Electromagnetic Waves

1
Electromagnetic Waves
Chapter
33
Todays information age is based almost
entirely on the physics of electromagnetic waves.
The connection between electric and magnetic
fields to produce light is own of the greatest
achievements produced by physics, and
electromagnetic waves are at the core of many
fields in science and engineering. In this
chapter we introduce fundamental concepts and
explore the properties of electromagnetic waves.

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2
hitt

• A charged capacitor and an inductor are connected
  in series. At time t 0 the current is zero, but
  the capacitor is charged. If T is the period of
  the resulting oscillations, the next time after
• t 0 that the current is a maximum is
• A. T
• B. T/4
• C. T/2
• D. T
• E. 2T

3
Maxwells Rainbow
The wavelength/frequency range in which
electromagnetic (EM) waves (light) are visible is
only a tiny fraction of the entire
electromagnetic spectrum
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4
The Travelling Electromagnetic (EM) Wave,
Qualitatively
An LC oscillator causes currents to flow
sinusoidally, which in turn produces oscillating
electric and magnetic fields, which then
propagate through space as EM waves
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The Travelling Electromagnetic (EM) Wave,
Qualitatively
EM fields at P looking back toward LC oscillator
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Mathematical Description of Travelling EM Waves
All EM waves travel a c in vacuum
EM Wave Simulation
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A Most Curious Wave

• Unlike all the waves discussed in Chs. 16 and 17,
  EM waves require no medium through/along which to
  travel. EM waves can travel through empty space
  (vacuum)!
• Speed of light is independent of speed of
  observer! You could be heading toward a light
  beam at the speed of light, but you would still
  measure c as the speed of the beam!

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The Travelling EM Wave, Quantitatively
Induced Electric Field
Changing magnetic fields produce electric fields,
Faradays law of induction
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The Travelling EM Wave, Quantitatively
Induced Magnetic Field
Changing electric fields produce magnetic fields,
Maxwells law of induction
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Energy Transport and the Poynting Vector
The magnitude of S is related to the rate at
which energy is transported by a wave across a
unit area at any instant (inst). The unit for S
is (W/m2)
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Energy Transport and the Poynting Vector
Note that S is a function of time. The
time-averaged value for S, Savg is also called
the intensity I of the wave.
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Variation of Intensity with Distance
Consider a point source S that is emitting EM
waves isotropically (equally in all directions)
at a rate PS. Assume energy of waves is conserved
as they spread from source.
How does the intesnity (power/area) change with
distance r?
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Radiation Pressure
EM waves have linear momentum as well as
energy?light can exert pressure
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Polarization
The polarization of light is describes how the
electric field in the EM wave oscillates. Vertica
lly plane-polarized (or linearly polarized)
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Polarized Light
Unpolarized or randomly polarized light has its
instantaneous polarization direction vary
randomly with time
One can produce unpolarized light by the addition
(superposition) of two perpendicularly polarized
waves with randomly varying amplitudes. If the
two perpendicularly polarized waves have fixed
amplitudes and phases, one can produce different
polarizations such as circularly or elliptically
polarized light.
Polarized Light Simulation
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Polarizing Sheet
I0
I
Only electric field component along polarizing
direction of polarizing sheet is passed
(transmitted), the perpendicular component is
blocked (absorbed)
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Intensity of Transmitted Polarized Light
Since only the component of the incident electric
field E parallel to the polarizing axis is
transmitted
For unpolarized light, q varies randomly in time
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Reflection and Refraction
Although light waves spread as they move from a
source, often we can approximate its travel as
being a straight line ? geometrical optics
What happens when a narrow beam of light
encounters a glass surface?
Law of Reflection
Snells Law
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n is the index of refraction of the material
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Sound Waves

• For light going from n1 to n2
• n2 n1 ? q2 q1
• n2 gt n1 ? q2ltq1, light bent towards normal
• n2 lt n1 ? q2 gt q1, light bent away from normal

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Chromatic Dispersion
The index of refraction n encountered by light in
any medium except vacuum depends on the
wavelength of the light. So if light consisting
of different wavelengths enters a material, the
different wavelengths will be refracted
differently ? chromatic dispersion
n2bluegtn2red
Chromatic dispersion can be good (e.g., used to
analyze wavelength composition of light) or bad
(e.g., chromatic aberration in lenses)
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Chromatic Dispersion
Chromatic dispersion can be good (e.g., used to
analyze wavelength composition of light)
prism
or bad (e.g., chromatic aberration in lenses)
lens
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Rainbows
Sunlight consists of all visible colors and water
is dispersive, so when sunlight is refracted as
it enters water droplets, is reflected off the
back surface, and again is refracted as it exits
the water drops, the range of angles for the
exiting ray will depend on the color of the ray.
Since blue is refracted more strongly than red,
only droplets that are closer the the rainbow
center (A) will refract/reflect blue light to the
observer (O). Droplets at larger angles will
still refract/reflect red light to the observer.
What happens for rays that reflect twice off the
back surfaces of the droplets?
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Total Internal Reflection
For light that travels from a medium with a
larger index of refraction to a medium with a
smaller medium of refraction n1gtn1 ? q2gtq1, as q1
increases, q2 will reach 90o (the largest
possible angle for refraction) before q1 does.
n2
n1
When q2gt qc no light is refracted (Snells Law
does not have a solution!) so no light is
transmitted ? Total Internal Reflection
Total internal reflection can be used, for
example, to guide/contain light along an optical
fiber
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Polarization by Reflection
When the refracted ray is perpendicular to the
reflected ray, the electric field parallel to the
page (plane of incidence) in the medium does not
produce a reflected ray since there is no
component of that field perpendicular to the
reflected ray (EM waves are transverse).

• Applications
• Perfect window since parallel polarization is
  not reflected, all of it is transmitted
• Polarizer only the perpendicular component is
  reflected, so one can select only this component
  of the incident polarization

Brewsters Law
In which direction does light reflecting off a
lake tend to be polarized?
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