AP Physics 2 Glossary & Definitions
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The AP Physics 2 glossary is a searchable definition library for the vocabulary used across all seven units. Each entry gives a concise meaning, a real physical context, an equation/model connection when useful, and direct links to the topic lessons that use the term.
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absolute temperature
absolute temperature: temperature measured on the kelvin scale from absolute zero.
A capped syringe compressed slowly at nearly constant temperature shows pressure increasing as volume decreases.
PV = nRT = Nk_B Tequilibrium states of an ideal gasabsorption spectrum
absorption spectrum: the set of wavelengths removed from incident light by allowed upward atomic transitions.
A low-pressure discharge gas produces bright emission lines at wavelengths corresponding to allowed downward transitions.
|ΔE| = hfone-photon absorption or emission between two allowed levelsadiabatic process
adiabatic process: a process with no energy transferred into or out of the system by thermal processes.
Rapidly compressing air in a bicycle pump raises its temperature because positive work is done on the gas.
U = (3/2)nRT = (3/2)Nk_B Tideal monatomic gas whose internal energy is translational kinetic energyalpha particle
alpha particle: a helium-4 nucleus containing two protons and two neutrons with charge +2e.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepingamplitude
amplitude: the maximum magnitude of the disturbance from equilibrium; larger amplitude corresponds to greater transported energy for otherwise comparable waves.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringangle of incidence
angle of incidence: the angle between the incident ray and the local normal.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfaceangle of reflection
angle of reflection: the angle between the reflected ray and the local normal.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfaceantinode
antinode: a location of maximum oscillation amplitude in a standing-wave pattern.
Two equal pulses meeting crest-to-crest briefly double the displacement, then pass through one another.
y_total = Σy_ilinear superposition when waves overlapantireflection coating
antireflection coating: a thin film designed so selected reflected waves destructively interfere.
Soap bubbles show changing colors because film thickness varies across the surface and therefore changes reflected-light interference.
optical path difference = 2ntthin-film reflected-light comparison at normal incidence before including reflection phase changesaperture
aperture: an opening through which a wave passes.
Red light creates a wider single-slit diffraction pattern than shorter-wavelength blue light through the same slit.
a sinθ_m = mλsingle-slit diffraction minimaapproaching
approaching: source and observer moving closer together.
An ambulance siren is heard at higher pitch while approaching and lower pitch while receding.
approaching → f_observed > f_restsource and observer move toward one anotherarea vector
area vector: a vector perpendicular to a surface whose direction sets the sign convention for flux.
Moving a magnet toward a coil changes the coil’s magnetic flux and produces an induced current whose field opposes that increase in flux.
Φ_B = BA cosθuniform magnetic field through a flat areaaverage translational kinetic energy
average translational kinetic energy: the mean kinetic energy associated with center-of-mass motion of gas particles.
Heating a rigid sealed container makes particles move faster on average, increasing the frequency and momentum transfer of wall collisions and therefore increasing pressure.
P = F⊥/Amacroscopic pressure from the perpendicular force exerted on a surfacebeat
beat: a periodic amplitude variation produced by superposing nearby frequencies.
Two equal pulses meeting crest-to-crest briefly double the displacement, then pass through one another.
y_total = Σy_ilinear superposition when waves overlapbeta-minus decay
beta-minus decay: a process in which a neutron changes to a proton while an electron and antineutrino are emitted.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepingbeta-plus decay
beta-plus decay: a process in which a proton changes to a neutron while a positron and neutrino are emitted.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepingbinding energy
binding energy: the energy required to remove an electron from the atom and ionize it from a specified bound state.
A low-pressure discharge gas produces bright emission lines at wavelengths corresponding to allowed downward transitions.
|ΔE| = hfone-photon absorption or emission between two allowed levelsblackbody
blackbody: an idealized object that absorbs all incident electromagnetic radiation and emits a spectrum determined only by its temperature.
As a hot object’s temperature rises, its continuous thermal spectrum becomes more intense and its peak shifts toward shorter wavelength.
λmax T = bpeak wavelength of an ideal blackbody spectrumblackbody spectrum
blackbody spectrum: the continuous distribution of emitted intensity per wavelength versus wavelength for a blackbody.
As a hot object’s temperature rises, its continuous thermal spectrum becomes more intense and its peak shifts toward shorter wavelength.
λmax T = bpeak wavelength of an ideal blackbody spectrumBohr model
Bohr model: a historical model in which an electron is represented in circular motion around the nucleus with allowed standing-wave conditions.
Nuclear notation distinguishes isotopes by proton and neutron counts even when the chemical element is the same.
A = Z + Nnnuclear notation and isotope bookkeepingbranch
branch: a path between nodes carrying one branch current.
A vehicle electrical system combines parallel loads with internal series resistances.
R_series = ΣR_icomponents carrying the same current with no branching between thembranch current
branch current: current assigned to one path between nodes.
Current splits at a parallel junction and recombines without being consumed.
ΣI_in = ΣI_outsteady-state junctioncalorimetry
calorimetry: energy-accounting measurements that use temperature changes to infer transferred energy or material properties.
Equal masses of water and aluminum receiving the same energy do not undergo the same temperature change because their specific heats differ.
Q = mcΔTtemperature change with no phase change and approximately constant ccapacitance
capacitance: the magnitude of charge stored on either plate per unit potential difference.
Camera-flash capacitors store energy at high voltage and release it rapidly.
C = Q/|ΔV|definition of capacitancecharge conservation
charge conservation: the principle that net charge changes only through transfer across a chosen system boundary.
Rubbing a balloon on fabric transfers electrons and leaves equal-and-opposite charge changes on the two-object system.
Q_system,f = Q_system,i + Q_transferredcharging analyzed with an explicit system boundarycharge continuity
charge continuity: conservation of charge as it moves through a network.
Current splits at a parallel junction and recombines without being consumed.
ΣI_in = ΣI_outsteady-state junctioncharging
charging: process in which capacitor charge and capacitor potential difference increase toward steady values.
Two identical capacitors in parallel have twice the capacitance of one; two identical capacitors in series have half the capacitance of one.
1/C_series = Σ(1/C_i)capacitors connected in seriesclosed system
closed system: a system that can exchange energy but not matter with its surroundings.
A hot object cools in a cooler isolated enclosure and the two systems approach one temperature; the reverse concentration of energy does not occur spontaneously.
Isolated system: total entropy never decreasesqualitative second-law reasoning for an isolated systemcoherent sources
coherent sources: sources with a stable phase relationship and the same frequency.
A double-slit pattern contains narrow interference fringes inside a broader single-slit diffraction envelope.
d sinθ_m = mλdouble-slit or diffraction-grating constructive maximacompound circuit
compound circuit: a network containing both series and parallel relationships.
A vehicle electrical system combines parallel loads with internal series resistances.
R_series = ΣR_icomponents carrying the same current with no branching between themcompression and rarefaction
compression and rarefaction: regions of increased and decreased density/pressure in a longitudinal wave such as sound.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringCompton scattering
Compton scattering: an interaction in which a photon scatters from an approximately free electron and transfers energy and momentum to it.
X-ray photons scattered by electrons show an angle-dependent wavelength increase that classical wave-only scattering cannot explain.
