# Objectives
for the AP Physics Courses B

**I.
NEWTONIAN MECHANICS**

**A.
Kinematics**

**1.
Motion in One Dimension **

a)
Students should understand the general relationships among position,
velocity, and acceleration for the motion of a particle along
a straight line, so that:

(1)
Given a graph of one of the kinematic quantities, position, velocity,
or acceleration, as a function of time, they can recognize in
what time intervals the other two are positive, negative, or
zero, and can identify or sketch a graph of each as a function
of time.

(2)
Given an expression for one of the kinematic quantities, position,
velocity, or acceleration, as a function of time, they can determine
the other two as a function of time, and find when these quantities
are zero or achieve their maximum and minimum values.

b)
Students should understand the special case of motion with constant
acceleration so that they can:

(1)
Write down expressions for velocity and position as functions
of time, and identify or sketch graphs of these quantities.

(2)
Use the equations , ,
and to
solve problems involving one-dimensional motion with constant
acceleration

**2.
Motion in Two Dimensions **

a)
Students should know how to deal with displacement and velocity
vectors so they can:

(1)
Relate velocity, displacement, and time for motion with constant
velocity.

(2)
Calculate the component of a vector along a specified axis, or
resolve a vector into components along two specified mutually
perpendicular axes.

(3)
Add vectors in order to find the net displacement of a particle
that undergoes successive straight-line displacements.

(4)
Subtract displacement vectors in order to find the location of
one particle relative to another, or calculate the average velocity
of a particle.

(5)
Add or subtract velocity vectors in order to calculate the velocity
change or average acceleration of a particle, or the velocity
of one particle relative to another.

b)
Students should understand the general motion of a particle in
two dimensions so that, given functions x(t) and y(t) which describe
this motion, they can determine the components, magnitude, and
direction of the particle's velocity and acceleration as functions
of time.

c)
Students should understand the motion of projectiles in a uniform
gravitational field so they can:

(1)
Write down expressions for the horizontal and vertical components
of velocity and position as functions of time, and sketch or
identify graphs of these components.

(2)
Use these expressions in analyzing the motion of a projectile
that is projected above level ground with a specified initial
velocity.

**B.
Newton's Laws of Motion**

**1.
Static Equilibrium (First Law) **

a)
Students should be able to analyze situations in which a particle
remains at rest, or moves with constant velocity, under the influence
of several forces.

**2.
Dynamics of a Single Particle (Second Law) **

a)
Students should understand the relation between the force that
acts on a body and the resulting change in the body's velocity
so they can:

(1)
Calculate, for a body moving in one direction, the velocity change
that results when a constant force F acts over a specified time
interval.

(2)
Determine, for a body moving in a plane whose velocity vector
undergoes a specified change over a specified time interval,
the average force that acted on the body.

b)
Students should understand how Newton's Second Law, F = ma, applies
to a body subject to forces such as gravity, the pull of strings,
or contact forces, so they can:

(1)
Draw a well-labeled diagram showing all real forces that act
on the body.

(2)
Write down the vector equation that results from applying Newton's

Second
Law to the body, and take components of this equation along appropriate
axes.

c)
Students should be able to analyze situations in which a body
moves with specified acceleration under the influence of one
or more forces so they can determine the magnitude and direction
of the net force, or of one of the forces that makes up the net
force, in situations such as the following:

(1)
Motion up or down with constant acceleration (in an elevator,
for example).

(2)
Motion in a horizontal circle (e.g., mass on a rotating merry-go-round,
or car rounding a banked curve).

(3)
Motion in a vertical circle (e.g., mass swinging on the end of
a string, cart rolling down a curved track, rider on a Ferris
wheel).

d)
Students should understand the significance of the coefficient
of friction so they can:

(1)
Write down the relationship between the normal and frictional
forces on a surface.

(2)
Analyze situations in which a body slides down a rough inclined
plane or is pulled or pushed across a rough surface.

(3)
Analyze static situations involving friction to determine under
what circumstances a body will start to slip, or to calculate
the magnitude of the force of static friction.

