in a parallel circuit (Ohm's Law applied)
Formula for voltage in a series circuit (Ohm's Law applied)
Formula for voltage in a series circuit (Ohm's Law applied)
Formula for voltage in a parallel circuit (Ohm's Law applied)
Formula for voltage in a parallel circuit (Ohm's Law applied)
Formula for Ohm's Law
V = IR; V=voltage in volts; I = current in amperes; R=resistance in ohms
Law of Magnets
Like poles repel, unlike poles attract. North repels north; south repels south; north attracts south
Magnetic Field
The region where a magentic influence can be detected as a force on a magnet
Left-Hand Rule
Grasp the wire with the left hand so that the thumb will point in the direction of the electron flow; fingers will then direct towards flux lines.
Electromagnet strength depends upon which three things
1) The number of turns in the coil of the solenoid; 2) the nature of the core; 3) The current through the core.
Galvenometer
Instrument which measures low values of current.
Voltmeter
an instrument calibrated to measure the potential difference connected to its terminals.
Alternating Current (AC)
Current whose direction is constantly reversing. This is the type of current you get from the wall outlet.
Direct Current (DC)
Current whose direction is one path, never reversing. This is the type of current you get from a battery.
Inertia
Tendency of an object to remain in its present state of motion
Mass
Quantitative measure of an object's inertia

How much that object will resist a change in motion

Measure in kilograms (kg)
Weight
Gravitational force an object experiences when near a much larger body of mass

Measured in newtons (N)

Weight = mg

Weight and mass are proportional, but are not the same physical quantity
Center of mass
Single point of an object where mass is concentrated

Point through which a single force may be applied in any direction causing object to accelerate equally

Does not always coincide with geometric center
Center of gravity
Single point at which the force of gravity can be applied to the entire mass
4 Forces in nature:
1. Strong nuclear forces
2. Weak nuclear forces
3. Gravitational force
4. Electromagnetic force

Only last 2 forces are tested on the MCAT
Contact forces
Must act in at least 1 of 2 directions:
1. Perpendicular to surface (normal force)
2. Parallel to surface (requires friction)

Exception is tension, which can act in any direction away from object
Considered electromagnetic forces

Something must be making visible contact with system

Not do act at distance
Gravitational force
F = mg

Act at distance
Electromagnetic force
Requires charged object or a magnet

Act at distance
Newton's 1st law
Law of inertia

An object in a state of rest or in a state of motion will tend to remain in that state unless it is acted upon by a net force
Newton's 2nd law
F = ma
Newton's 3rd law
For every action there exist an equal and opposite reaction

Forces never act on same system
Newton's law of universal gravitation
Every mass in the universe exerts an attractive force on every other mass in the universe

F = Gm1m2/r^2

G = 6.67e^-11 m^3 kg^-1 s^-2

Gives magnitude of force but not direction
Normal force (Fn)
Force perpendicular to surface

Force of inclined plan pushing back against gravitational force

Normal force of inclined plane:
Fn = mgcos0

Normal force of curved surface:
Fn = mgcos0 + mv^2/r (centripetal force)
Net force of incline plane (no friction)
Fnet = mg + Fn

Fnet = mgsin0

Points directly along inclined plane
Circular motion
Object spinning or moving in circles
Centripetal acceleration
Ac = v^2/r

Always points toward the center of circle that is circumscribed by motion

Direction is always changing

Magnitude is always constant
Centripetal force
Fc = mv^2/r

Always points toward center of circle

Must be created by another force

Must be at least one of three forces:
1. Gravity
2. Electromagnetic
3. Contact
Acceleration down inclined plane
a = gsin0
2 Directions of contact force:
1. Normal force (Fn) is always perpendicular to contact surface
2. Frictional force is always parallel to contact surface
Friction
Cause by attractive molecular forces between contiguous surfaces

Opposes relation motion between surfaces
2 types of friction:
1. Static friction (Fs)
2. Kinetic friction (Fk)
Static Friction
Force opposing motion when 2 contiguous forces are not moving relative to each other

No sliding

Fs = uFn
Kinetic Friction
Force resisting motion once the 2 contiguous surfaces are sliding relative to each other

Yes sliding

Fk = uFn
Coefficients of friction (u)
Represent fractions of normal force that will equal static and kinetic frictional forces

Usually have a value less than 1

u(static) is greater than u(kinetic)
Drag
Air resistance

Type of friction

Fluid resistance to an object's motion through that fluid
Viscosity
Type of friction

Fluid's resistance to motion through itself
Tension
Force acting through a flexible object with no mass, such as a string or rope

Equal throughout rope as long as there is no friction acting on the rope

At any point in rope, there is tension force pulling in equal and opposite directions, but only use force pulling away from system

Replace rope with force vector acting on system
Hooke's Law
Force due to a compressed or stretched object

Force applied by most objects against a deforming force

F = -k(Xf - Xi)

Negative sign can usually be ignored

Usually refers to springs
Equilibrium
No translational (straight line) or angular (rotational) acceleration

All velocities are constant

Does not mean motionless

Sum of all forces acting on system equal to zero (ie. Net Force = 0)