Δλ = (h/mec)(1 − cosθ)Compton scattering of a photon from an approximately free electronconduction
conduction: thermal energy transfer through microscopic interactions within or between materials.
A metal spoon in hot soup warms because energy is transferred through thermal contact, primarily by conduction through the spoon.
T_hot > T_cold → spontaneous thermal transfer hot → coldtwo systems in thermal contact at different temperaturesconduction rate
conduction rate: energy transferred by conduction per unit time, measured in watts.
Equal masses of water and aluminum receiving the same energy do not undergo the same temperature change because their specific heats differ.
Q = mcΔTtemperature change with no phase change and approximately constant cconservative interaction
conservative interaction: an interaction for which potential-energy change depends on endpoints rather than the path taken.
Separating opposite charges requires external work and raises their potential energy toward zero.
U_E = q₁q₂/(4πεr)two point charges using zero potential energy at infinite separationconstructive interference
constructive interference: overlap that produces a larger-magnitude resultant displacement.
Two equal pulses meeting crest-to-crest briefly double the displacement, then pass through one another.
y_total = Σy_ilinear superposition when waves overlapconstructive reflected interference
constructive reflected interference: reflected waves arriving in phase and reinforcing.
Soap bubbles show changing colors because film thickness varies across the surface and therefore changes reflected-light interference.
optical path difference = 2ntthin-film reflected-light comparison at normal incidence before including reflection phase changesconvection
convection: thermal energy transfer associated with bulk motion of a fluid.
A metal spoon in hot soup warms because energy is transferred through thermal contact, primarily by conduction through the spoon.
T_hot > T_cold → spontaneous thermal transfer hot → coldtwo systems in thermal contact at different temperaturesconventional current
conventional current: current direction defined by positive-charge motion.
A 1 A current means one coulomb of net charge crosses a section each second.
I = ΔQ/Δtaverage current through a chosen cross sectionconverging lens
converging lens: a thin convex lens that refracts incident rays parallel to the principal axis toward a focal point on the transmitted side.
A camera lens forms a real inverted image on a sensor when the object is outside the focal distance of a converging lens.
1/f = 1/s_o + 1/s_ithin-lens image calculations with a consistent sign conventioncooling
cooling: energy transferred out of a system by thermal processes.
A metal spoon in hot soup warms because energy is transferred through thermal contact, primarily by conduction through the spoon.
T_hot > T_cold → spontaneous thermal transfer hot → coldtwo systems in thermal contact at different temperaturescrest and trough
crest and trough: maximum positive and negative displacement locations in a transverse sinusoidal representation.
If a source oscillates faster while wave speed in the medium stays fixed, the wavelength decreases.
v = fλany periodic wave when speed, frequency, and wavelength refer to the same wave in the same mediumcritical angle
critical angle: the incidence angle in the higher-index medium for which the refracted ray is at 90° to the normal.
A light ray entering glass from air bends toward the normal because its speed decreases in the higher-index medium.
n = c/vrelating propagation speed and refractive index in a transparent mediumcrossed fields
crossed fields: a region in which electric and magnetic fields act independently on a moving charged object.
A positive charge moving perpendicular to a uniform magnetic field follows a curved path while keeping the same speed if magnetic force is the only force doing work.
F_B = |q|vB sinθmoving charge in a magnetic field; numerical angle treatment here is limited to 0°, 90°, and 180°current density
current density: current per unit cross-sectional area.
A 1 A current means one coulomb of net charge crosses a section each second.
I = ΔQ/Δtaverage current through a chosen cross sectionde Broglie wavelength
de Broglie wavelength: the wavelength associated with a material particle of momentum p.
Electron diffraction from a crystal or slit pattern provides evidence that material particles can show wave behavior.
E = hfphoton energy or an energy transfer involving one photondecay constant
decay constant: the probability-rate parameter λ that characterizes exponential radioactive decay of a sample.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangeddestructive interference
destructive interference: overlap in opposite directions that reduces resultant displacement.
Two equal pulses meeting crest-to-crest briefly double the displacement, then pass through one another.
y_total = Σy_ilinear superposition when waves overlapdestructive reflected interference
destructive reflected interference: reflected waves arriving out of phase and reducing the reflected intensity.
Soap bubbles show changing colors because film thickness varies across the surface and therefore changes reflected-light interference.
optical path difference = 2ntthin-film reflected-light comparison at normal incidence before including reflection phase changesdielectric constant
dielectric constant: the dimensionless factor κ describing how a dielectric increases capacitance relative to vacuum.
Camera-flash capacitors store energy at high voltage and release it rapidly.
C = Q/|ΔV|definition of capacitancedielectric polarization
dielectric polarization: induced charge separation in an insulating material that creates a field opposing the applied field.
Camera-flash capacitors store energy at high voltage and release it rapidly.
C = Q/|ΔV|definition of capacitancediffraction
diffraction: wave spreading associated with passage through an opening or around an obstacle.
Red light creates a wider single-slit diffraction pattern than shorter-wavelength blue light through the same slit.
a sinθ_m = mλsingle-slit diffraction minimadiffraction envelope
diffraction envelope: the broad single-slit intensity pattern that modulates a double-slit fringe pattern.
A double-slit pattern contains narrow interference fringes inside a broader single-slit diffraction envelope.
d sinθ_m = mλdouble-slit or diffraction-grating constructive maximadiffraction grating
diffraction grating: many equally spaced openings that produce narrow interference maxima.
A double-slit pattern contains narrow interference fringes inside a broader single-slit diffraction envelope.
d sinθ_m = mλdouble-slit or diffraction-grating constructive maximadiffraction minimum
diffraction minimum: a direction or screen position where destructive interference from different parts of the slit produces low intensity.
Red light creates a wider single-slit diffraction pattern than shorter-wavelength blue light through the same slit.
a sinθ_m = mλsingle-slit diffraction minimadiffuse reflection
diffuse reflection: reflection from a rough surface whose local normals vary, sending reflected rays in many directions.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfacedischarging
discharging: process in which capacitor charge, capacitor potential difference, stored energy, and branch-current magnitude decrease toward steady state.
Two identical capacitors in parallel have twice the capacitance of one; two identical capacitors in series have half the capacitance of one.
1/C_series = Σ(1/C_i)capacitors connected in seriesdiverging lens
diverging lens: a thin concave lens that refracts parallel rays so they diverge as if from a focal point on the incident side.
A camera lens forms a real inverted image on a sensor when the object is outside the focal distance of a converging lens.
1/f = 1/s_o + 1/s_ithin-lens image calculations with a consistent sign conventiondrift speed
drift speed: small average carrier velocity superimposed on random thermal motion.
A 1 A current means one coulomb of net charge crosses a section each second.
I = ΔQ/Δtaverage current through a chosen cross sectionelastic collision
elastic collision: a collision in which total kinetic energy of the colliding system is conserved.
Heating a rigid sealed container makes particles move faster on average, increasing the frequency and momentum transfer of wall collisions and therefore increasing pressure.
P = F⊥/Amacroscopic pressure from the perpendicular force exerted on a surfaceelectric acceleration
electric acceleration: change in a charged object’s kinetic energy caused by electric-force work.
A proton released in an electric field accelerates toward lower electric potential.
ΔU_E = qΔVa charged object moves between two locations with known electric potentialselectric charge
electric charge: a signed fundamental property of matter measured in coulombs.