**3.
Systems of Two or More Bodies (Third Law) **

a)
Students should understand Newton's Third Law so that, for a
given force, they can identify the body on which the reaction
force acts and state the magnitude and direction of this reaction.

b)
Students should be able to apply Newton's Third Law in analyzing
the force of contact between two bodies that accelerate together
along a horizontal or vertical line, or between two surfaces
that slide across one another.

c)
Students should know that the tension is constant in a light
string that passes over a massless pulley and should be able
to use this fact in analyzing the motion of a system of two bodies
joined by a string.

**C.
Work, Energy, and Power **

**1.
Work and the Work-Energy Theorem **

a)
Students should understand the definition of work so they can:

(1)
Calculate the work done by a specified constant force on a body
that undergoes a specified displacement.

(2)
Relate the work done by a force to the area under a graph of
force as a function of position, and calculate this work in the
case where the force is a linear function of position.

(3)
Use integration to calculate the work performed by a force F(x)
on a body that undergoes a specified displacement in one dimension.

(4)
Use the scalar product operation to calculate the work performed
by a specified constant force F on a body that undergoes a displacement
in a plane.

b)
Students should understand the work-energy theorem so they can:

(1)
Calculate the change in kinetic energy or speed that results
from performing a specified amount of work on a body.

(2)
Calculate the work performed by the net force, or by each of
the forces that makes up the net force, on a body that undergoes
a specified change in speed or kinetic energy.

(3)
Apply the theorem to determine the change in a body's kinetic
energy and speed that results from the application of specified
forces, or to determine the force that is required in order to
bring a body to rest in a specified distance.

**2.
Conservative Forces and Potential Energy **

a)
Students should understand the concept of potential energy so
they can:

(1)
Write an expression for the force exerted by an ideal spring
and for the potential energy stored in a stretched or compressed
spring.

(2)
Calculate the potential energy of a single body in a uniform
gravitational field.

**3.
Conservation of Energy **

a)
Students should understand conservation of energy so they can:

(1)
Identify situations in which mechanical energy is or is not conserved.

(2)
Apply conservation of energy in analyzing the motion of bodies
that are moving in a gravitational field and are subject to constraints
imposed by strings or surfaces.

(3)
Apply conservation of energy in analyzing the motion of bodies
that move under the influence of springs.

**4.
Power **

a)
Students should understand the definition of power so they can:

(1)
Calculate the power required to maintain the motion of a body
with constant acceleration (e.g., to move a body along a level
surface, to raise a body at a constant rate, or to overcome friction
for a body that is moving at a constant speed).

(2)
Calculate the work performed by a force that supplies constant
power, or the average power supplied by a force that performs
a specified amount of work.

**D.
Systems of Particles, Linear Momentum**

**1.
Impulse and Momentum:** Students should understand impulse
and linear momentum so they can:

a)
Relate mass, velocity, and linear momentum for a moving body,
and calculate the total linear momentum of a system of bodies.

b)
Relate impulse to the change in linear momentum and the average
force acting on a body.

**2.
Conservation of Linear Momentum, Collisions **

a)
Students should understand linear momentum conservation so they
can:

(1)
Identify situations in which linear momentum, or a component
of the linear momentum vector, is conserved.

(2)
Apply linear momentum conservation to determine the final velocity
when two bodies that are moving along the same line, or at right
angles, collide and stick together, and calculate how much kinetic
energy is lost in such a situation.

(3)
Analyze collisions of particles in one or two dimensions to determine
unknown masses or velocities, and calculate how much kinetic
energy is lost in a collision.

**E.
Circular Motion and Rotation**

**1.
Uniform Circular Motion:** Students should understand the
uniform circular motion of a particle so they can:

a)
Relate the radius of the circle and the speed or rate of revolution
of the particle to the magnitude of the centripetal acceleration.

b)
Describe the direction of the particle's velocity and acceleration
at any instant during the motion.

c)
Determine the components of the velocity and acceleration vectors
at any instant, and sketch or identify graphs of these quantities.