Fup = Fdown
Fright = Fleft
Static Equilibrium
If all velocities are zero
Dynamic Equilibrium
If all velocities are constant and nonzero
Translational Equilibrium
Upward forces equal downward forces and rightward forces equal leftward forces
System not in equilibrium
Center of mass of system is accelerating translationally or its parts are accelerating rotationally

Sum Forces = ma

1. Write equations as if system in equilibrium
2. Add "ma" to side with less force
(all numbers should be positive)
Torque
Twisting force, clockwise or counterclockwise

T = Frsin0
F: force
r: position (distance from point of rotation to point of application of force)

T = Fl
F: force
l: lever arm
0: angle between force and position vectors
Point of Rotation
Any fixed point of your choosing

Center of mass
Lever arm (l)
Position vector is from point of rotation to point where force acts at 90 degress

T = Fl
How to solve Torque problems:
1. Fup = Fdown
2. Fright = Fleft
3. Tclockwise = Tcounterclockwise
Energy
Capacity to do work

Units:
1. joules (J) = kg m^2/s^2
2. electron-volt (eV)

Scalar

2 types:
1. mechanical
2. nonmechanical
Mechanical Energy
Kinetic energy and potential energy of macroscopic systems (system you can examine without a microscope)
Kinetic Energy (K)
Energy of motion

Any moving mass has kinetic energy

K = (1/2)mv^2
Potential Energy (U)
Energy of position

Several types:
1. gravitational potential energy (Ug)
2. elastic potential energy (Ue)
3. electric potential energy (Uelectric)
Gravitational Potential Energy (Ug)
Energy due to force of gravity

Ug = -Gm1m2/r
G: universal gravitational constant
m1 & m2: 2 masses
r: distance from 2 centers of gravity
neg sign: indicates energy decreases as distance decreases
Gravitational Potential Energy near Earth's surface
Ug = mgh
m: mass
g: gravity
h: height of object
Elastic Potential Energy (Ue)
Energy due to resistive force applied by deformed object

Follows Hooke's Law

Ue = (1/2) k (change in x^2)
k: Hooke's law constant
change in x: displacement of object from relaxed position
Law of Conservation of Energy
Since universe is an isolated system (mass nor energy is exchanged with environment), the energy of universe remains constant
2 types of energy transfer:
1. work (W)
2. heat (Q)
Work
Transfer of energy via a force

Scalar

Measured in units of energy (joules)

W = Fdcos0 (for all forces except friction)
F = force
d = displacement
0 = angle between F & d
Heat (Q)
Transfer of energy by natural flow from a warmer body to a colder body
Frictional Force
Change internal energy as well as mechanical energy

Therefore are not forces which can do work
Work = forces & no heat
W = (change in K) + (change in U) + (change in Ei)

Ei = internal energy, frictional energy
W = forces & no heat & no friction
W = (change in K) + (change in U)
Work-Energy Theorem
W = (change in K)

Only true when all energy transfer results on in change of K
1st Law of Thermodynamics
Energy is always conserved

Change in E = W + Q
Conservative Force
Mechanical energy is conserved within system. Net Work = zero.
Has potential energy associated with them
Types:
1. gravitational forces
2. hooke's law forces
3. electrical forces
4. magnetic field forces
Law of conservation of mechanical energy
When only conservative forces are acting, the sum of mechanical energies remains constant

K1 + U1 = K2 + U2 (no heat, only conservative forces)

0 = (change in K) + (change in U) (no heat, conservative forces only)
What work is done by a conservative force?
Consider conservative force is not part of system

1. W = Fdcos0
2. Calculate change in Ug
3. W = (Change in K) + (Change in U) + (Change in Ei) (do not include calculation of conservative force being questioned)

Technically conservative forces do not do work because energy is never lost no gained by system
Nonconservative forces
Forces that change mechanical energy of a system when they do work

types:
1. kinetic frictional forces
2. pushing and pulling forces

W = (change in K) + (change in U) (except for frictional forces, no heat)
Kinetic frictional forces
Increase internal energy of systems to which applied

Amount of work done by such a force does not go into changing mechanical energy

W = (Change in K) + (change in U) = (Change in Ei)

K = Ei
Power
Rate of energy transfer

Unit: watt (W) = J/s

P = (change in E)/t (E: energy = W + Q)

Rate at which force does work

P = W/t (work /time)
Instantaneous Power due to Force
P = Fvcos0
0: angle between F & v
v: velocity
F: force

Scalar
Momentum (p)
measure of a moving object's tendency to continue along its present path. closely related to inertia

p = mv (mass * velocity) in kg m/s

1. in an isolated system, momentum is always conserved
2. momentum is a vector

initial momentum of an isolated system is always equal to final momentum in magnitude and direction
M1V1 = M2V2
Elastic collisions
--- mechanical energy is conserved
--- no energy dissipates to internal energy
--- example is atomic collisions
--- conservation of mechanical energy
--- Uinitial + Kinitial = Ufinal + Kfinal
Inelastic collisions
--- lose some mechanical energy to internal energy
--- must use conservation of momentum to solve inelastic collision probelms
--- Pinitial = Pfinal

completely inelastic collision stick together
M1V1 + M2V2 = (M1+M2)V3
Px (initial) = Px (final)
Py (initial) = Py (final)
Reverse collisions
--- Objects start together and suddenly burst apart
--- Final and initial momentum are equal
--- Example is explosion or radioactive decay where species start from rest
--- in a 2 piece explosion, 2 pieces must separate in exactly opposite directions because of vector nature of momentum