Two like-charged pith balls repel along the line joining their centers.
F_E = |q₁q₂|/(4πεr²)point charges or spherically symmetric charged objects when the point-charge model is validelectric current
electric current: rate of net charge flow through a cross section.
A 1 A current means one coulomb of net charge crosses a section each second.
I = ΔQ/Δtaverage current through a chosen cross sectionelectric energy conservation
electric energy conservation: energy conservation when electric potential energy is an important storage term.
A proton released in an electric field accelerates toward lower electric potential.
ΔU_E = qΔVa charged object moves between two locations with known electric potentialselectric field
electric field: the electric force per unit positive test charge at a location.
Field vectors around a positive point charge point radially outward.
E = F_E/q_test (vector relation)definition of electric field using a sufficiently small positive test chargeelectric field line
electric field line: a simplified curve tangent to the local electric-field direction, with spacing used only qualitatively for relative strength.
Field vectors around a positive point charge point radially outward.
E = F_E/q_test (vector relation)definition of electric field using a sufficiently small positive test chargeelectric permittivity
electric permittivity: a measure of how a medium responds through polarization to an electric field.
Two like-charged pith balls repel along the line joining their centers.
F_E = |q₁q₂|/(4πεr²)point charges or spherically symmetric charged objects when the point-charge model is validelectric potential
electric potential: electric potential energy per unit charge at a point, measured in volts.
A battery maintains a potential difference that transfers energy to moving charge in a circuit.
V = U_E/q_testdefinition of electric potential at a pointelectric potential energy
electric potential energy: energy associated with the configuration of interacting charged objects.
Separating opposite charges requires external work and raises their potential energy toward zero.
U_E = q₁q₂/(4πεr)two point charges using zero potential energy at infinite separationelectric power
electric power: rate at which electrical energy is transferred or transformed.
A 60 W lamp transforms electrical energy faster than a 10 W lamp at rated conditions.
P = IΔVany circuit element when current and potential difference are knownelectromagnetic spectrum
electromagnetic spectrum: the ordered family of electromagnetic-wave categories classified primarily by wavelength/frequency.
Radio waves and visible light are both electromagnetic waves; they differ in wavelength and frequency rather than in the need for a material medium.
c = fλelectromagnetic radiation propagating in vacuumelectromagnetic wave
electromagnetic wave: an oscillating electric-and-magnetic-field disturbance that can propagate through vacuum.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringelectrostatic equilibrium
electrostatic equilibrium: a condition in a conductor in which mobile charges have finished redistributing and no net charge motion persists.
Field vectors around a positive point charge point radially outward.
E = F_E/q_test (vector relation)definition of electric field using a sufficiently small positive test chargeemf
emf: energy supplied per unit charge by a source.
A battery and two resistors in one loop have voltage drops summing to the source emf.
ΣΔV_loop = 0any closed loop in the lumped circuit modelemission spectrum
emission spectrum: the set of discrete photon wavelengths emitted by downward atomic transitions.
A low-pressure discharge gas produces bright emission lines at wavelengths corresponding to allowed downward transitions.
|ΔE| = hfone-photon absorption or emission between two allowed levelsenergy bar chart
energy bar chart: a representation comparing energy stores and transfers before and after a process.
A proton released in an electric field accelerates toward lower electric potential.
ΔU_E = qΔVa charged object moves between two locations with known electric potentialsenergy level
energy level: an allowed discrete energy state of the atomic system.
Nuclear notation distinguishes isotopes by proton and neutron counts even when the chemical element is the same.
A = Z + Nnnuclear notation and isotope bookkeepingenergy use
energy use: power multiplied by elapsed time.
A 60 W lamp transforms electrical energy faster than a 10 W lamp at rated conditions.
P = IΔVany circuit element when current and potential difference are knownenergy-level diagram
energy-level diagram: a diagram whose horizontal lines represent allowed atomic energy states on an energy axis.
A low-pressure discharge gas produces bright emission lines at wavelengths corresponding to allowed downward transitions.
|ΔE| = hfone-photon absorption or emission between two allowed levelsentropy
entropy: a state quantity used qualitatively here to describe energy spreading and how much system energy is unavailable for useful work.
A hot object cools in a cooler isolated enclosure and the two systems approach one temperature; the reverse concentration of energy does not occur spontaneously.
Isolated system: total entropy never decreasesqualitative second-law reasoning for an isolated systemequilibrium state
equilibrium state: a macroscopic state whose measured properties are stable enough to be described by state variables.
A capped syringe compressed slowly at nearly constant temperature shows pressure increasing as volume decreases.
PV = nRT = Nk_B Tequilibrium states of an ideal gasequipotential
equipotential: a line or surface on which electric potential has the same value everywhere.
A battery maintains a potential difference that transfers energy to moving charge in a circuit.
V = U_E/q_testdefinition of electric potential at a pointequivalent capacitance
equivalent capacitance: single capacitance that reproduces the terminal charge–potential-difference behavior of a capacitor network.
Two identical capacitors in parallel have twice the capacitance of one; two identical capacitors in series have half the capacitance of one.
1/C_series = Σ(1/C_i)capacitors connected in seriesequivalent network
equivalent network: a reduced circuit with the same terminal behavior.
A vehicle electrical system combines parallel loads with internal series resistances.
R_series = ΣR_icomponents carrying the same current with no branching between themequivalent resistance
equivalent resistance: single resistance with the same terminal current-voltage behavior as a network.
Adding resistance in series with an ideal voltage source reduces total current.
closed loop ⇒ charge can flowqualitative circuit-state reasoningexcited state
excited state: an allowed atomic energy state above the ground state.
A low-pressure discharge gas produces bright emission lines at wavelengths corresponding to allowed downward transitions.
|ΔE| = hfone-photon absorption or emission between two allowed levelsfar-field pattern
far-field pattern: a diffraction pattern observed sufficiently far from the aperture for angular relationships to be useful.
Red light creates a wider single-slit diffraction pattern than shorter-wavelength blue light through the same slit.
a sinθ_m = mλsingle-slit diffraction minimafission
fission: splitting of a nucleus into two or more smaller nuclei plus possible subatomic particles.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangedfocal point
focal point: the point where parallel reflected rays converge or appear to diverge from.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventionfrequency
frequency: the number of cycles per second, measured in hertz.
If a source oscillates faster while wave speed in the medium stays fixed, the wavelength decreases.
v = fλany periodic wave when speed, frequency, and wavelength refer to the same wave in the same mediumfrequency shift
frequency shift: the difference between observed and rest frequency.
An ambulance siren is heard at higher pitch while approaching and lower pitch while receding.
approaching → f_observed > f_restsource and observer move toward one anotherfusion
fusion: combination of two or more smaller nuclei into a larger nucleus plus possible subatomic particles.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangedgamma decay
gamma decay: de-excitation of a nucleus to a lower energy state by emitting a photon without changing proton or nucleon number.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepinggas pressure
gas pressure: the perpendicular force exerted by gas particles per unit area on a surface.
Heating a rigid sealed container makes particles move faster on average, increasing the frequency and momentum transfer of wall collisions and therefore increasing pressure.
