Chapter 1

The Nature of Light

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Summary

The part of optics dealing with the ray aspect of light is called geometric optics The index of refraction of a material is n = c / v , where v is the speed of light in a material and c is the speed of light in a vacuum The ray model of light describes the path of light as straight lines. When a light ray strikes a smooth surface, the angle of reflection equals the angle of incidence

Key terms

refraction

changing of a light ray’s direction when it passes through variations in matter

geometric optics

part of optics dealing with the ray aspect of light

ray

straight line that originates at some point

Brewster’s law

tan θ b = n 2 n 1 , where n 1 is the medium in which the incident and reflected light travel and n 2 is the index of refraction of the medium that forms the interface that…

corner reflector

object consisting of two (or three) mutually perpendicular reflecting surfaces, so that the light that enters is reflected back exactly parallel to the direction from which it came

Huygens’s principle

every point on a wave front is a source of wavelets that spread out in the forward direction at the same speed as the wave itself; the new wave front is a plane tangent to all of…

Chapter 2

Geometric Optics and Image Formation

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Summary

Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright A plane mirror always forms a virtual image (behind the mirror) The focal length of a spherical mirror is one-half of its radius of curvature: f = R / 2

Key terms

image and object

the same distance from a flat mirror, the image size is the same as the object size, and the image is upright

coma

similar to spherical aberration, but arises when the incoming rays are not parallel to the optical axis

spherical aberration

distortion in the image formed by a spherical mirror when rays are not all focused at the same point

virtual image

image that cannot be projected on a screen because the rays do not physically go through the image, they only appear to originate from the image

object

observed through a plane interface between two media, then it appears at an apparent distance h i that differs from the actual distance h o : h i = ( n 2 / n 1 ) h o

ray tracing

technique that uses geometric constructions to find and characterize the image formed by an optical system

focal length

distance along the optical axis from the focal point to the optical element that focuses the light rays

aberration

distortion in an image caused by departures from the small-angle approximation

Chapter 3

Interference

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Summary

An interference pattern is obtained by the superposition of light from two slits As the number of slits is increased, the intensity of the principal maxima increases and the width decreases When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a 180 ° phase change (or a λ / 2 shift) occurs Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film.

Key terms

number of slits

increased, the intensity of the principal maxima increases and the width decreases

thin-film interference

interference between light reflected from different surfaces of a thin film

interference pattern

obtained by the superposition of light from two slits

coherent waves

waves are in phase or have a definite phase relationship

Newton’s rings

circular interference pattern created by interference between the light reflected off two surfaces as a result of a slight gap between them

order

integer m used in the equations for constructive and destructive interference for a double slit

secondary maximum

bright interference fringes of intensity lower than the principal maxima

Chapter 4

Diffraction

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Summary

Missing orders occur when an interference maximum and a diffraction minimum are located together A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a double slit Diffraction can send a wave around the edges of an opening or other obstacle The intensity pattern for diffraction due to a single slit can be calculated using phasors as I = I 0 ( sin β ) 2 , where β = ϕ 2 = π a sin θ λ , a is the slit width, λ is the wavelength, and θ is the angle from the…

Key terms

diffraction

bending of a wave around the edges of an opening or an obstacle

missing order

interference maximum that is not seen because it coincides with a diffraction minimum

diffraction grating

large number of evenly spaced parallel slits

hologram

three-dimensional image recorded on film by lasers; the word hologram means entire picture (from the Greek word holo , as in holistic)

Rayleigh criterion

two images are just-resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other

two-slit diffraction pattern

diffraction pattern of two slits of width D that are separated by a distance d is the interference pattern of two point sources separated by d multiplied by the diffraction…

X-ray diffraction

technique that provides the detailed information about crystallographic structure of natural and manufactured materials

Chapter 5

Relativity

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Summary

The second postulate of special relativity is that the speed of light c is the same in all inertial frames of reference, independent of the relative motion of the observer and the light source Relativity is the study of how observers in different reference frames measure the same event An inertial frame of reference is a reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted upon by an outside force The first postulate of special relativity is that the laws of physics are the same in all inertial frames of reference.

Key terms

first postulate of special relativity

laws of physics are the same in all inertial frames of reference

event

occurrence in space and time specified by its position and time coordinates ( x , y , z , t ) measured relative to a frame of reference

inertial frame of reference

reference frame in which a body at rest remains at rest and a body in motion moves at a constant speed in a straight line unless acted on by an outside force

second postulate of special relativity

light travels in a vacuum with the same speed c in any direction in all inertial frames

speed of light

ultimate speed limit for any particle having mass

classical (Galilean) velocity addition

method of adding velocities when v < c ; velocities add like regular numbers in one-dimensional motion: u = v + u ′ , where v is the velocity between two observers, u is the…

Galilean relativity

if an observer measures a velocity in one frame of reference, and that frame of reference is moving with a velocity past a second reference frame, an observer in the second frame…

length contraction

decrease in observed length of an object from its proper length L 0 to length L when its length is observed in a reference frame where it is traveling at speed v

Chapter 6

Photons and Matter Waves

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Summary

Planck’s hypothesis of energy quanta led to the theoretical Planck’s radiation law, which agrees with the experimental blackbody radiation curve; it also explains Wien’s and Stefan’s laws The classical approach does not explain the blackbody radiation curve To explain the blackbody radiation curve, Planck assumed that the exchange of energy between radiation and cavity walls takes place only in discrete quanta of energy. The experimental Stefan’s law states that the total power of radiation emitted across the entire spectrum of wavelengths at a given temperature is proportional to the fourth power of the Kelvin temperature of the…