M3V3 = M1V1 + M2V2
M1V1 = M2V2
Impulse (J)
--- equal to change in momentum
--- J = change in momentum
--- Force during time of collisions is not constant
--- Average force:
--- J = (Favg)(change in time)
--- Change in p = (Favg)(change in t)
--- If time over which collision occurs is increased, than force is decreased
Machines
mechanical devices that reduce force when doing work

ideal machines reduce force but don't change work

nonideal machines increase work because they increase internal energy through friction

3 machines:
1. ramp
2. lever
3. pulley
Ramp
W = mgh
work =mass*gravity*height
F = mgsin0
fraction by which we reduce the force must be equal to fraction by which we increase the length of the ramp

work is not changed
Lever
based on principle of torque
increases distance through which force acts
clockwise torque must equal counter-clockwise torque
T = Fl
torce=force * lever arm

work is not changed
Pulley
based on principle of ramp and lever

allows force to act on a greater distance and thus do same amount of work with less force

tension through a massless rope attached to a frictionless, massless pulley is constant

tension is the same at every point in the rope
Radioactive Decay
concerns atoms that spontaneously break apart
hydrogen does not undergo spontaneous decay
No atoms with more than 83 protons are considered stable
5 types:
1. alpha decay ---- 2. beta decay
3. positron emission (beta decay)
4. gamma ray production
5. electron capture (beta decay)
Half-life
--- predictable rate of decay of any substance (large group of identical atoms)
--- of time necessary for 1/2 of given amount of substance to decay
--- 4 variables:
1/2. initial and final amount of substance
3. # of half-lives (time period/half-life)
4. length of half-life
Alpha decay
alpha particle is a helium nucleus = 2 protons and 2 neutrons

an alpha particle is lost

mass number (A) decreases by 4

atomic number (Z) decreases by 2
Beta decay
expulsion of an electron

beta particle is an electron or a positron (an electron with a positive charge)

not the destruction of an electron, instead it is the creation of an electron and a proton from a neutron and the expulsion of the newly created electron

mass number (A) doesn't change
atomic number (Z) increases by 1
Positron emission
--- type of beta decay
--- emission of a positron when a proton becomes a neutron
--- a proton is transformed into a neutron and a positron is emitted
--- mass number (A) doesn't change
--- atomic number (Z) decreases by 1
Electron capture
capture of an electron along with the merging of that electron with a proton to create a neutron

a proton is destroyed and a neutron is created

mass number (A) doesn't change

atomic number (Z) decreases by 1
Gamma ray production
--- high frequency photon
--- has no charge and doesn't change the identify (atomic number, Z) of the atom from which it is given off
--- often accompanies other decay types
when an electron and a positron collide
--- mass number (A) and atomic number (Z) doesn't change
--- matter-antimatter collision (annihilation), where mass is destroyed releasing energy in the form of gamma rays
Rest mass energy
E = mc^2
E: energy
m: mass created or destroyed
c: speed of light (3e^8 m/s)

latent energy within the mass of an object

use when mass is created or destroyed
Mass defect
difference in masses before and after creation or destruction of mass
Fusion
combining of 2 nuclei to form a single heavier nucleus

binding energy increases, new bonds are more stable and stronger

large amount of energy is released, energy comes from mass defect

more energy was released in formation of stronger bonds than was absorbed in breaking of weaker bonds
Fission
splitting of single nucleus to form 2 lighter nuclei

large amount of energy is released, energy comes from mass defect
Fluid
---- liquid or gas
---- molecular bonds are constantly breaking and reforming due to high KE of molecules
---- molecules not arranged in any order or structure, move about in random directions, therefore has only temporal resistance to forces that are not perpendicular to its surface
---- can create permanent force outward, allowing resistance to forces perpendicular (normal) to surface
Density (p)
--- heaviness of a fluid
--- how much mass it contains in a specified volume
--- p = m/V p: density (kg/m^3)
--- intrinsic property, amount of substance will not change density
--- assume all liquids and solids are totally incompressible, meaning constant density
--- gases change their volume, and thus their density as per PV=nRT
Specific gravity (S.G.)
density of that substance compared to density of water