P = F⊥/Amacroscopic pressure from the perpendicular force exerted on a surfaceground state
ground state: the lowest allowed energy state of an atom.
A low-pressure discharge gas produces bright emission lines at wavelengths corresponding to allowed downward transitions.
|ΔE| = hfone-photon absorption or emission between two allowed levelsgrounding
grounding: electrically connecting a system to a much larger approximately neutral system such as Earth.
Rubbing a balloon on fabric transfers electrons and leaves equal-and-opposite charge changes on the two-object system.
Q_system,f = Q_system,i + Q_transferredcharging analyzed with an explicit system boundaryhalf-life
half-life: the time required for half of the initial radioactive nuclei in a sample to have decayed statistically.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangedHall effect
Hall effect: a potential difference produced across a conductor when moving charges are deflected by a magnetic field.
A positive charge moving perpendicular to a uniform magnetic field follows a curved path while keeping the same speed if magnetic force is the only force doing work.
F_B = |q|vB sinθmoving charge in a magnetic field; numerical angle treatment here is limited to 0°, 90°, and 180°harmonic
harmonic: an allowed resonant mode satisfying the system boundary conditions.
Two equal pulses meeting crest-to-crest briefly double the displacement, then pass through one another.
y_total = Σy_ilinear superposition when waves overlapheating
heating: energy transferred into a system by thermal processes.
A metal spoon in hot soup warms because energy is transferred through thermal contact, primarily by conduction through the spoon.
T_hot > T_cold → spontaneous thermal transfer hot → coldtwo systems in thermal contact at different temperaturesideal gas
ideal gas: a model gas whose particles have negligible volume, random velocities, elastic collisions and negligible interactions except during collisions.
A capped syringe compressed slowly at nearly constant temperature shows pressure increasing as volume decreases.
PV = nRT = Nk_B Tequilibrium states of an ideal gasimage distance
image distance: the signed distance from the image to the mirror in the chosen sign convention.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventioninduced charge separation
induced charge separation: redistribution of positive and negative charge caused by an external electric interaction without required contact.
Rubbing a balloon on fabric transfers electrons and leaves equal-and-opposite charge changes on the two-object system.
Q_system,f = Q_system,i + Q_transferredcharging analyzed with an explicit system boundaryinduced emf
induced emf: an electric potential difference produced by changing magnetic flux.
Moving a magnet toward a coil changes the coil’s magnetic flux and produces an induced current whose field opposes that increase in flux.
Φ_B = BA cosθuniform magnetic field through a flat areainelastic collision
inelastic collision: an interaction in which kinetic energy of the particle components need not be conserved separately even though total energy is conserved.
X-ray photons scattered by electrons show an angle-dependent wavelength increase that classical wave-only scattering cannot explain.
Δλ = (h/mec)(1 − cosθ)Compton scattering of a photon from an approximately free electronintensity
intensity: average wave power delivered per unit area, measured in W/m².
A pulse on a light string meeting a heavier-string region partly reflects and partly transmits; the source-set frequency does not change at the junction.
f_reflected = f_transmitted = f_incidentreflection and transmission at a stationary boundaryinterference fringe
interference fringe: a bright or dark band created by constructive or destructive interference.
A double-slit pattern contains narrow interference fringes inside a broader single-slit diffraction envelope.
d sinθ_m = mλdouble-slit or diffraction-grating constructive maximainternal energy
internal energy: the sum of microscopic kinetic energy and microscopic potential energy inside the chosen system.
Rapidly compressing air in a bicycle pump raises its temperature because positive work is done on the gas.
U = (3/2)nRT = (3/2)Nk_B Tideal monatomic gas whose internal energy is translational kinetic energyinverted reflection
inverted reflection: a reflected pulse whose displacement is reversed relative to the incident pulse.
A pulse on a light string meeting a heavier-string region partly reflects and partly transmits; the source-set frequency does not change at the junction.
f_reflected = f_transmitted = f_incidentreflection and transmission at a stationary boundaryion
ion: an atom or molecule with nonzero net electric charge because its electron count differs from its proton count.
Nuclear notation distinguishes isotopes by proton and neutron counts even when the chemical element is the same.
A = Z + Nnnuclear notation and isotope bookkeepingirreversible process
irreversible process: a real spontaneous process that produces total entropy.
A hot object cools in a cooler isolated enclosure and the two systems approach one temperature; the reverse concentration of energy does not occur spontaneously.
Isolated system: total entropy never decreasesqualitative second-law reasoning for an isolated systemisolated system
isolated system: a system that exchanges neither energy nor matter with its surroundings in the ideal model.
A hot object cools in a cooler isolated enclosure and the two systems approach one temperature; the reverse concentration of energy does not occur spontaneously.
Isolated system: total entropy never decreasesqualitative second-law reasoning for an isolated systemisotherm
isotherm: a set of gas states at the same absolute temperature; on a P–V graph an ideal-gas isotherm curves downward.
A capped syringe compressed slowly at nearly constant temperature shows pressure increasing as volume decreases.
PV = nRT = Nk_B Tequilibrium states of an ideal gasisothermal process
isothermal process: a process at constant temperature.
Rapidly compressing air in a bicycle pump raises its temperature because positive work is done on the gas.
U = (3/2)nRT = (3/2)Nk_B Tideal monatomic gas whose internal energy is translational kinetic energyisotope
isotope: atoms of the same element with the same proton number but different neutron numbers.
Nuclear notation distinguishes isotopes by proton and neutron counts even when the chemical element is the same.
A = Z + Nnnuclear notation and isotope bookkeepingJoule heating
Joule heating: thermal energy production caused by resistance to current.
A 60 W lamp transforms electrical energy faster than a 10 W lamp at rated conditions.
P = IΔVany circuit element when current and potential difference are knownjunction
junction: a node where multiple branches meet.
Current splits at a parallel junction and recombines without being consumed.
ΣI_in = ΣI_outsteady-state junctionLenz’s law
Lenz’s law: the rule that the induced current creates a magnetic effect opposing the change in magnetic flux that produced it.
Moving a magnet toward a coil changes the coil’s magnetic flux and produces an induced current whose field opposes that increase in flux.
Φ_B = BA cosθuniform magnetic field through a flat arealepton number
lepton number: a conserved bookkeeping quantity involving electrons/positrons and neutrinos/antineutrinos in the beta-decay processes treated here.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepinglight ray
light ray: a straight-line geometric model that points in the direction light travels and is perpendicular to the local wavefront.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfacelong straight wire model
long straight wire model: an idealized current-carrying wire whose field magnitude varies as I/r at perpendicular distance r.
A compass moved around a straight current-carrying wire turns so its tangent direction follows the circular magnetic-field pattern.
B = μ₀I/(2πr)long straight current-carrying wire in free spacelongitudinal wave
longitudinal wave: a wave whose disturbance is parallel to the direction of propagation.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringloop
loop: a closed path through a circuit.
A battery and two resistors in one loop have voltage drops summing to the source emf.
ΣΔV_loop = 0any closed loop in the lumped circuit modelmagnetic dipole
magnetic dipole: a magnetic system with inseparable north and south polarity.
A compass needle tends to align with the local magnetic field, so many compass readings can be used to map field direction.
magnetic field lines form closed loopsrepresenting magnetic-field direction around magnets and magnetic materialsmagnetic domain
magnetic domain: a region in a magnetic material in which many microscopic magnetic dipoles are similarly aligned.