Key terms

Planck’s hypothesis of energy quanta

energy exchanges between the radiation and the walls take place only in the form of discrete energy quanta

given temperature

proportional to the fourth power of the Kelvin temperature of the…

blackbody radiation

radiation emitted by a blackbody

blackbody

perfect absorber/emitter

nuclear model of the atom

heavy positively charged nucleus at the center is surrounded by electrons, proposed by Rutherford

Compton effect

the change in wavelength when an X-ray is scattered by its interaction with some materials

inelastic scattering

scattering effect where kinetic energy is not conserved but the total energy is conserved

Chapter 7

Quantum Mechanics

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Summary

In quantum mechanics, the state of a physical system is represented by a wave function In Born’s interpretation, the square of the particle’s wave function represents the probability density of finding the particle around a specific location in space The expectation value is the average value of a quantity that requires a wave function and an integration Wave functions must first be normalized before using them to make predictions

Key terms

energy-time uncertainty principle

energy-time relation for uncertainties in the simultaneous measurements of the energy of a quantum state and of its lifetime

expectation value

average value of the physical quantity assuming a large number of particles with the same wave function

wave function

function that represents the quantum state of a particle (quantum system)

probability density

square of the particle’s wave function

product of experimental uncertainties

always larger than or equal to ℏ / 2

state of a physical system

represented by a wave function

Copenhagen interpretation

states that when an observer is not looking or when a measurement is not being made, the particle has many values of measurable quantities, such as position

field emission

electron emission from conductor surfaces when a strong external electric field is applied in normal direction to conductor’s surface

Chapter 8

Atomic Structure

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Summary

The quantum numbers of an electron in a hydrogen atom can be used to calculate the magnitude and direction of the orbital magnetic dipole moment of the atom A hydrogen atom can be described in terms of its wave function, probability density, total energy, and orbital angular momentum The state of an electron in a hydrogen atom is specified by its quantum numbers ( n , l , m ) In contrast to the Bohr model of the atom, the Schrödinger model makes predictions based on probability statements

Key terms

orbital magnetic dipole moment

measure of the strength of the magnetic field produced by the orbital angular momentum of the electron

spin-flip transitions

atomic transitions between states of an electron-proton system in which the magnetic moments are aligned and not aligned

transition metal

element that is located in the gap between the first two columns and the last six columns of the table of elements that contains electrons that fill the d subshell

selection rules

rules that determine whether atomic transitions are allowed or forbidden (rare)

braking radiation

radiation produced by targeting metal with a high-energy electron beam (or radiation produced by the acceleration of any charged particle in a material)

spin-orbit coupling

interaction between the electron magnetic moment and the magnetic field produced by the orbital angular momentum of the electron

stimulated emission

when a photon of energy triggers an electron in a metastable state to drop in energy emitting an additional photon

Chapter 9

Condensed Matter Physics

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Summary

Molecules form by two main types of bonds: the ionic bond and the covalent bond. An ionic bond transfers an electron from one atom to another, and a covalent bond shares the electrons Energy differences between adjacent vibrational energy levels are larger than those between rotational energy levels The energy change associated with ionic bonding depends on three main processes: the ionization of an electron from one atom, the acceptance of the electron by the second atom, and the Coulomb attraction of the…

Key terms

hybridization

change in the energy structure of an atom in which energetically favorable mixed states participate in bonding

ionic bond

bond formed by the Coulomb attraction of a positive and negative ions

covalent bond

bond formed by the sharing of one or more electrons between atoms

vibrational energy level

energy level associated with the vibrational energy of a molecule

rotational energy level

energy level associated with the rotational energy of a molecule

absorption spectrum

inversely related to the moment of inertia

repulsion constant

experimental parameter associated with a repulsive force between ions brought so close together that the exclusion principle is important

body-centered cubic (BCC)

crystal structure in which an ion is surrounded by eight nearest neighbors located at the corners of a unit cell

Chapter 10

Nuclear Physics

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Summary

The atomic mass of an element is the weighted average of the masses of its isotopes The mass defect of a nucleus is the difference between the total mass of a nucleus and the sum of the masses of all its constituent nucleons The binding energy (BE) of a nucleus is equal to the amount of energy released in forming the nucleus, or the mass defect multiplied by the speed of light squared The atomic nucleus is composed of protons and neutrons

Key terms

mass defect of a nucleus

the difference between the total mass of a nucleus and the sum of the masses of all its constituent nucleons

mass defect

difference between the mass of a nucleus and the total mass of its constituent nucleons

binding energy (BE)

energy needed to break a nucleus into its constituent protons and neutrons

isotopes

nuclei having the same number of protons but different numbers of neutrons

atomic mass

total mass of the protons, neutrons, and electrons in a single atom

atomic nucleus

tightly packed group of nucleons at the center of an atom

nucleons

protons and neutrons found inside the nucleus of an atom

atomic mass of an element

the weighted average of the masses of its isotopes

Chapter 11

Particle Physics and Cosmology

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Summary

Quarks interact via the strong force, but leptons do not. Both quark and leptons interact via the electromagnetic, weak, and gravitational forces Elementary particles are classified into fermions and boson. Quarks and leptons belong to particle families composed of three members each.

Key terms

cosmology

study of the origin, evolution, and ultimate fate of the universe

fermion

particle with half-integral spin that is antisymmetric on exchange

boson

particle with integral spin that are symmetric on exchange

fundamental force

one of four forces that act between bodies of matter: the strong nuclear, electromagnetic, weak nuclear, and gravitational forces

quark

a fermion that participates in the electroweak and strong nuclear force

lepton

a fermion that participates in the electroweak force

baryon number

baryon number has the value B = + 1 for baryons, - 1 for antibaryons, and 0 for all other particles and is conserved in particle interactions

lepton number

electron-lepton number L e , the muon-lepton number L μ , and the tau-lepton number L τ are conserved separately in every particle interaction