**2.
Angular Momentum and Its Conservation **

a)
Students should understand angular momentum conservation so they
can:

(1)
Recognize the conditions under which the law of conservation
is applicable and relate this law to one- and two-particle systems
such as satellite orbits.

**3.
Torque and Rotational Statics**

a)
Students should understand the concept of torque so they can:

(1)
Calculate the magnitude and sense of the torque associated with
a given force.

(2)
Calculate the torque on a rigid body due to gravity.

b)
Students should be able to analyze problems in statics so they
can:

(1)
State the conditions for translational and rotational equilibrium
of a rigid body.

(2)
Apply these conditions in analyzing the equilibrium of a rigid
body under the combined influence of a number of coplanar forces
applied at different locations. __ __

**F.
Oscillations**

1.
Students should understand the kinematics of simple harmonic
motion so they can:

a)
Sketch or identify a graph of displacement as a function of time,
and determine from such a graph the amplitude, period, and frequency
of the motion.

b)
Write down an appropriate expression for displacement of the
form or to
describe the motion.

c)
Identify points in the motion where the velocity is zero or achieves
its maximum positive or negative value.

d)
State qualitatively the relation between acceleration and displacement.

e)
Identify points in the motion where the acceleration is zero
or achieves its greatest positive or negative value.

f)
State and apply the relation between frequency and period.

g)
State how the total energy of an oscillating system depends on
the amplitude of the motion, sketch or identify a graph of kinetic
or potential energy as a function of time, and identify points
in the motion where this energy is all potential or all kinetic.

h)
Calculate the kinetic and potential energies of an oscillating
system as functions of time, sketch or identify graphs of these
functions, and prove that the sum of kinetic and potential energy
is constant.

2.
Students should be able to apply their knowledge of simple harmonic
motion to the case of a mass on a spring, so they can:

a)
Apply the expression for the period of oscillation of a mass
on a spring.

3.
Students should be able to apply their knowledge of simple harmonic
motion to the case of a pendulum, so they can:

a)
Apply the expression for the period of a simple pendulum.

b)
State what approximation must be made in deriving the period.

**G.
Gravitation **

1.
Students should know Newton's Law of Universal Gravitation so
they can:

a)
Determine the force that one spherically symmetrical mass exerts
on another.

b)
Determine the strength of the gravitational field at a specified
point outside a spherically symmetrical mass.

2.
Students should understand the motion of a body in orbit under
the influence of gravitational forces so they can:

a)
For a circular orbit:

(1)
Recognize that the motion does not depend on the body's mass;
describe qualitatively how the velocity, period of revolution,
and centripetal acceleration depend upon the radius of the orbit;
and derive expressions for the velocity and period of revolution
in such an orbit.

b)
For a general orbit:

(1)
Apply conservation of angular momentum to determine the velocity
and radial distance at any point in the orbit.

(2)
Apply angular momentum conservation and energy conservation to
relate the speeds of a body at the two extremes of an elliptic
orbit.

**II.
Heat, Kinetic Theory, and Thermodynamics**

**A.
Fluid Mechanics**

**1.
Hydrostatic Pressure**

a)
Students should understand that a fluid exerts pressure in all
directions

b)
Students should understand that a fluid at rest exerts pressure
perpendicular to any surface that it contacts

c)
Students should understand and be able to use the relationship
between pressure and depth in a liquid, .

**2.
Buoyancy**

a)
Students should understand that the difference in the pressure
on the upper and lower surfaces of an object immersed in liquid
results in an upward force on the object.

b)
Students should understand and be able to apply ArchimedesÕ principle:
the buoyant force on a submersed object is equal to the weight
of the liquid it displaces.

**3.
Fluid flow continuity**

a)
Students should understand that for laminar flow, the flow rate
of a liquid through its cross section is the same at any point
along its path.

b)
Students should understand and be able to apply the equation
of continuity,

**4.
BernoulliÕs Equation**

a)
Students should understand that the pressure of a flowing liquid
is low where the velocity is high, and vice versa.

b)
Students should understand and be able to apply BernoulliÕs equation, .