A compass needle tends to align with the local magnetic field, so many compass readings can be used to map field direction.
magnetic field lines form closed loopsrepresenting magnetic-field direction around magnets and magnetic materialsmagnetic field
magnetic field: a vector field used to describe magnetic interactions with moving charges, electric currents, and magnetic materials.
A compass needle tends to align with the local magnetic field, so many compass readings can be used to map field direction.
magnetic field lines form closed loopsrepresenting magnetic-field direction around magnets and magnetic materialsmagnetic field of a current
magnetic field of a current: the magnetic field produced by moving charge in a conducting path.
A compass moved around a straight current-carrying wire turns so its tangent direction follows the circular magnetic-field pattern.
B = μ₀I/(2πr)long straight current-carrying wire in free spacemagnetic flux
magnetic flux: a signed measure of the component of magnetic field passing through an oriented area.
Moving a magnet toward a coil changes the coil’s magnetic flux and produces an induced current whose field opposes that increase in flux.
Φ_B = BA cosθuniform magnetic field through a flat areamagnetic force on a charge
magnetic force on a charge: the force exerted by a magnetic field on a charged object that is moving relative to the field.
A positive charge moving perpendicular to a uniform magnetic field follows a curved path while keeping the same speed if magnetic force is the only force doing work.
F_B = |q|vB sinθmoving charge in a magnetic field; numerical angle treatment here is limited to 0°, 90°, and 180°magnetic force on a wire
magnetic force on a wire: the net magnetic force transferred to a current-carrying conductor placed in an external magnetic field.
A compass moved around a straight current-carrying wire turns so its tangent direction follows the circular magnetic-field pattern.
B = μ₀I/(2πr)long straight current-carrying wire in free spacemagnetic permeability
magnetic permeability: a measure of how strongly a material responds magnetically to an applied magnetic field.
A compass needle tends to align with the local magnetic field, so many compass readings can be used to map field direction.
magnetic field lines form closed loopsrepresenting magnetic-field direction around magnets and magnetic materialsmagnification
magnification: the signed ratio comparing image height with object height and therefore encoding relative size and orientation.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventionmatter wave
matter wave: the quantum wave description associated with a material particle; it is not a classical material disturbance.
Electron diffraction from a crystal or slit pattern provides evidence that material particles can show wave behavior.
E = hfphoton energy or an energy transfer involving one photonMaxwell–Boltzmann distribution
Maxwell–Boltzmann distribution: a graph showing how molecular speeds or energies are distributed at a given temperature.
Heating a rigid sealed container makes particles move faster on average, increasing the frequency and momentum transfer of wall collisions and therefore increasing pressure.
P = F⊥/Amacroscopic pressure from the perpendicular force exerted on a surfacemechanical wave
mechanical wave: a wave that requires matter to provide the restoring interaction and inertia needed for propagation.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringmole
mole: an amount of substance containing Avogadro’s number of particles.
A capped syringe compressed slowly at nearly constant temperature shows pressure increasing as volume decreases.
PV = nRT = Nk_B Tequilibrium states of an ideal gasneutrino / antineutrino
neutrino / antineutrino: electrically neutral, negligible-mass particles included in beta-decay conservation bookkeeping.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepingnode
node: ideal-wire connected points treated as one potential.
Adding resistance in series with an ideal voltage source reduces total current.
closed loop ⇒ charge can flowqualitative circuit-state reasoningnode potential
node potential: electric potential shared by ideal-wire connected points.
A vehicle electrical system combines parallel loads with internal series resistances.
R_series = ΣR_icomponents carrying the same current with no branching between themnonohmic element
nonohmic element: a device whose V–I relationship is not linear through the origin.
A longer nichrome wire has greater resistance when material and area are unchanged.
R = ρL/Auniform conductornormal
normal: a line perpendicular to the reflecting surface at the point where the ray strikes.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfacenormal incidence
normal incidence: incidence along the normal, for which the transmitted ray does not change direction.
A light ray entering glass from air bends toward the normal because its speed decreases in the higher-index medium.
n = c/vrelating propagation speed and refractive index in a transparent mediumnucleon
nucleon: a proton or neutron in an atomic nucleus.
Nuclear notation distinguishes isotopes by proton and neutron counts even when the chemical element is the same.
A = Z + Nnnuclear notation and isotope bookkeepingnucleon number
nucleon number: the total number of protons and neutrons, conserved in the nuclear-reaction bookkeeping used here.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangednucleus
nucleus: the small positively charged central region of an atom containing protons and neutrons.
Nuclear notation distinguishes isotopes by proton and neutron counts even when the chemical element is the same.
A = Z + Nnnuclear notation and isotope bookkeepingobject distance
object distance: the signed distance from the object to the mirror in the chosen sign convention.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventionobserved frequency
observed frequency: the frequency measured by the observer.
An ambulance siren is heard at higher pitch while approaching and lower pitch while receding.
approaching → f_observed > f_restsource and observer move toward one anotherohmic behavior
ohmic behavior: approximately linear V–I behavior under fixed conditions.
A longer nichrome wire has greater resistance when material and area are unchanged.
R = ρL/Auniform conductoroptical path difference
optical path difference: the phase-relevant path difference accounting for travel through a medium of refractive index n.
Soap bubbles show changing colors because film thickness varies across the surface and therefore changes reflected-light interference.
optical path difference = 2ntthin-film reflected-light comparison at normal incidence before including reflection phase changesorder
order: the integer m labeling constructive-interference maxima.
A double-slit pattern contains narrow interference fringes inside a broader single-slit diffraction envelope.
d sinθ_m = mλdouble-slit or diffraction-grating constructive maximapair interaction
pair interaction: one distinct two-charge contribution to the total electric potential energy.
Separating opposite charges requires external work and raises their potential energy toward zero.
U_E = q₁q₂/(4πεr)two point charges using zero potential energy at infinite separationparallel connection
parallel connection: components connected across the same two nodes.
Adding resistance in series with an ideal voltage source reduces total current.
closed loop ⇒ charge can flowqualitative circuit-state reasoningparallel-plate capacitor
parallel-plate capacitor: two separated parallel conducting surfaces carrying equal-magnitude opposite charges.
Camera-flash capacitors store energy at high voltage and release it rapidly.
C = Q/|ΔV|definition of capacitancepath difference
path difference: the difference in distance traveled by waves from the two openings to the observation point.
A double-slit pattern contains narrow interference fringes inside a broader single-slit diffraction envelope.
d sinθ_m = mλdouble-slit or diffraction-grating constructive maximapeak wavelength
peak wavelength: the wavelength at which a blackbody spectrum has its greatest intensity per wavelength.
As a hot object’s temperature rises, its continuous thermal spectrum becomes more intense and its peak shifts toward shorter wavelength.
λmax T = bpeak wavelength of an ideal blackbody spectrumperiod
period: the time for one complete cycle, measured in seconds.
If a source oscillates faster while wave speed in the medium stays fixed, the wavelength decreases.
v = fλany periodic wave when speed, frequency, and wavelength refer to the same wave in the same mediumphase
phase: where a point lies within a repeating wave cycle.
