The EM Spectrum:
http://www.lon-capa.org/~mmp/applist/Spectrum/s.htm
Energy increases with increasing frequency.
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electronic
sound
Microphone receives sound
wave and converts to
oscillating electrical current
(20 Hz – 20 kHz)
modulator
An electrical “carrier” signal
is produced (90.9 MHz for
WILL FM) indepedently
AM
FM
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Example: Find the frequency of blue light with a
wavelength of 470 nm.
As you drive by an AM radio station, you notice a sign
saying that its antenna is 122 m high. If this height
represents one quarter-wavelength of its signal, what is the
frequency of the station?
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Energy Transport by EM Waves
The intensity of a wave is
I =(
P
A
) avg .
This is a measure of how much energy strikes a surface of
area A every second for normal incidence.
Surface
The rays make a
90° angle with the
surface.
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Energy Transport by EM Waves
The Poynting vector describes the energy flux
(J·m−2·s−1) of an electromagnetic field. It is named after its
inventor John Henry Poynting
The direction of the Poynting vector of an electromagnetic wave at any point
gives the wave's direction of travel and the direction of energy transport at that
point.
E
with B =
c
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Savg is called the intensity I of the wave
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An observer is 1.8 m from an isotropic point source of light
with power Ps = 250 W. Calculate the rms values of the
electric and magnetic fields due to the source at the
position of the observer.
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Radiation pressure
…. is the pressure exerted upon any surface exposed to electromagnetic
radiation. If absorbed, the pressure is the energy flux density divided by the
speed of light. If the radiation is totally reflected, the radiation pressure is
doubled. For example, the radiation of the Sun at the Earth has an energy
flux density of 1370 W/m2, so the radiation pressure is 4.6 µPa (absorbed)
If you know the total amount of energy U in a pulse of radiation, as you might for
a laser pulse, then it is most convenient to use formulas for the amount of
momentum p imparted to an object that either absorbs or reflects the pulse:
p
p
The radiation pressure formulas are
Pr
Pr
Because of the factor of c in the denominators of these pressure and momentum
formulas, these effects are usually quite small.
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Polarization
A wave on a string is linearly polarized.
The vibrations occur in the same plane.
The orientation of this plane determines
the polarization state of a wave.
For an EM wave, the direction of
polarization is given by the direction of
the E-field.
The EM waves emitted by an
antenna are polarized; the E-field is
always in the same direction.
When light is polarized, the electric
field always points in the same
direction.
A source of EM waves is unpolarized if the E-fields are
in random directions.
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A polarizer will transmit linear polarized waves in the same
direction independent of the incoming wave.
It is only the
component of the
wave’s amplitude
parallel to the
transmission axis
that is transmitted.
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If unpolarized light is incident on
1 polarizer, the intensity of the
light passing through is I= ½ I0.
If the incident wave is already
polarized, then the transmitted
intensity is I=I0cos2θ where θ is
the angle between the incident
wave’s direction of polarization
and the transmission axis of the
polarizer. (Law of Malus)
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Example Unpolarized light passes through two polarizers in
turn with axes at 45° to each other. What is the fraction of
the incident light intensity that is transmitted?
After passing through the first polarizer, the intensity is ½
of its initial value. The wave is now linearly polarized.
Direction of
linear
polarization
Transmission axis
of 2nd polarizer.
45°
I 2 = I1 cos 2 θ
1
1
2
I 0 cos 45° = I 0
=
4
2
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Reflection and Refraction
When a light ray travels from one medium to another, part of the
incident light is reflected and part of the light is transmitted at the
boundary between the two media.
The transmitted part is said to be refracted in the second medium.
http://www.geocities.com/CapeCanaveral/Hall/6645/propagation/propagation.html
*In 1678 the great Dutch physicist Christian Huygens (1629-1695) wrote a treatise called
Traite de la Lumiere on the wave theory of light, and in this work he stated that the wavefront
of a propagating wave of light at any instant conforms to the envelope of spherical wavelets
emanating from every point on the wavefront at the prior instant. From this simple principle
Huygens was able to derive the laws of reflection and refraction
incident ray
reflected ray
refracted ray
Types of Reflection
When light reflects from a
smooth surface, it undergoes
specular reflection (parallel
rays will all be reflected in the
same direction).
When light reflects from a
rough surface, it undergoes
diffuse reflection (parallel rays
will be reflected in a variety of
directions).
The Law of Reflection
For specular reflection the incident angle θi
equals the reflected angle θr:
θi = θr
The angles are
measured relative
to the normal,
shown here as a
dotted line.
The Refraction of Light
The speed of light is different in different materials. We
define the index of refraction, n, of a material to be the ratio
of the speed of light in vacuum to the speed of light in the
material:
n = c/v
When light travels from one medium to another, its velocity
and wavelength change, but its frequency remains
constant. http://www.geocities.com/CapeCanaveral/Hall/6645/propagation/propagation.html
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Example: Which way will the rays bend?
n = 1.4
n=2
n = 1.6
n = 1.2
Which of these rays can be the refracted ray?
You have a semicircular disk of glass with an index of
refraction of n = 1.52. Find the incident angle θ for
which the beam of light in the figure will hit the
indicated point on the screen.
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Total Internal Reflection
When light travels from a medium with n1 > n2,
there is an angle, called the critical angle θc, at
which all the light is reflected and none is
transmitted. This process is known as total
internal reflection. The critical angle occurs
when θ2= 90 degrees:
n
sin θ c = 2
n1
The incident ray is both reflected and
refracted.
Total Internal Reflection
A ray of light enters the long side of a 45°-90°-45° prism and
undergoes two total internal reflections, as indicated in the
figure. The result is a reversal in the ray’s direction of
propagation. Find the minimum value of the prism’s index of
refraction, n, for these internal reflections to be total.
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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. The dependence of n on wavelength implies that
when a light beam consists of rays of different
wavelengths, the rays will be refracted at different angles
by a surface; that is, the light will be spread out by the
refraction. This spreading of light is called chromatic
dispersion, i
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Rainbows
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The index of refraction for red light in a certain liquid is 1.320; the index
of refraction for violet light in the same liquid is 1.332. Find the
dispersion (θv – θr) for red and violet light when both are incident on the
flat surface of the liquid at an angle of 45.00° to the normal.
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Polarization by Scattering
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Polarization by Reflection
Brewster's Law
when the light is incident at a
particular incident angle, called
the Brewster angle θB, the
reflected light has only
perpendicular components
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