S.G. = p(substance)/p(water)
< 1: lighter than water
= 1: equally heavy as water
> 1: heavier than water
Density of water
p(water) = 1000 kg/m^3

p(water) = 1 mg/cm^3
Fluid pressure
pressure experience by object as result of fluid
results from impulse of molecular collisions
P = F/A
P(fluid pressure (pascals, Pa)) = F(avg force of collisions) * area
scalar, no direction
exists in fluid whether or not object is immersed in fluid
measure of KE due to random velocities of molecules within fluid distributed over fluid volume
type of stored energy per unit volume
Fluid at rest
--- experiences only forces perpendicular to its surface, --- normal force and gravitational force
--- fluid at rest, uniform density, sealed container
P = pgy P(fluid pressure) = p(density) * gravity * y(fluid depth)
--- additional fluids on top of 1st fluid, add their weight
Ptotal = p1gy1 + p2gy2 + p3gy3
--- open container, must add atmospheric pressure to fluid
P = pgy + P(atm) P(atm) = 101,000 Pa
Gauge pressure
measure of pressure compared to local atmospheric pressure (given value of zero)

example:
negative pressure created in your chest when you breathe, higher Patm pushes air into lungs

suck through a straw, create vacuum inside straw and Patm pushes down on fluid outside straw, pushing fluid up inside straw
Absolute pressure
pressure measured relative to a vacuum (zero)

Pabs = Pgauge + Patm
Pascal's principle
pressure applied anywhere to an enclosed incompressible fluid, will be distribute undiminished throughout fluid

does not apply to gas, because gas is compressible
Hydraulic lift
machine that works via Pascal's principle

does not change work, but decreases distance through which force is applied

piston 1 applies P to incompressible fluid, which transfers to piston 2 undiminished, since piston 2 has greater area than piston 1, force on piston 2 is greater
Archimede's principle
object submerged in fluid displaces volume of fluid equal to its own volume

buoyant force is an upward force acting on submerged object and is equal to weight of fluid displaced by submerged object
Buoyant force
before submerged, upward force on fluid that it will displace must equal weigh of fluid

Fb = mg(water)
upward force acts on submerged object

Fb = p(fluid)Vg
Fb(buoyant force) = p(density of fluid) * (volume displaced) * (gravitational constant)

due to difference in pressure, therefore doesn't change with depth
fully submerged object displaces its volume in fluid
Floating object
displaces amount of fluid equal to its own weight

submerged fraction of floating object equals ratio of object density to fluid density in which object is floating

if in water, ratio is S.G. of floating object

Fraction submerged = p(object)/p(fluid)

floating object displaced its weight in fluid
Center of buoyancy
point where buoyant force acts

point where center of mass would be if object had uniform density

if center of mass and center of buoyancy do not coincide (object is not uniformly dense) then torque will result and cause object to spin
molecules of moving fluid
1. random translational motion
2. uniform translational motion
Random translational motion
contributes to fluid pressure as in a fluid at rest
Uniform translational motion
shared equally by all molecules at a give location in a fluid

motion of fluid as a whole

doesn't contribute to fluid pressure
ideal fluid
1. no viscosity (tendency to resist flow)
2. incompressible, uniform density, constant volume
3. no turbulence, steady flow, same velocity
4. irrotational flow, object moving with fluid will not rotate
5. constant Q (flow rate)
Continuity equation
Q = Av
Q: volume flow rate = rate at which volume passes through pipe
A: cross-sectional area of pipe
v: velocity of fluid flow, v = d/t
Bernoulli's equation
K = P + pgh + 1/2pv^2
K: constant specific to fluid
P: pressure
h: height
v: velocity
p: density

given one continuous ideal flow, the sum of its 3 terms is a constant at any point in the fluid

describes conservation of energy within an ideal fluid
Direction of fluid flow
Change P = QR
P: pressure
Q: flow rate
R: resistance to flow
surface tension
intensity of intermolecular forces per unit length

reason why needle (more dense) floats on surface of water

not buoyant force because no water is displaced

responsible for formation of water droplets

higher the temperature, weaker the surface tension because less intermolecular forces
Capillary action
fluid is pulled up a thin tube

1. intermolecular forces responsible for surface tension (cohesive forces)
2. forces between molecules of tube and fluid (adhesive forces)

> cohesive forces = convex & fluid pulled down
> adhesive forces = concave & fluid pulled up
Stress
force applied to object divided by area over which force is applied

same units as pressure (N/m^2, not Pa)

Stress = F/A

done to an object
Strain
fractional change in object's shape

ratio of change in dimension compared to original dimension

no units

Strain = change dimension/original dimension

how object responds to stress
Modulus of elasticity
stress and strain are proportional to each other

Modulus of elasticity = stress/strain

up to a max (yield point, still intact, deformation), modulus of elasticity is constant for specific substance

fracture point, object breaks
3 types of moduli
1. young's modulus (E)
2. shear modulus (G)
3. bulk modulus (B)
Young's modulus (E)
tensile stress

E = (F/A)/(change h/h)
h: height
Shear modulus (G)
shear stress

G = (F/A)/(change x/h)
x: length
h: height
Bulk Modulus (B)
compression and expansion

B = (change P)/(change V/V)
P: pressure
V: volume
Equations for fluids at rest
p = m/V

P = F/A

S.G. = p(substance)/p(water)

P = pgy

Fb = pVg
Equations for fluids in motion
Q = Av

K = P + 1/2pv^2 + pgh

v = square root (2gh)
Equations for Solids
Modulus of elasticity = stress/strain
wave
transfer of momentum and energy from one point to another

