Electromagnetic Waves

Chapter 23

EM Waves are Transverse Waves

Imagine a snapshot of the electromagnetic waveThe electric field is along the x-axisThe wave travels in the z-direction

Determined by the right-hand rule #2The magnetic field is along the y-directionBecause both fields are perpendicular to each other, the wave is a

transverse wave

Section 23.2

EM Waves Carry Energy, finalAs the wave propagates, the energies per unit

volume oscillateThe electric and magnetic energies are equal and

this leads to the proportionality between the peak electric and magnetic fields

o o oo

o o

ε E Bμ

E c B

2 21 1

2 2

Section 23.3

Intensity of an EM WaveThe strength of an em wave is usually measured in

terms of its intensityUnits W/m2

Intensity is the amount of energy transported per unit time across a surface of unit area

Intensity also equals the energy density multiplied by the speed of the wave

I = utotal x c = ½ εo c Eo2

Since E = c B, the intensity is also proportional to the square of the magnitude field amplitude

Section 23.3

Radiation PressureWhen an electromagnetic wave is absorbed by an

object, it exerts a force on the objectThe total force on the object is proportional to its

exposed areaRadiation pressure is the force of the

electromagnetic force divided by the areaThis can also be expressed in terms of the intensity

radiation

F IP

A c

Section 23.3

AntennasThe simple antenna

with two wires is called a dipole antenna

At any particular moment, the two wires are oppositely charged

The waves propagate perpendicular to the antenna’s axis

Section 23.5

Polarizers, finalIf the incident light is

polarized perpendicular to the axis of the polarizer, no light is transmitted

If the incident light is polarized at an angle θ relative to the axis of the polarizer, only a component of electric field is transmitted

Malus’ Law and Unpolarized LightUnpolarized light can be thought of as a collection of

many separate light waves, each linearly polarized in different and random directions

Each separate wave is transmitted through the polarizer according to Malus’ Law

The average outgoing intensity is the average of all the incident waves:

Iout = (Iin cos2 θ)ave = ½ Iin Since the average value of the cos2 θ is ½

Section 23.6

Polarizers, SummaryWhen analyzing light as it passes through several

polarizers in succession, always analyze the effect of one polarizer at a time

The light transmitted by a polarizer is always linearly polarizedThe polarization direction is determined solely by the

polarizer axisThe transmitted wave has no “memory” of its original

polarization

Section 23.6

Geometrical Optics

Chapter 24- Review

Refraction

Snell’s Law

n1 sin θ1 = n2 sin θ2

Section 24.3

Critical AngleFrom Snell’s Law, with θ2 = 90°, θ1 = θcrit

When the angle of incidence is equal to or greater than the critical angle, light is reflected completely at the interface

1 2

1

sincrit

nn

Section 24.3

Drawing A Ray Diagram

Three rays are particularly easy to drawThere are an infinite number of actual rays

The focal rayFrom the tip of the object through the focal pointReflects parallel to the principal axis

Section 24.4

Mirror Equation

Section 24.4

i

o

i

o

sC

Cs

h

h

i

o

i

o

s

s

h

h

i

i

o

o

s

sR

s

Rs

io sRsR

1111

Mirror Equation and MagnificationThe mirror equation can be written in terms of the

focal length

The magnification can also be found from the similar triangles shown in fig. 24.30

1 1 1ƒo is s

Section 24.4

i i

o o

h sm

h s

Sign Convention, Summary

Section 24.4

Rays for a Converging LensThe parallel ray is initially

parallel to the principal axisRefracts and passes

through the focal point on the right (FR)

The focal ray passes through the focal point on the left (FL)Refracts and goes parallel

to the principal axis on the right

The center ray passes through the center of the lens, C

Section 24.5

Thin-Lens EquationGeometry can be used

to find a mathematical relation for locating the image produced by a converging lens

The shaded triangles are pairs of similar triangles

Section 24.5

Thin-Lens Equation and MagnificationThe thin-lens equation is found from an analysis of

the similar triangles

The magnification can also be found from the similar triangles shown

These results are identical to the results found for mirrors

1 1 1ƒo is s

Section 24.5

i i

o o

h sm

h s

Wave Optics

Chapter 25

InterferenceOne property unique to

waves is interferenceInterference of sound

waves can be produced by two speakers

When the waves are in phase, their maxima occur at the same time at a given point in space

Section 25.1

Frequency of a Wave at an InterfaceWhen a light wave

passes from one medium to another, the waves must stay in phase at the interface

The frequency must be the same on both sides of the interface

Section 25.3

Phase Change and Reflection, Diagram

Section 25.3

Thin-Film Interference

Section 25.3

2

12

2

film

film

md constructive interference

n

md destructive interference

n

12

2

2

film

film

md constructive interference

n

md destructive interference

n

m=0,1,2..