**B.
Temperature and Heat **

1.
Students should understand the "mechanical equivalent of
heat' so they can calculate how much a substance will be heated
by the performance of a specified quantity of mechanical work.

2.
Students should understand the concepts of specific heat, heat
of fusion, and heat of vaporization so they can:

a)
Identify, given a graph relating the quantity of heat added to
a substance and its temperature, the melting point, and boiling
point and determine the heats of fusion and vaporization and
the specific heat of each phase.

b)
Determine how much heat must be added to a sample of a substance
to raise its temperature from one specified value to another,
or to cause it to melt or vaporize.

3.
Students should understand heat transfer and thermal expansion
so they can:

a)
Determine the final temperature achieved when substances, all
at different temperatures, are mixed and allowed to come to thermal
equilibrium.

b)
Calculate how the flow of heat through a slab of material is
affected by changes in the thickness or area of the slab, or
the temperature difference between the two faces of the slab.

c)
Analyze qualitatively what happens to the size and shape of a
body when it is heated.

**C.
Kinetic Theory and Thermodynamics**

**1.
Ideal Gases **

a)
Students should understand the kinetic theory model of an ideal
gas so they can:

(1)
State the assumptions of the model.

(2)
State the connection between temperature and mean translational
kinetic energy, and apply it to determine the mean speed of gas
molecules as a function of their mass and the temperature of
the gas.

(3)
State the relationship among Avogadro's number, Boltzmann's constant,
and the gas constant R, and express the energy of a mole of a
monatomic ideal gas as a function of its temperature.

(4)
Explain qualitatively how the model explains the pressure of
a gas in terms of collisions with the container walls, and explain
how the model predicts that, for fixed volume, pressure must
be proportional to temperature.

b)
Students should know how to apply the ideal gas law and thermodynamic
principles so they can:

(1)
Relate the pressure and volume of a gas during an isothermal
expansion or compression.

(2)
Relate the pressure and temperature of a gas during constant-volume
heating or cooling, or the volume and temperature during constant-pressure
heating or cooling.

(3)
Calculate the work performed on or by a gas during an expansion
or compression at constant pressure.

(4)
Understand the process of adiabatic expansion or compression
of a gas.

(5)
Identify or sketch on a pV diagram the curves that represent
each of the above processes.

**2.
Laws of Thermodynamics **

a)
Students should know how to apply the first law of thermodynamics
so they can:

(1)
Relate the heat absorbed by a gas, the work performed by the
gas, and the internal energy change of the gas for any of the
processes above.

(2)
Relate the work performed by a gas in a cyclic process to the
area enclosed by a curve on a p V diagram.

b)
Students should understand the second law of thermodynamics,
the concept of entropy, and heat engines and the Carnot cycle
so they can:

(1)
Determine whether entropy will increase, decrease, or remain
the same during a particular situation.

(2)
Compute the maximum possible efficiency of a heat engine operating
between two given temperatures.

(3)
Compute the actual efficiency of a heat engine.

(4)
Relate the heats exchanged at each thermal reservoir in a Carnot
cycle to the temperatures of the reservoirs.

**III.
ELECTRICITY AND MAGNETISM**

**A.
Electrostatics**

**1.
Charge, Field, and Potential **

a)
Students should understand the concept of electric field so they
can:

(1)
Define it in terms of the force on a test charge.

(2)
Calculate the magnitude and direction of the force on a positive
or negative charge placed in a specified field.

(3)
Given a diagram on which an electric field is represented by
flux lines, determine the direction of the field at a given point,
identify locations where the field is strong and where it is
weak, and identify where positive or negative charges must be
present.

(4)
Analyze the motion of a particle of specified charge and mass
in a uniform electric field.

b)
Students should understand the concept of electric potential
so they can:

(1)
Calculate the electrical work done on a positive or negative
charge that moves through a specified potential difference.

(2)
Given a sketch of equipotentials for a charge configuration,
determine the direction and approximate magnitude of the electric
field at various positions.