3 types:
1. mechanical
2. electromagnetic
3. matter
Mechanical waves
obey law of classical physics

require some medium through which to propogate

non dispersive medium is momemtarily displaced by wave and then returned to its position

2 types:
1. transverse wave
2. longitudinal wave
transverse wave
medium is displaced perpendicularly to direction of wave propagation

ex:
wave on a string

can be represented by sine function (vertical displacement of medium with respect to time or displacement of wave)
longitudinal wave
medium displaced parallel to direction of wave propagation

ex:
sound wave in air

can be represented by sine function (change in pressure or horizontal displacement of medium with respect to time or displacement of wave)
wavelength
if x-axis is displacement of wave, it is measured from any point in wave to point where wave begins to repeat itself

ex: trough to trough or peak to peak

units of meters
wave
transfer of momentum and energy from one point to another

3 types:
1. mechanical
2. electromagnetic
3. matter
Mechanical waves
obey law of classical physics

require some medium through which to propogate

non dispersive medium is momemtarily displaced by wave and then returned to its position

2 types:
1. transverse wave
2. longitudinal wave
transverse wave
medium is displaced perpendicularly to direction of wave propagation

ex:
wave on a string

can be represented by sine function (vertical displacement of medium with respect to time or displacement of wave)
longitudinal wave
medium displaced parallel to direction of wave propagation

ex:
sound wave in air

can be represented by sine function (change in pressure or horizontal displacement of medium with respect to time or displacement of wave)
wavelength
if x-axis is displacement of wave, it is measured from any point in wave to point where wave begins to repeat itself

ex: trough to trough or peak to peak

units of meters
frequency (f)
number of wavelengths that pass a fixed point in 1 second

measured in hertz (Hz) or cycles/sec (1/s)
velocity
product of wavelength and frequency

v = wf

dictated by medium through which wave travels

change in frequency or wavelength does not change velocity of wave
period (T)
reciprocal of frequency

number of seconds required for 1 wavelength to pass a fixed point

where x-axis is time, any point on wave to next point where wave begins to repeat itself

T = 1/f
amplitude (A)
maximum displacement from zero

always positive
medium
only thing that affects velocity

1. medium's resistance to change in shape (elasticity)
2. medium's resistance to change in motion (inertia)

for a gas, velocity always increases with temperature

elastic component stores PE

inertial component stores KE
intensity (I)
power of waves

rate at which waves transfer energy

units of W/m^2

proportional to A^2 and f^2
decibels (dB)
dB = 10log (I/Io)
dB: decibels
I: intensity
Io: threshold intensity of human hearing

I > 10X, dB > 10
I > 10^2, dB > 20
I > 10^3, dB > 30
I > 10^4, dB > 40

ex: I > from 30 to 3000, dB > 20 (added 2 zeros to I, so add 20 to dB)
phase
relates to its wavelength, frequency, place and time of origin

horizontal shift of a wave on a graph

in phase: same wavelength & begin at same point

out of phase: same wavelength & different distances but arrive at same point
constructive interference
waves occupy same space and superposition occurs

sum of displacements results in greater displacement
destructive interference
occurs when sum of displacements results in smaller displacement
beats
2 waves with slightly different frequencies are superimposed

at some points waves will experience constructive interference and at others destructive interference

points will alternate with frequency equal to difference between frequencies of original 2 waves

alternating increase and decrease in noise intensity
pitch correlates to frequency: high note = high pitch = high frequency
fbeat = |f1 - f2|
wave reflection
if wave reflects off denser medium, wave is inverted

if wave reflects off less dense medium, wave is upright

when wave reflects from 1 medium to the next, wavelength changes but frequency remains the same
Node
2 waves traveling in opposite directions with same wavelength, point of intersection has zero displacement
antinode
2 waves traveling in opposite directions with same wavelength, point of maximum constructive interference, greatest amplitude
standing wave
string holds still at nodes and moves violently up and down at antinodes

endless sine waves, with same wavelength, traveling in opposite directions
harmonic series
list of wavelengths from largest to smallest of possible standing waves

harmonics are number from longest to shortest wavelength
1st harmonic (fundamental wavelength)
longest wavelength

created with fewest number of nodes = 2

distance from 1 wall to other is 1/2 wavelength

each successive harmonic is created by adding a wavelength
pipe open or closed at both ends or string tide at both ends
L = (nfn)/2 (n= 1, 2, 3, etc)
L: distance between 2 ends of string
n: number of harmonic
both ends are nodes
pipe open or closed at 1 end or string tide at 1 end
L = (nfn)/4 (n= 1, 3, 5, etc)
L: distance between 2 ends of string
n: number of harmonic
one end is an antinode
resonate
--- standing waves cause string to resonate
--- vibrate at its natural frequency or resonant frequency
--- v = fw (velocity = resonant frequency * wavelength)
--- velocity is constant for a given medium
--- at resonant frequency, structure experiences maximum vibration velocities and displacement amplitudes
resonance
situation where natural frequency and driving frequency are equal
simple harmonic motion
- sinusoidal function
- acceleration is proportional to displacement but opposite in sign
- acceleration and displacement are related by f^2
- oscillation between KE and PE, no energy is lost to surroundings
- ex: mass bouncing on end of massless spring OR pendulum swinging at a small angle OR plant's orbit