Coherent Interference Intensity

22

21 )()( IIIT

Huygens’ Principle

Section 25.4

Double Slit Analysis

Section 25.5

Constructive interferenced sin θ = m λ

Destructive interferenced sin θ = (m + ½) λ

Single-Slit AnalysisDestructive interference

w sin θ = ±m λ

Section 25.6

Diffraction Grating

ΔL = d sin θ = m λ

Section 25.7

Rayleigh Criterion

D1.22

Section 25.8

Applications of Optics

Far-Sighted Correction

Section 26.1

no ssf

111

Near-Sighted Correction

isf

111

zero

Compound Microscope

Section 26.2

i Ntotal obj eyepiece

obj eyepiece

s sm m m , ƒ ƒ

Refracting Telescope

Section 26.3

Tm

obj

eyepiece

mƒ

ƒ

Shutter Speed and ƒ-NumberThere is a trade-off

between shutter speed and ƒ-number If you reduce shutter speed,

you need to compensate by increasing the ƒ-number

Same Exposure Value (Camera settings) can have different f-number and time

Halving f-number reduces EV by sqrt(2)

Section 26.4

time

fEV n

2

Relativity

Chapter 27

Relativity

Section 27.1

A reference frame can be thought of as a set of coordinate axes

Inertial reference frames move with a constant velocityThe principle of Galilean relativity is the idea that the

laws of motion should be the same in all inertial frames

Postulates of Special RelativityAll the laws of physics are the same in all inertial

reference frames The speed of light in a vacuum is a constant,

independent of the motion of the light source and all observers

Section 27.2

Simultaneity

Two events are simultaneous if they occur at the same timeThe two bolts are not simultaneous in Ted’s viewSimultaneity is relative and can be different in different

reference framesThis is different from Newton’s theory, in which time is an

absolute, objective quantity

Section 27.4

Time Dilation

ottv

c2

21

Section 27.3

Proper Time - The time interval Δto is measured by the observer at rest relative to the clock

Length Contraction

The proper length, Lo, is the length measured by the observer at rest relative to the meterstick

Section 27.5

oL L v c2 21 /

Relativistic Addition of VelocitiesThe result of special relativity for the addition of velocities

is

The velocities are:vOT – the velocity of an object relative to an observervTA – the velocity of one observer relative to a second

observervOA – the velocity of the object relative to the second

observer

OT TAOA

OT TA

v vv

v vc2

1

Section 27.6

Relativistic MomentumFrom time dilation and length contraction,

measurements of both Δx and Δt can be different for observers in different inertial reference frames

Should proper time or proper length be used?Einstein showed that you should use the proper time

to calculate momentumUses a clock traveling along with the particle

The result from special relativity is o

o oo

m vx xp m m

t t v c v c2 2 2 21 1

Section 27.7

Newton’s vs. Relativistic MomentumAs v approaches the

speed of light, the relativistic result is very different than Newton’s

There is no limit to how large the momentum can be

However, even when the momentum is very large, the particle’s speed never quite reaches the speed of light

Section 27.7

Relativistic MassWhen the postulates of special relativity are applied

to Newton’s second law, the mass needs to be replaced with a relativistic factor

At low speeds, the relativistic term approaches mo and the two acceleration equations will be the same

When v ≈ c, the acceleration is very small even when the force is very large

o

o

mm

v c3

2 2 21

Section 27.8

Mass and EnergyRelativistic effects need to be taken into account

when dealing with energy at high speedsFrom special relativity and work-energy,

For v << c, this gives KE ≈ ½ m v2 which is the expression for kinetic energy from Newton’s results

oo

m cKE m c

v c

22

2 21

Section 27.9

Kinetic Energy and SpeedFor small velocities, KE is

given by Newton’s resultsAs v approaches c, the

relativistic result has a different behavior than does Newton

Although the KE can be made very large, the particle’s speed never quite reaches the speed of light