If a source oscillates faster while wave speed in the medium stays fixed, the wavelength decreases.
v = fλany periodic wave when speed, frequency, and wavelength refer to the same wave in the same mediumphotocurrent
photocurrent: electric current associated with collected photoelectrons in a photoelectric apparatus.
At a fixed above-threshold frequency, increasing light intensity can increase photocurrent while leaving the maximum electron kinetic energy unchanged.
Kmax = hf − φphotoelectric emission when hf≥φphotoelectric effect
photoelectric effect: emission of electrons from a photoactive material when incident electromagnetic radiation has sufficient photon energy.
At a fixed above-threshold frequency, increasing light intensity can increase photocurrent while leaving the maximum electron kinetic energy unchanged.
Kmax = hf − φphotoelectric emission when hf≥φphotoelectron
photoelectron: an electron emitted from a material by the photoelectric effect.
At a fixed above-threshold frequency, increasing light intensity can increase photocurrent while leaving the maximum electron kinetic energy unchanged.
Kmax = hf − φphotoelectric emission when hf≥φphoton
photon: a massless, electrically neutral quantum of electromagnetic radiation whose energy is proportional to frequency.
Electron diffraction from a crystal or slit pattern provides evidence that material particles can show wave behavior.
E = hfphoton energy or an energy transfer involving one photonphoton momentum
photon momentum: the momentum carried by a photon, with magnitude h/λ.
Electron diffraction from a crystal or slit pattern provides evidence that material particles can show wave behavior.
E = hfphoton energy or an energy transfer involving one photonplane wavefront
plane wavefront: an idealized wavefront represented by parallel planes perpendicular to propagation.
Radio waves and visible light are both electromagnetic waves; they differ in wavelength and frequency rather than in the need for a material medium.
c = fλelectromagnetic radiation propagating in vacuumpoint charge
point charge: a model in which the size of a charged object is negligible compared with the distances in the situation.
Two like-charged pith balls repel along the line joining their centers.
F_E = |q₁q₂|/(4πεr²)point charges or spherically symmetric charged objects when the point-charge model is validpolarization
polarization: restriction of transverse-wave oscillations to a particular direction.
A pulse on a light string meeting a heavier-string region partly reflects and partly transmits; the source-set frequency does not change at the junction.
f_reflected = f_transmitted = f_incidentreflection and transmission at a stationary boundarypolarizer
polarizer: a device or material that preferentially transmits one transverse polarization direction.
A pulse on a light string meeting a heavier-string region partly reflects and partly transmits; the source-set frequency does not change at the junction.
f_reflected = f_transmitted = f_incidentreflection and transmission at a stationary boundarypositron
positron: the electron antiparticle with the same mass as an electron and charge +e.
In alpha decay the daughter nucleus has A reduced by 4 and Z reduced by 2 because a helium-4 nucleus is emitted.
alpha: A→A−4, Z→Z−2 + ⁴₂Healpha-decay nuclear bookkeepingpotential difference
potential difference: the change in electric potential between two locations, equal to potential-energy change per unit charge.
A battery maintains a potential difference that transfers energy to moving charge in a circuit.
V = U_E/q_testdefinition of electric potential at a pointpotential drop
potential drop: negative change in electric potential along a traversal.
A battery and two resistors in one loop have voltage drops summing to the source emf.
ΣΔV_loop = 0any closed loop in the lumped circuit modelpotential rise
potential rise: positive change in electric potential along a traversal.
A battery and two resistors in one loop have voltage drops summing to the source emf.
ΣΔV_loop = 0any closed loop in the lumped circuit modelpower dissipation
power dissipation: conversion of electrical energy per unit time.
A 60 W lamp transforms electrical energy faster than a 10 W lamp at rated conditions.
P = IΔVany circuit element when current and potential difference are knownprincipal axis
principal axis: the reference line through the mirror vertex and the center of curvature of a spherical mirror.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventionP–V diagram
P–V diagram: a graph of pressure versus volume used to represent thermodynamic states and processes.
Rapidly compressing air in a bicycle pump raises its temperature because positive work is done on the gas.
U = (3/2)nRT = (3/2)Nk_B Tideal monatomic gas whose internal energy is translational kinetic energyquantization
quantization: restriction of some bound-system energy and momentum values to discrete allowed values.
Electron diffraction from a crystal or slit pattern provides evidence that material particles can show wave behavior.
E = hfphoton energy or an energy transfer involving one photonquantized radiation
quantized radiation: the photon/quantum assumption needed to model the observed blackbody spectrum rather than the failed classical high-frequency prediction.
As a hot object’s temperature rises, its continuous thermal spectrum becomes more intense and its peak shifts toward shorter wavelength.
λmax T = bpeak wavelength of an ideal blackbody spectrumradiation
radiation: energy transfer by electromagnetic waves that does not require matter between source and receiver.
A metal spoon in hot soup warms because energy is transferred through thermal contact, primarily by conduction through the spoon.
T_hot > T_cold → spontaneous thermal transfer hot → coldtwo systems in thermal contact at different temperaturesradioactive decay
radioactive decay: spontaneous transformation of a nucleus into one or more different nuclei, or to a lower energy level of the same nucleus.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangedreal image
real image: an image formed where reflected light rays actually intersect.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventionreceding
receding: source and observer moving farther apart.
An ambulance siren is heard at higher pitch while approaching and lower pitch while receding.
approaching → f_observed > f_restsource and observer move toward one anotherrecoil electron
recoil electron: the electron that receives energy and momentum from the incident photon.
X-ray photons scattered by electrons show an angle-dependent wavelength increase that classical wave-only scattering cannot explain.
Δλ = (h/mec)(1 − cosθ)Compton scattering of a photon from an approximately free electronreference configuration
reference configuration: the chosen zero-energy configuration, conventionally infinite separation for isolated point charges.
Separating opposite charges requires external work and raises their potential energy toward zero.
U_E = q₁q₂/(4πεr)two point charges using zero potential energy at infinite separationreflection
reflection: the portion of a wave that returns into the original medium at a boundary.
A pulse on a light string meeting a heavier-string region partly reflects and partly transmits; the source-set frequency does not change at the junction.
f_reflected = f_transmitted = f_incidentreflection and transmission at a stationary boundaryreflection phase reversal
reflection phase reversal: a 180° phase change for reflection from a boundary toward a higher refractive index.
Soap bubbles show changing colors because film thickness varies across the surface and therefore changes reflected-light interference.
optical path difference = 2ntthin-film reflected-light comparison at normal incidence before including reflection phase changesrefraction
refraction: a change in light-ray direction associated with a change in propagation speed at a boundary.
A light ray entering glass from air bends toward the normal because its speed decreases in the higher-index medium.
n = c/vrelating propagation speed and refractive index in a transparent mediumrefractive index
refractive index: the dimensionless ratio n=c/v comparing vacuum light speed with light speed in a medium.
A light ray entering glass from air bends toward the normal because its speed decreases in the higher-index medium.
n = c/vrelating propagation speed and refractive index in a transparent mediumrelative motion
relative motion: motion of source and observer compared with one another along the relevant direction.
An ambulance siren is heard at higher pitch while approaching and lower pitch while receding.
approaching → f_observed > f_restsource and observer move toward one anotherresistance
resistance: ratio of potential difference to current for an ohmic element.