WACK'EM: w = square root (k/m)
angular frequency for mass on a string
WIGGLE: w = square root (g/L)
angular frequency for pendulum
doppler effect
results because waves are unaffected by speed of source with produces them

(change f/fs) = v/c
frequency/frequency source = (relative velocity) * (wave velocity

(change w/ws) = v/c
wavelength
Wave equations
v = fw

T = 1/f
Sound equations
dB = 10log(I/Io)

fbeat = |f1 - f2|

L = (nwn)/4 (n= 1, 3, 5, etc)

L = (nwn)/2 (n= 1, 2, 3, etc)
Doppler effect equations
(fo - fs)/fs = v/c

(wo - ws)/ws = v/c
charge
--- positive and negative charge
--- current runs in opposite direction of electrons
--- charge = q (units of coulombs C)
--- it is quantized, which means any charge must be at least as large as certain smallest unit
--- smallest unit of charge, e = 1.6e-19 C = charge of 1 electron or proton
--- opposite charges attract each other, like charges repel each other
universal law of conservation of charge
universe has zero net charge

net charge is created by separating electrons from protons

anytime a positive charge is created, a negative charge is created as well
Coulomb's law
formula describing magnitude of force of repulsion or attraction between 2 charged objects

analogous to gravitation force formula

F = kq1q2/r^2
k: coulomb constant = 8.988e9
q: respective charges
r: distance between centers of charge

force due to gravity is negligible compared to force due to charge
center of charge
point from which charge generated by object or system can be considered to originate
field
man-made concept designed to explain action at a distance

forces created by fields can act at a distance
lines of force
--- can represent any field
--- lines point in direction of field
--- positive to negative for electric field
--- towards the mass creating the field for gravitational fields
--- relative distance between lines indicate strength of field
--- no lines of forces inside a uniformly charged sphere
electric field (E)
electrostatic force per unit charge

vector point in direction of field

units of N/C or V/m
electric field of point charge
E = kq1/r^2

system of point charges:
summing (vector addition) of each electric field for each charge
force on charge in electric field
F = Eq
F: force
E: electric field
q: charge
potential energy (U) of charge in electric field
U = Eqd
U: potential energy
E: electric field
q: charge
d: displacement
electric potential energy
U = kq1q2/r
U: electric potential energy
k: coulomb constant
q: charge
r: distance between charges
voltage (V)
potential of the field

potential for work by an electric field in moving any charge from 1 point to another

V = Ed
V: voltage (volts, V), scalar or J/C
E: electric field
d: displacement
voltage due to point charge
V = kq1/r

voltage due to group of point charges:
voltage due to each individual charge is summed directly
work due to electric field
W = mgh

W = qEd
equipotential surfaces
all points are same voltage

surface normal to field that describes set of points all with same potential
electric dipole
created by 2 opposite charges with equal magnitude
conductors
allow electrons to flow relatively freely

good conductors of electricity, poor resistors

such as metals
resistors
poor conductors

hold electrons tightly in place

such as: networks solids such as diamond and glass
induction
ability to charge a conductor because of easy flow of electrons

1. if negatively charged object is moved close to electrically insulated conductor, electrons on conductor will repel to opposite side
2. touch conductor with 2nd conductor, electrons will repel further and move to 2nd conductor
3. remove 2nd conductor, 1st conductor has less electrons than protons (induced positive charge)
current
moving charge

given in amps (A) or C/s

scalar, flow in direction of movement of positive charge

because electrons were designated as negative charge, current created by flowing electrons is in opposite direction of flow of electrons

flow of electrons resembles fluid flow
circuit
cyclical pathway for moving charge
resistivity (p)
quantitative measure of property that all substances resist flow of charge
resistance (R)
quantitative measure of an object of a particular shape and size to resit flow of charge

measured in ohms
Ohm's law
product of resistance and current

V = IR
V: voltage (gh)
I: current
R: resistance
Kirchoff's 1st rule
amount of current flowing into a node must be same amount that flows out

rate at which fluid flows into an intersection much match rate at which fluid flows out
node
any intersection of wires
kirchoff's second rule
voltage around any path in a circuit must sum to zero
electromotive force (EMF)
not a force, but instead voltage provided by battery
capacitor
used to temporarily store energy in a circuit

stores it in the form of separated charges
parallel plate capacitor
2 plates made from conductive material are separated by a very small distance

on a charged capacitor, 1 plate holds positive charge and the other holds same amount of negative charge

separation of charge creates electric field that is constant
capacitance
ability to store charge per unit voltage

something with high capacitance can store a lot of charge at low voltage

C = Q/V
C: capacitance
Q: charge of plate
V: votlage
energy stored by capacitor
U = 1/2QV
U = 1/2CV^2
U = 1/2Q^2/C
U: energy stored
Q: charge
V: voltage
C: capacitance
dielectric constant (K)
acts to resist creation of electric field, allowing capacitor to store more charge (greater capacitance)

higher K means greater capacitance
Kvacuum = 1

limits value of possible voltage across plates, at max voltage K will breakdown and conduct electricity

work is done on K and energy is stored in K
Series
components lined up in row, like train cars

any 2 components not separated by a node
parallel
single components in alternate paths connecting same node
resistor in series
total resistance (effective resistance, Reff) is sum of resistances