(3)
Apply conservation of energy to determine the speed of a charged
particle that has been accelerated through a specified potential
difference.

(4)
Calculate the potential difference between two points in a uniform
electric field, and state which is at the higher potential.

**2.
Coulomb's Law and Field and Potential of Point Charges **

a)
Students should understand Coulomb's Law and the principle of
superposition so they can:

(1)
Determine the force that acts between specified point charges,
and describe the electric field of a single point charge.

(2)
Use vector addition to determine the electric field produced
by two or more point charges.

b)
Students should know the potential function for a point charge
so they can:

(1)
Determine the electric potential in the vicinity of one or more
point charges.

**3.
Fields and Potentials of Other Charge Distributions **

a)
Students should know the fields of highly symmetric charge distributions
so they can:

(1)
Describe the electric field of:

(a)
Parallel charged plates.

**B.
Conductors, Capacitors, Dielectrics**

**1.
Electrostatics with Conductors **

a)
Students should understand the nature of electric fields in and
around conductors so they can:

(1)
Explain the mechanics responsible for the absence of electric
field inside a conductor, and why all excess charge must reside
on the surface of the conductor.

(2)
Explain why a conductor must be an equipotential, and apply this
principle in analyzing what happens when conductors are connected
by wires.

(3)
Determine the direction of the force on a charged particle brought
near an uncharged or grounded conductor.

b)
Students should be able to describe and sketch a graph of the
electric field and potential inside and outside a charged conducting
sphere.

c)
Students should understand induced charge and electrostatic shielding
so they can:

(1)
Describe qualitatively the process of charging by induction.

(2)
Determine the direction of the force on a charged particle brought
near an uncharged or grounded conductor.

**2.
Capacitors **

a)
Students should know the definition of capacitance so they can
relate stored charge and voltage for a capacitor.

b)
Students should understand energy storage in capacitors so they
can:

(1)
Relate voltage, charge, and stored energy for a capacitor.

(2)
Recognize situations in which energy stored in a capacitor is
converted to other forms.

c)
Students should understand the physics of the parallel-plate
capacitor so they can:

(1)
Describe the electric field inside the capacitor, and relate
the strength of this field to the potential difference between
the plates and the plate separation.

(2)
Determine how changes in dimension will affect the value of the
capacitance.

**C.
Electric Circuits**

**1.
Current, Resistance, Power **

a)
Students should understand the definition of electric current
so they can relate the magnitude and direction of the current
in a wire or ionized medium to the rate of flow of positive and
negative charge.

b)
Students should understand conductivity, resistivity, and resistance
so they can:

(1)
Relate current and voltage for a resistor.

(2)
Describe how the resistance of a resistor depends upon its length
and cross-sectional area.

(3)
Apply the relationships for the rate of heat production in a
resistor.

**2.
Steady-State Direct Current Circuits with Batteries and Resistors
Only **

a)
Students should understand the behavior of series and parallel
combinations of resistors so they can:

(1)
Identify on a circuit diagram whether resistors are in series
or in parallel.

(2)
Determine the ratio of the voltages across resistors connected
in series or the ratio of the currents through resistors connected
in parallel.

(3)
Calculate the equivalent resistance of two or more resistors
connected in series or in parallel, or of a network of resistors
that can be broken down into series and parallel combinations.

(4)
Calculate the voltage, current, and power dissipation for any
resistor in such a network of resistors connected to a single
battery.

(5)
Design a simple series-parallel circuit that produces a given
current and terminal voltage for one specified component, and
draw a diagram for the circuit using conventional symbols.

b)
Students should understand the properties of ideal and real batteries
so they can:

(1)
Calculate the terminal voltage of a battery of specified emf
and internal resistance from which a known current is flowing.

c)
Students should be able to apply Ohm's Law and Kirchhoff's rules
to direct-current circuits in order to:

(1)
Determine a single unknown current, voltage, or resistance.

d)
Students should understand the properties of voltmeters and ammeters
so they can:

(1)
State whether the resistance of each is high or low.

(2)
Identify or show correct methods of connecting meters into circuits
in order to measure voltage or current.