A longer nichrome wire has greater resistance when material and area are unchanged.
R = ρL/Auniform conductorresistivity
resistivity: material property connecting conductor geometry to resistance.
A longer nichrome wire has greater resistance when material and area are unchanged.
R = ρL/Auniform conductorrest frequency
rest frequency: the source frequency associated with no relative source-observer motion.
An ambulance siren is heard at higher pitch while approaching and lower pitch while receding.
approaching → f_observed > f_restsource and observer move toward one anotherreversible process
reversible process: an ideal limiting process that can be reversed without net entropy production.
A hot object cools in a cooler isolated enclosure and the two systems approach one temperature; the reverse concentration of energy does not occur spontaneously.
Isolated system: total entropy never decreasesqualitative second-law reasoning for an isolated systemright-hand rule
right-hand rule: a directional convention used to relate a positive charge’s velocity, magnetic field, and magnetic-force direction.
A positive charge moving perpendicular to a uniform magnetic field follows a curved path while keeping the same speed if magnetic force is the only force doing work.
F_B = |q|vB sinθmoving charge in a magnetic field; numerical angle treatment here is limited to 0°, 90°, and 180°root-mean-square speed
root-mean-square speed: the square root of the average of particle speed squared, linked directly to temperature.
Heating a rigid sealed container makes particles move faster on average, increasing the frequency and momentum transfer of wall collisions and therefore increasing pressure.
P = F⊥/Amacroscopic pressure from the perpendicular force exerted on a surfacescalar superposition
scalar superposition: algebraic addition of electric-potential contributions including their signs.
A battery maintains a potential difference that transfers energy to moving charge in a circuit.
V = U_E/q_testdefinition of electric potential at a pointscattering angle
scattering angle: the angle between the incident photon direction and the outgoing photon direction.
X-ray photons scattered by electrons show an angle-dependent wavelength increase that classical wave-only scattering cannot explain.
Δλ = (h/mec)(1 − cosθ)Compton scattering of a photon from an approximately free electronseries connection
series connection: components connected so the same current passes through them.
Adding resistance in series with an ideal voltage source reduces total current.
closed loop ⇒ charge can flowqualitative circuit-state reasoningsingle-slit pattern
single-slit pattern: a broad central bright region with weaker side maxima separated by minima.
Red light creates a wider single-slit diffraction pattern than shorter-wavelength blue light through the same slit.
a sinθ_m = mλsingle-slit diffraction minimasmall-angle approximation
small-angle approximation: the approximation sinθ≈tanθ≈θ for sufficiently small θ in radians.
Red light creates a wider single-slit diffraction pattern than shorter-wavelength blue light through the same slit.
a sinθ_m = mλsingle-slit diffraction minimaSnell’s law
Snell’s law: the relationship linking the two refractive indices with the sine of the incident and refracted angles.
A light ray entering glass from air bends toward the normal because its speed decreases in the higher-index medium.
n = c/vrelating propagation speed and refractive index in a transparent mediumspecific heat capacity
specific heat capacity: energy required per unit mass per kelvin of temperature change for a material in the model.
Equal masses of water and aluminum receiving the same energy do not undergo the same temperature change because their specific heats differ.
Q = mcΔTtemperature change with no phase change and approximately constant cspecular reflection
specular reflection: reflection from a smooth surface whose local normals are nearly parallel, producing an organized reflected beam.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfacestanding wave
standing wave: a persistent interference pattern with fixed nodes and antinodes.
Two equal pulses meeting crest-to-crest briefly double the displacement, then pass through one another.
y_total = Σy_ilinear superposition when waves overlapstate function
state function: a property whose change depends only on the initial and final states, not on the path between them.
Rapidly compressing air in a bicycle pump raises its temperature because positive work is done on the gas.
U = (3/2)nRT = (3/2)Nk_B Tideal monatomic gas whose internal energy is translational kinetic energystate variable
state variable: a macroscopic property such as pressure, volume or temperature that describes an equilibrium state.
A capped syringe compressed slowly at nearly constant temperature shows pressure increasing as volume decreases.
PV = nRT = Nk_B Tequilibrium states of an ideal gassteady current
steady current: current that causes no net charge accumulation at a node.
Current splits at a parallel junction and recombines without being consumed.
ΣI_in = ΣI_outsteady-state junctionStefan–Boltzmann law
Stefan–Boltzmann law: the relationship showing that ideal-blackbody power is proportional to surface area and the fourth power of absolute temperature.
As a hot object’s temperature rises, its continuous thermal spectrum becomes more intense and its peak shifts toward shorter wavelength.
λmax T = bpeak wavelength of an ideal blackbody spectrumstopping potential
stopping potential: the retarding potential difference that reduces the measured photoelectric current to zero by stopping even the most energetic emitted electrons.
At a fixed above-threshold frequency, increasing light intensity can increase photocurrent while leaving the maximum electron kinetic energy unchanged.
Kmax = hf − φphotoelectric emission when hf≥φstrong force
strong force: the short-range interaction that dominates nucleon interactions at nuclear scales.
In a fission or fusion reaction, total energy and momentum remain conserved even when the total rest mass of the products differs from that of the reactants.
ΔE = Δmc²nuclear reactions/processes where rest mass and other energy forms are exchangedsuperposition
superposition: vector addition of the separate electric-force contributions from multiple sources.
Two like-charged pith balls repel along the line joining their centers.
F_E = |q₁q₂|/(4πεr²)point charges or spherically symmetric charged objects when the point-charge model is validsystem boundary
system boundary: the conceptual boundary that determines which energy stores and transfers are inside the analysis.
A proton released in an electric field accelerates toward lower electric potential.
ΔU_E = qΔVa charged object moves between two locations with known electric potentialstemperature
temperature: a macroscopic quantity tied to the average translational kinetic energy of particles.
Heating a rigid sealed container makes particles move faster on average, increasing the frequency and momentum transfer of wall collisions and therefore increasing pressure.
P = F⊥/Amacroscopic pressure from the perpendicular force exerted on a surfacetemperature difference
temperature difference: the difference between temperatures on opposite sides of a conducting region.
Equal masses of water and aluminum receiving the same energy do not undergo the same temperature change because their specific heats differ.
Q = mcΔTtemperature change with no phase change and approximately constant ctest charge
test charge: an ideal point charge small enough not to significantly disturb the field being measured.
Field vectors around a positive point charge point radially outward.
E = F_E/q_test (vector relation)definition of electric field using a sufficiently small positive test chargethermal conductivity
thermal conductivity: an intrinsic material property that sets the rate of conductive energy transfer for a given geometry and temperature difference.
Equal masses of water and aluminum receiving the same energy do not undergo the same temperature change because their specific heats differ.
Q = mcΔTtemperature change with no phase change and approximately constant cthermal contact
thermal contact: a condition in which systems can transfer energy through thermal processes.
A metal spoon in hot soup warms because energy is transferred through thermal contact, primarily by conduction through the spoon.
T_hot > T_cold → spontaneous thermal transfer hot → coldtwo systems in thermal contact at different temperaturesthermal equilibrium
thermal equilibrium: a state with no net thermal transfer between systems in thermal contact.
Equal masses of water and aluminum receiving the same energy do not undergo the same temperature change because their specific heats differ.
