electromagnetic waves chapter 23. em waves are transverse waves imagine a snapshot of the...
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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