**3.
Capacitors in Circuits **

a)
Students should understand the behavior of capacitors connected
in series or in parallel so they can:

(1)
Calculate the equivalent capacitance of a series or parallel
combination.

(2)
Describe how stored charge is divided between two capacitors
connected in parallel.

(3)
Determine the ratio of voltages for two capacitors connected
in series.

b)
Students should be able to calculate the voltage or stored charge,
under steady-state conditions, for a capacitor connected to a
circuit consisting of a battery and resistors.

c)
Students should develop skill in analyzing the behavior of circuits
containing several capacitors and resistors so they can:

(1)
Determine voltages and currents immediately after a switch has
been closed and also after steady-state conditions have been
established.

**D.
Magnetostatics**

**1.
Forces on Moving Charges in Magnetic Fields **

a)
Students should understand the force experienced by a charged
particle in a magnetic field so they can:

(1)
Calculate the magnitude and direction of the force in terms of
q, v, and B, and explain why the magnetic force can perform no
work.

(2)
Deduce the direction of a magnetic field from information about
the forces experienced by charged particles moving through that
field.

(3)
State and apply the formula for the radius of the circular path
of a charge that moves perpendicular to a uniform magnetic field,
and derive this formula from Newton's Second Law and the magnetic
force law.

(4)
Describe the most general path possible for a charged particle
moving in a uniform magnetic field, and describe the motion of
a particle that enters a uniform magnetic field moving with specified
initial velocity.

(5)
Describe quantitatively under what conditions particles will
move with constant velocity through crossed electric and magnetic
fields.

**2.
Forces on Current-carrying Wires in Magnetic Fields **

(a)
Students should understand the force experienced by a current
in a magnetic field so they can:

(1)
Calculate the magnitude and direction of the force on a straight
segment of current-carrying wire in a uniform magnetic field.

(2)
Indicate the direction of magnetic forces on a current-carrying
loop of wire in a magnetic field, and determine how the loop
will tend to rotate as a consequence of these forces.

**3.
Fields of Long Current-carrying Wires **

a)
Students should understand the magnetic field produced by a long
straight current-carrying wire so they can:

(1)
Calculate the magnitude and direction of the field at a point
in the vicinity of such a wire.

(2)
Use superposition to determine the magnetic field produced by
two long wires.

(3)
Calculate the force of attraction or repulsion between two long
current-carrying wires.

**E.
Electromagnetism**

**1.
Electromagnetic Induction **

a)
Students should understand the concept of magnetic flux so they
can:

(1)
Calculate the flux of a uniform magnetic field through a loop
of arbitrary orientation.

b)
Students should understand Faraday's Law and Lenz's Law so they
can:

(1)
Recognize situations in which changing flux through a loop will
cause an induced emf or current in the loop.

(2)
Calculate the magnitude and direction of the induced emf and
current in:

(a)
A square loop of wire pulled at a constant velocity into or out
of a uniform magnetic field.

(b)
A loop of wire placed in a spatially uniform magnetic field whose
magnitude is changing at a constant rate.

(c)
A loop of wire that rotates at a constant rate about an axis
perpendicular to a uniform magnetic field.

(d)
A conducting bar moving perpendicular to a uniform magnetic field.

**WAVES
AND OPTICS **

**A.
Wave Motion** (including Sound)

**1.
Students should understand the description of traveling waves** so
they can:

a)
Sketch or identify graphs that represent traveling waves and
determine the amplitude, wavelength, and frequency of a wave
from such a graph.

b)
State and apply the relation among wavelength, frequency, and
velocity for a wave.

c)
Sketch or identify graphs that describe reflection of a wave
from the fixed or free end of a string.

d)
Know qualitatively what factors determine the speed of waves
on a string and the speed of sound.

**2.
Students should understand the physics of standing waves** so
they can:

a)
Sketch possible standing wave modes for a stretched string that
is fixed at both ends, and determine the amplitude, wavelength,
and frequency of such standing waves.

b)
Describe possible standing sound waves in a pipe that has either
open or closed ends, and determine the wavelength and frequency
of such standing waves.