Q = mcΔTtemperature change with no phase change and approximately constant cthermodynamic equilibrium
thermodynamic equilibrium: a macroscopic equilibrium state associated with maximum entropy for an isolated system under fixed constraints.
A hot object cools in a cooler isolated enclosure and the two systems approach one temperature; the reverse concentration of energy does not occur spontaneously.
Isolated system: total entropy never decreasesqualitative second-law reasoning for an isolated systemthin film
thin film: a transparent layer whose thickness is comparable to the wavelength of light.
Soap bubbles show changing colors because film thickness varies across the surface and therefore changes reflected-light interference.
optical path difference = 2ntthin-film reflected-light comparison at normal incidence before including reflection phase changesthreshold frequency
threshold frequency: the minimum incident-light frequency that can produce photoelectron emission for a given material.
At a fixed above-threshold frequency, increasing light intensity can increase photocurrent while leaving the maximum electron kinetic energy unchanged.
Kmax = hf − φphotoelectric emission when hf≥φtime constant
time constant: characteristic time τ = RC describing how quickly an ideal RC transient approaches steady state.
Two identical capacitors in parallel have twice the capacitance of one; two identical capacitors in series have half the capacitance of one.
1/C_series = Σ(1/C_i)capacitors connected in seriestotal internal reflection
total internal reflection: complete reflection that occurs for incidence beyond the critical angle when light attempts to pass from higher index to lower index.
A light ray entering glass from air bends toward the normal because its speed decreases in the higher-index medium.
n = c/vrelating propagation speed and refractive index in a transparent mediumtransmission
transmission: the portion of a wave that crosses into the second medium.
A pulse on a light string meeting a heavier-string region partly reflects and partly transmits; the source-set frequency does not change at the junction.
f_reflected = f_transmitted = f_incidentreflection and transmission at a stationary boundarytransverse
transverse: having field oscillations perpendicular to the propagation direction.
Radio waves and visible light are both electromagnetic waves; they differ in wavelength and frequency rather than in the need for a material medium.
c = fλelectromagnetic radiation propagating in vacuumtransverse wave
transverse wave: a wave whose disturbance is perpendicular to the direction of propagation.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringtwo-dimensional momentum conservation
two-dimensional momentum conservation: vector conservation of momentum in perpendicular components or an equivalent vector diagram.
X-ray photons scattered by electrons show an angle-dependent wavelength increase that classical wave-only scattering cannot explain.
Δλ = (h/mec)(1 − cosθ)Compton scattering of a photon from an approximately free electronvacuum
vacuum: a region without a material medium; electromagnetic waves can propagate through it.
Radio waves and visible light are both electromagnetic waves; they differ in wavelength and frequency rather than in the need for a material medium.
c = fλelectromagnetic radiation propagating in vacuumvirtual image
virtual image: an image located where diverging reflected rays appear to have originated when extended backward.
A concave makeup mirror can form an upright enlarged virtual image when the object is inside the focal distance.
1/f = 1/s_o + 1/s_iplane or spherical-mirror image calculations with a consistent sign conventionvisible light
visible light: the electromagnetic-spectrum region perceived by human vision.
Radio waves and visible light are both electromagnetic waves; they differ in wavelength and frequency rather than in the need for a material medium.
c = fλelectromagnetic radiation propagating in vacuumwave
wave: a disturbance that transfers energy from one region to another without net transport of the medium as a whole.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringwave pulse
wave pulse: a single disturbance that travels through a medium or field.
A pulse travels along a rope while individual rope elements move around their equilibrium positions rather than traveling to the far end.
v_string = √(F_T/μ)a transverse wave on a stretched uniform stringwave-particle duality
wave-particle duality: the need to choose wave-like or particle-like descriptions according to the evidence and interaction being modeled.
Electron diffraction from a crystal or slit pattern provides evidence that material particles can show wave behavior.
E = hfphoton energy or an energy transfer involving one photonwavefront
wavefront: a surface joining points of a light wave that have the same phase; the ray direction is perpendicular to it in the ray model.
A laser aimed at a plane mirror reflects symmetrically about the normal even when the mirror is tilted.
θ_i = θ_rreflection of a light ray from a surfacewavelength
wavelength: the shortest spatial separation between points in the same phase, measured in meters.
If a source oscillates faster while wave speed in the medium stays fixed, the wavelength decreases.
v = fλany periodic wave when speed, frequency, and wavelength refer to the same wave in the same mediumWien displacement law
Wien displacement law: the inverse relationship between peak wavelength and absolute temperature.
As a hot object’s temperature rises, its continuous thermal spectrum becomes more intense and its peak shifts toward shorter wavelength.
λmax T = bpeak wavelength of an ideal blackbody spectrumwork done on a gas
work done on a gas: energy transferred mechanically into a gas by an external force as the system boundary moves.
Rapidly compressing air in a bicycle pump raises its temperature because positive work is done on the gas.
U = (3/2)nRT = (3/2)Nk_B Tideal monatomic gas whose internal energy is translational kinetic energywork function
work function: the minimum energy required to emit an electron from the material.
At a fixed above-threshold frequency, increasing light intensity can increase photocurrent while leaving the maximum electron kinetic energy unchanged.
Kmax = hf − φphotoelectric emission when hf≥φDefinitions students should not collapse into one idea
Many errors come from using two related words as though they were interchangeable.
| Pair | Difference that matters | Quick check |
|---|---|---|
| Temperature vs thermal energy | Temperature tracks a particle kinetic-energy scale; thermal/internal energy depends on the system state and amount of matter. | Two objects can share a temperature but store different internal energies. |
| Electric field vs electric potential | Electric field is a vector force-per-charge quantity; electric potential is scalar energy-per-charge. | Direction belongs to E, not to V. |
| Current vs charge | Charge is an amount; current is the rate at which net charge crosses a surface. | I = ΔQ/Δt, so amperes are coulombs per second. |
| Real image vs virtual image | A real image forms where rays actually converge; a virtual image forms where backward extensions appear to meet. | A real image can be projected onto a screen. |
| Interference vs diffraction | Interference describes superposition from multiple coherent contributions; diffraction is wave spreading associated with finite apertures/obstacles. | A multi-slit pattern can show both an interference structure and a diffraction envelope. |
| Photon energy vs light intensity | Photon energy depends on frequency; intensity describes energy delivered per area per time and can change photon count. | At fixed frequency, higher intensity does not raise the energy of each photon. |
AP Physics 2 glossary questions
How many definitions are in this glossary?
This build contains 235 unique glossary terms drawn from 247 topic-term placements across all 46 lessons.
Does every term link to a lesson?
Yes. Every glossary card links to the exact topic or topics where the term is used so you can move from a short definition to equations, examples and practice.
Should I memorize definitions word for word?
No. You should be able to state the physical meaning accurately and use it in a diagram, equation, graph or explanation.
Why are equations shown in a glossary?
A definition is more useful when you can connect it to the model that operationalizes the idea. The equation snippet is a bridge to the deeper lesson, not a replacement for it.
Can I print the glossary?
Yes. Use Print / Save Glossary to create a paper or PDF copy. Search and unit filters are best used on screen.
What if two topics use the same term?
The glossary keeps one definition card and links that card to each relevant topic, reducing duplication while preserving context.