Reff = R1 + R2 + R3 + ...
Resistor in parallel
1/Reff = 1/R1 + 1/R2 + 1/R3 + ...
Capacitors in series
1/Ceff = 1/C1 + 1/C2 + 1/C3 +...
Capacitors in parallel
Ceff = C1 + C2 + C3 + ...
Power
same quality as mechanical power

P = IV
P = I^2R
P = V^2/R

rate at which heat is generated by current as it flows through resistor is equal to power dissipated
Direct current (DC current)
net movement of electrons is in one direction around circuit
Alternating current (AC current)
created by oscillating electrons back and forth in simple harmonic motion

voltage or current can be described by sine wave

since movement of electrons creates power regardless of direction, electrons do not have to be driven in one direction

current commonly used in home outlets
Max current
occurs when electrons are at max velocity

Imax = square root (2Irms)
Imax: max current
Irms: root mean square current
Max voltage
Vmax = square root (2Vrms)
Vmax: max voltage
Vrms: root mean square voltage
RMS
root mean square

square root of average of squares

square all terms, take average, then take square root

average value of sine wave = 0

Vrms = 120V --> Vmax = 170V
magnetic fields (B)
--- generated by moving charge, which experiences force when moving through a magnetic field
--- similarities to electric fields, measured in units of Telsa (T)
--- north and south poles; like poles repel and opposite poles attract, poles never exist separately
--- can be represented by lines of force, point from N to S pole (earth's magnetic field points in opposite direction)
Right hand rule (RHR)
predicts direction of magnetic field due to current carrying wire

thumb: direction of current
fingers: grab wire, direction in which fingers wrap around wire is direction of magnetic field
force experience by charge moving through magnetic field
F = qvBsin0 = mv^2/r (find radius of curvature)
F(force) = q(charge) * v(velocity) * (B)magnetic field) * sin 0( angle between magnetic field and velocity)

--- force is directed perpendicularly to both velocity and magnetic field, therefore does not work, leaving only 2 possible directions for force
--- RHR
thumb: direction of moving positive charge
fingers: direction of magnetic field
palm: direction of force
negative charge reverses direction of force
Faraday's law of induction
a changing magnetic flux induces an EMF (E) and a current, which creates an induced magnetic field

forces due to induced electric field (EMF) are nonconservative, thus mechanical energy is transferred to internal energy
Lenz's law
induced current will create a magnetic field opposing induced magnetic field
electric fields due to point charge equations
F = kq1q2/r^2

U = kq1q2/r

E = kq1/r^2

V = kq1/r
constant electric fields equations
F = Eq

U = qEd = Fd = Vq

V = Ed
Resistors equations
V = IR

P = IV
P = I^2R
P = V^2/R

Series:
Reff = R1 + R2 +...

Parallel:
1/Reff = 1/R1 + 1/R2 +...
Capacitors equations
C = Q/V

U = (1/2)QV
U = (1/2)Q^2/C
U = (1/2)CV^2

Series:
1/Ceff = 1/C1 + 1/C2 +...

Parallel:
Ceff = C1 + C2 +...
AC current equations
Vmax = square root (2Vrms)

Imax = square root (2Irms)
magnetism equations
F = qvBsin0
Electromagnetic wave
traveling oscillation of an electric and a magnetic field

fields are perpendicular to each other and directions of propagation is perpendicular to both fields

it is a transverse wave

generated by acceleration of electric charge
Speed of electromagnetic wave (c)
constant speed and always equal to ratio of magnitudes of electric field and magnetic field

c = E/B

energies of 2 fields are equal
Poynting vector (S)
describeds the rate and direction in which an electromagnetic wave is transporting energy per unit area

always perpendicular to both E and B

has a magnitude of EBsin0
Light
tiny sliver from the electromagnetic spectrum
visible light
includes wavelengths from 390 to 700 nm

shorter wavelengths correspond to violet light and longer wavelengths to red light
ultraviolet light
just beyond visible spectrum on smaller wavelength side
infrared
just beyond visible spectrum on longer wavelength side
colors of visible spectrum
Roy G. Biv

Red, orange, yellow, green, blue, indigo, violet

wavelengths toward violet have more energy
index of refraction (n)
constant for the medium light propagates through

n = c/v
n( index of refraction) = c(speed of light in vacuum) / v(speed of light in medium)