**3.
Students should understand the Doppler effect for sound **so
they can:

a)
Explain the mechanism that gives rise to a frequency shift in
both the moving-source and moving-observer case, and derive an
expression for the frequency heard by the observer.

b)
Write and apply the equations that describe the moving-source
and moving-observer Doppler effect, and sketch or identify graphs
that describe the effect.

**4.
Students should understand the principle of superposition** so
they can apply it to traveling waves moving in opposite directions,
and describe how a standing wave may be formed by superposition.

**B.
Physical Optics **

**1.
Students should understand the interference and diffraction
of waves** so they can:

a)
Apply the principles of interference to coherent sources oscillating
in phase in order to:

(1)
Describe the conditions under which the waves reaching an observation
point from two or more sources will all interfere constructively,
or under which the waves from two sources will interfere destructively.

(2)
Determine locations of interference maxima or minima for two
sources or determine the frequencies or wavelengths that can
lead to constructive or destructive interference at a certain
point.

(3)
Relate the amplitude and intensity produced by two or more sources
that interfere constructively to the amplitude and intensity
produced by a single source.

b)
Apply the principles of interference and diffraction to waves
that pass through a single or double slit or through a diffraction
grating so they can:

(1)
Sketch or identify the intensity pattern that results when mono-chromatic
waves pass through a single slit and fall on a distant screen,and
describe how this pattern will change if the slit width or the
wavelength of the waves is changed.

(2)
Calculate, for a single-slit pattern, the angles or the positions
on a distant screen where the intensity is zero.

(3)
Sketch or identify the intensity pattern that results when monochromatic
waves pass through a double slit, and identify which features
of the pattern result from single-slit diffraction and which
from two-slit interference.

4)
Calculate, for a two-slit interference pattern, the angles or
the positions on a distant screen at which intensity maxima or
minima occur.

(5)
Describe or identify the interference pattern formed by a grating
of many equally spaced narrow slits, calculate the location of
intensity maxima, and explain qualitatively why a multiple-slit
grating is better than a two-slit grating for making accurate
determinations of wavelength.

c)
Apply the principles of interference to light reflected by thin
films so they can:

(1)
State under what conditions a phase reversal occurs when light
is reflected from the interface between two media of different
indices of refraction.

(2)
Determine whether rays of monochromatic light reflected from
two such interfaces will interfere constructively or destructively,
and thereby account for Newton's rings and similar phenomena,
and explain how glass may be coated to minimize reflection of
visible light.

**2.
Students should understand dispersion and the electromagnetic
spectrum** so they can:

a)
Relate a variation of index of refraction with frequency to a
variation in refraction.

b)
Know the names associated with electromagnetic radiation and
be able to arrange in order of increasing wavelength the following:
visible light of various colors, ultraviolet light, infrared
light, radio waves, x-rays, and gamma rays.

**3.
Students should understand the transverse nature of light waves** so
they can explain qualitatively why light can exhibit polarization.

**4.
Students should understand the inverse-square law** so they
can calculate the intensity of light at a given distance from
a source of specified power and compare the intensity of light
at different distances from the source.

**C.
Geometrical Optics **

**1.
Students should understand the principles of reflection and
refraction** so they can:

a)
Determine how the speed and wavelength of light change when light
passes from one medium into another.

b)
Show on a diagram the directions of reflected and refracted rays.

c)
Use Snell's Law to relate the directions of the incident ray
and the refracted ray, and the indices of refraction of the media.

d)
Identify conditions under which total internal reflection will
occur.

**2.
Students should understand image formation by plane or spherical
mirrors** so they can:

a)
Relate the focal point of a spherical mirror to its center of
curvature.

b)
Given a diagram of a mirror with the focal point shown, locate
by ray tracing the image of a real object and determine whether
the image is real or virtual, upright or inverted, enlarged or
reduced in size.