Section 27.9

Ch 28Quantum Mechanics

Work Function and Photoelectric Effect

PhotonsEphoton = hƒ

h is Planck’s constanth = 6.626 x 10-34 J ∙ s

photon

E hƒ hp

c c λ

De Broglie WavelengthWave Particle Duality of

Classical Objects

h hλ

p m(KE)

2

Electron ‘Spin’

Stern Gerlach Experiment

Chapter 29Atomic Theory

Bohr and de Broglie

The allowed electron orbits in the Bohr model correspond to standing waves that fit into the orbital circumference

Since the circumference has to be an integer number of wavelengths, 2 π r = n λ

This leads to Bohr’s condition for angular momentum

Section 29.3

Angular Momentum and rTo determine the allowed values of r, Bohr proposed

that the orbital angular momentum of the electron could only have certain values

n = 1, 2, 3, … is an integer and h is Planck’s constantCombining this with the orbital motion of the

electron, the radii of allowed orbits can be found

Section 29.3

2h

nL

22

22

4 mke

hnr

Values of rThe only variable is n

The other terms in the equation for r are constantsThe orbital radius of an electron in a hydrogen atom

can have only these valuesShows the orbital radii are quantized

The smallest value of r corresponds to n = 1This is called the Bohr radius of the hydrogen atom

and is the smallest orbit allowed in the Bohr modelFor n = 1, r = 0.053 nm

Section 29.3

Energy ValuesThe energies corresponding to the allowed values of r

can also be calculated

The only variable is n, which is an integer and can have values n = 1, 2, 3, …

Therefore, the energy levels in the hydrogen atom are also quantized

For the hydrogen atom, this becomes

tot elec

π k e mE KE PE

h n

2 2 4

2 2

2 1

tot

. eVE

n

2

13 6

Section 29.3

Quantum Numbers, Summary

Section 29.4

Electron Clouds

Section 29.4

Electric Distribution

The direction of the arrow represents the electron’s spin

In C, the He electrons have different spins and obey the Pauli exclusion principle Section 29.5

Chapter 30Nuclear Physics

Mass NumberThe number of neutrons is symbolized by N

The value of N for a particular element can varyThe mass number, A, is the sum of the number of

protons and neutronsA = Z + N

Notation:X is the symbol for the element

Example:The element is HeThe mass number, A, is 4The atomic number, Z, is 2Therefore, there are 2 neutrons in the nucleus

AZ X

He42

Section 30.1

Alpha ParticlesAn alpha particle is

composed of two protons and two neutronsThis is a He nucleus

and is denoted as The alpha particle

generally does not carry any electrons, so it has a charge of +2e

He42

Section 30.2

Beta ParticlesThere are two varieties of beta particles

Negatively charged particle is an electronPositively charged positron

The antiparticle of the electron Except for charge, identical to the electron

Electrons and positrons have the same massThey are both point charges

Section 30.2

Gamma ParticlesGamma decay produces photonsDecays follow the following pattern

Parent nucleus → daughter nucleus + gamma rayExample of a nuclear decay that produces a gamma

ray:

The asterisk denotes that the nucleus is in an excited state

N* N γ 14 147 7

Section 30.2

Half-life, cont.At time t = 2 T1/2, there

will be No / 4 nuclei remaining

This decay curve is described by an exponential function

The decay constant, λ, is defined so that

λtoN N e

Section 30.2

Measuring DamageRadiation absorbed dose – rad

1 rad is the amount of radiation that deposits 10-2 J of energy into 1 kg of absorbing material The unit accounts for both the amount of energy carried by

the particle and the efficiency with which the energy is absorbed

Relative biological effectiveness – RBE This measures how efficiently a particular type of

particle damages tissueThis accounts for the fact that different types of

particles can do different amounts of damage even if they deposit the same amount of energy

Section 30.4

Measuring Damage, cont.RBE value tends to

increase as the mass of the particle increases

Röntgen Equivalent in Man – rem Dose in rem = (dose in

rad) x RBEThis combines the

amount and effectiveness of the radiation absorbed

Section 30.4

Tickling the Dragon’s TailLouis Slotin –

Chief Armourer of the United States

Radiation effectsBlue Haze from

Nitrogen IonizationHeat WaveSour Taste in mouthBurning in hand2,100,000 mrems