--- since nothing exceeds the speed of light in a vacuum, all media have an index of refraction greater than 1
--- the greater the index of refraction, the slower light moves through that medium

n for water = 1.3
n for glass = 1.5
plane-polarized light
light with electric fields in one particular direction as a result of screening out photons not have an electric field in one particular direction (filter)
isotropic light
unpolarized light, white light

electric fields point in all directions

when polarized, it loses 1/2 of its intensity
dual nature
acts both as a wave and a particle

propagation properties can be described with wave theory

energy transformation properties are best described by particle theory
angle of incidence
angle at which light ray strikes the interface as measured from a line normal to the interface

equals angle of reflection
angle of reflection
angle at which light ray reflects off of interface as measured from a line normal to the interface

equals angle of incidence
angle of refraction
angle at which light ray refracts through the interface as measured from a line normal to the interface

given by Snell's law: n1sin01 = n2sin02
Snell's law
gives you angle of refraction

n1sin01 = n2sin02
Energy of a single photon
E = hf
E: energy of single photon
h: planck's constant
f: frequency

when light crosses into a new medium, frequency remains the same and wavelength changes
total internal reflection
occurs when light coming from a medium with higher index of refraction, causes angle of incidence to be so large that entire amount of photons will be reflected at the angle of reflection and none will refract

this angle of reflection is the critical angle
critical angle
angle at which light reflects when there is total internal reflection (no refraction)

0critical = sin^-1(n2/n1)
0critical: critical angle
n: index of refraction
refraction of different waves at interface
longer wavelengths (lower frequencies) move faster through a medium and therefore bend less at interface

shorter wavelengths (higher frequencies) move slower through medium and therefore bend more at interface
diffraction
--- another type of wave-bending phenomenon
--- when wave moves through a small opening, it bends around the corners of that opening
--- the smaller the opening and the larger the wavelength, the greater the diffraction
--- smaller the hole the greater the spreading of light
--- results in an image of light and dark bands or in dispersion and the creation of colors (depend upon destructive and constructive interference)
virtual image
does not actually exist outside the mind of the observer

no light rays emanate from virtual image

if a sheet of white paper is placed at the position of a virtual image, no image will appear on the paper

ex: reflection in a flat mirror, a mirage, image under water
real image
exists separately from the observer

rays of light actually intersect and then emanate from the point of intersection to form a real image

if a sheet of white paper is placed at the position of a real image, the image will appear on the paper
two types of mirrors
1. convex
2. concave
two types of lenses
1. diverging (concave), acts like convex mirror
2. converging (convex), acts like concave mirror (3Cs: a thiCk Center Converges light)
radius of curvature
for small section of curve is radius of extended circle

smaller radius of curvature indicates a sharper curve
focal point
where light from horizontal rays is reflected by concave mirrors (or refracted by converging lenses) to focus on a single point

varies with frequencies
focal length
--- length of separation between mirror or lens and the focal point
--- it is related to radius of curvature

fmirror = 1/2r
fmirror( focal length) = 1/2 (radius of curvature(

--- focal point for a lens (flens) is affected by the refractive indices of the lens and the medium that the lens is in
--- flens is also affected by radii of curvature of both sides of the lens
lens maker's equation
1/flens = [(n1/n2)-1][(1/r1)-(1/r2)]

when n1=n2, lens will not refract light
power
measured in diopters, which has equivalent units of m^-1

the inverse of the focal length

P = 1/f
P: power
f: focal length of lens
lateral magnification (m)
ratio of size of image to size of object (compare heights)

equal to negative of ratio of distance of image and distance of object from mirror or lens

negative sign indicates that if both distances are positive, than the image is inverted

m = -(di/do) = (hi/ho)
m(magnification) = di(distance of image) / do(distance of object) = hi(height of image) / ho(height of object)
thin lens equation
for any mirror or lens, distance of image is related to focal length and distance of object

(1/f) = (1/do) + (1/di)
focal length --- object distance --- image distance

--- applies to mirrors as well
--- all measurements are given positive or negative values based upon their position relative to the mirror or lens
1st rule of mirrors and lenses
draw an eye where observer will stand, and label side: positive, real and inverted (PRI)

"I (eye) am positive that real is inverted"

images on side opposite the eye, are: negative, virtual and upright (NVU)
2nd rule of mirrors and lenses
front of mirror is side that I (eye) am on

back of lens is side that I (eye) am on (stand behind camera to view object)

objects are always positive when they are in front of a lens or mirror and always negative when they are behind a lens or mirror
3rd rule of mirrors and lenses
if object is in front:
convex mirrors and diverging lenses make negative, virtual and upright images (NVU)

concave mirrors and converging lenses make positive, real and inverted images (PRI), except when object is within the focal distance, in which case, they make a negative, virtual and upright image (NVU)
concave mirror and converging lens
f is always positive
convex mirror and divergent lens
f is always negative
lateral magnification of a 2 lens system
product of lateral magnification of each lens

M = m1m2
Effective power of 2 lenses in contact with each other
equal to sum of their individual powers

Peff = P1 + P2
Electromagnetic radiation equations
c = f (wavelength)
c(speed of light) = frequency * wavelength

n = c/v
n(refractive index) = (speed of light in vacuum) * v(speed of light in medium)

E = hf
E:(energy of one photon) = h(planck's constant * freq

n1sin01 = n2sin02
n: refractive index
Mirrors and lenses equations
fmirror = (1/2)r
(focal length of mirror) = 1/2 * (radius of curvature)

P = 1/f
power = 1/focal length

(1/f) = (1/di) + (1/do)
f: focal length --- distance (image and object)

m = -(di/do) = hi/ho
m(magnification) --- height (image and object)