**3.
Students should understand image formation by converging or
diverging lenses** so they can:

a)
Determine whether the focal length of a lens is increased or
decreased as a result of a change in the curvature of its surfaces
or in the index of refraction of the material of which the lens
is made or the medium in which it is immersed.

b)
Determine by ray tracing the location of the image of a real
object located inside or outside the focal point of the lens,
and state whether the resulting image is upright or inverted,
real or virtual.

c)
Use the thin lens equation to relate the object distance, image
distance, and focal length for a lens, and determine the image
size in terms of the object size.

d)
Analyze simple situations in which the image formed by one lens
serves as the object for another lens.

**V.
MODERN PHYSICS **

**A.
Atomic Physics and Quantum Effects**__ __

**1.
Students should know the properties of photons and understand
the photoelectric effect** so they can:

a)
Relate the energy of a photon in joules or electron-volts to
its wavelength or frequency.

b)
Relate the linear momentum of a photon to its energy or wavelength,
and apply linear momentum conservation to simple processes involving
the emission, absorption, or reflection of photons.

c)
Calculate the number of photons per second emitted by a monochromatic
source of specific wavelength and power.

d)
Describe a typical photoelectric effect experiment, and explain
what experimental observations provide evidence for the photon
nature of light.

e)
Describe qualitatively how the number of photoelectrons and their
maximum kinetic energy depend on the wavelength and intensity
of the light striking the surface, and account for this dependence
in terms of a photon model of light.

f)
When given the maximum kinetic energy of photoelectrons ejected
by photons of one energy or wavelength, determine the maximum
kinetic energy of photoelectrons for a different photon energy
or wavelength.

g)
Sketch or identify a graph of stopping potential versus frequency
for a photoelectric effect experiment, determine from such a
graph the threshold frequency and work function, and calculate
an approximate value of h/e.

**2.
Students should understand the concept of energy levels for
atoms **so they can:

a)
Calculate the energy or wavelength of the photon emitted or absorbed
in a transition between specified levels, or the energy or wavelength
required to ionize an atom.

b)
Explain qualitatively the origin of emission or absorption spectra
of gases.

c)
Given the wavelengths or energies of photons emitted or absorbed
in a two-step transition between levels, calculate the wavelength
or energy for a single-step transition between the same levels.

d)
Write an expression for the energy levels of hydrogen in terms
of the ground-state energy, draw a diagram to depict these levels,
and explain how this diagram accounts for the various "series" in
the hydrogen spectrum.

**3.
Students should understand the concept of DeBroglie wavelength** so
they can:

a)
Calculate the wavelength of a particle as a function of its momentum.

b)
Describe the Davisson-Germer experiment, and explain how it provides
evidence for the wave nature of electrons.

**4.
Students should understand the nature and production of x-rays** so
they can calculate the shortest wavelength of x-rays that may
be produced by electrons accelerated through a specified voltage.

**5.
Students should understand Compton scattering** so they can:

a)
Describe Compton's experiment, and state what results were observed
and by what sort of analysis these results may be explained.

b)
Account qualitatively for the increase of photon wavelength that
is observed, and explain the significance of the Compton wavelength.

**B.
Nuclear Physics**

**1.
Students should understand the significance of the mass number
and charge of nuclei** so they can:

a)
Interpret symbols for nuclei that indicate these quantities.

b)
Use conservation of mass number and charge to complete nuclear
reactions.

c)
Determine the mass number and charge of a nucleus after it has
undergone specified decay processes.

d)
Describe the process of a, B, and A decay and write a reaction
to describe each.

e)
Explain why the existence of the neutrino had to be postulated
in order to reconcile experimental data from B decay with fundamental
conservation laws.

**2.
Students should know the nature of the nuclear force** so
they can compare its strength and range with those of the electromagnetic
force.

**3.
Students should understand nuclear fission** so they can
describe a typical neutron-induced fission and explain why
a chain reaction is possible.

**4.
Students should understand the relationship between mass and
energy (mass-energy equivalence)** so they can:

a)
Qualitatively relate the energy released in nuclear processes
to the change in mass.

b)
Apply the relationship in
analyzing nuclear processes.