Download Chapter 24 Notes - Valdosta State University

CHAPTER 24 ELECTROMAGNETIC WAVES
The Nature Of Electromagnetic Waves
An electromagnetic wave consists of the traveling
fluctuation of both electric and magnetic fields.
Electromagnetic waves are generated near an antenna
by charges moving in the antenna.
In diagram a, time = 0, there is no separation of charge,
the electric field strength is zero.
In diagram b, maximum voltage has caused maximum
separation of charge and maximum electric field
strength in the direction shown.
In diagram c, the voltage has returned to zero as has the
charge separation and the electric field strength.
In diagram d, we have maximum voltage, charge
separation, and electric field strength in the opposite
direction.
In diagram e, the voltage, charge separation, and
electric field strength have returned to zero.
This constitutes a disturbance in the equilibrium
electric field of the region which travels out in all
directions as a wave.
A changing electric field causes the existence of a
changing magnetic field. The magnetic field changes
associated with the propagating disturbance form a
right angle with the electric field changes.
Since the direction of propagation of the wave is at 90°
with respect to both the electric field changes and the
magnetic field changes, an electromagnetic wave is a
transverse wave.
Since electric and magnetic fields exist everywhere in
space(they are normally = 0 in empty space)
electromagnetic waves can travel anywhere even if
there is no matter to travel through.
In fact, electromagnetic waves travel fastest through a
vacuum. The speed of light(electromagnetic radiation)
in a vacuum is c = 3.0 x 108 m/s. In matter, the speed of
light is always less.
The Electromagnetic Spectrum
The electromagnetic spectrum consists of all the
frequencies of electromagnetic radiation.
The lowest frequencies are radio waves, both AM and
FM. This includes TV signals. Microwaves are part of
the radio signal spectrum and are sometimes used to
transmit information.
The infrared region is between radio waves and visible
light. Infrared is absorbed and converted to heat energy
very well. It is not visible.
Visible light frequencies occupy a very small part of the
complete electromagnetic spectrum. These are the
frequencies we actually see. Our eyes and brain
interpret different frequencies as different colors. We
use ROYGBIV to help us remember the order of the
colors with red being the lowest frequency sensed and
violet the highest.
Ultraviolet frequencies are not visible. They are beyond
violet and are used to kill bacteria, attract insects, and
tan skin. They have more energy per photon than
visible light.
X - rays are higher frequency than ultraviolet light and
have more energy. They pass through soft tissue with a
relatively low absorption rate but the higher energy
content makes exposure to large amounts of them
dangerous. They are useful in forming images of
internal objects.
Gamma rays are higher frequency and energy than Xrays. They are produced in nuclear reactions and can
cause serious damage to living tissue.
Electromagnetic radiation obeys the same relationship
between frequency and wavelength as other waves. The
equation relating them is:
V = fλ
where V is the speed of the wave, f is its frequency and λ is its
wavelength.
Example
Find the range of the wavelengths in a vacuum for visible light
ranging from 4.0 x 1014 Hz to 7.9 x 1014 Hz. c = 3.0 x 108 m/s.
The Speed of Light
The speed of light was first measured accurately by Albert
Michelson in 1926. His result was less than 1/100 % off.
His work confirmed the theory of Maxwell who theoretically
calculated the speed of light. His equation was:
C = 1/(ε0μ0)½
It gave a value of 3.00 x 108 m/s.
The Doppler Effect and Electromagnetic Waves
The Doppler Effect in sound waves caused an apparent
increase or decrease in the observed frequency due to the
motion of the source or the observer of the sound wave.
The same effect occurs in electromagnetic waves but the
equations are a little different.
In the case of sound waves, the motion of the source, observer
and the medium all were considered. In the case of
electromagnetic waves only the motion of the source and the
observer must be considered. The simplified equation is:
f0 = fs(1 + vrel/c)
In this equation, f0 is the observed frequency, fs is the
frequency emitted by the source, vrel is the magnitude of the
relative velocity between the two and c is the speed of light.
Use the + sign if the observer and source are approaching each
other. Use the - sign if they are moving apart.
Example
A distant galaxy emits light that has a wavelength of 434.1 nm.
On Earth, the wavelength of this light is measured to be 438.6
nm. (a) Is this galaxy approaching or receding from the Earth?
(b) Find the speed of the galaxy relative to the Earth.
Polarization
Transverse waves can be polarized. This means that their
displacements from equilibrium can be confined to one plane.
The example above uses a polarized mechanical wave as an
example. The wave is said to be linearly polarized because the
rope vibrations are all in one plane. Another term that is used
is plane polarized.
The wave passes through the top slit since it is oriented in the
same direction as the vibrations. The wave does not pass
through the bottom slit since there is no room for vertical
displacements.
Longitudinal waves cannot be polarized since the vibrations
are oriented in the same direction as the direction of travel of
the wave.
Unpolarized light contains light waves with random
orientations of electric and magnetic field vibrations.
Polarized light can be formed from unpolarized light with the
use of Polaroid film, a type of polarizing material. Components
of light waves with vibrations oriented along the transmission
axis of the film pass through. Those oriented at right angles do
not.
Since the component of the electric field perpendicular to the
axis of transmission does not pass through, the intensity of the
light is reduced by ½. For unpolarized light, the polarizing
material absorbs ½ of the light energy incident on it and
transmits ½.
When two pieces of polarizing film are used to study light, the
first piece is called the polarizer and the second is called the
analyzer. The polarizer converts unpolarized light to polarized
light and the analyzer can be used to control brightness or
investigate optically active substances(optically active
substances cause the plane of polarization to rotate as the light
passes through).
The intensity of the light transmitted by the analyzer is
determined by Malus's Law. It states:
S = S0cos2θ
where S is the average intensity leaving the analyzer, S0 is the
average intensity of light entering the analyzer, and θ is the
angle between the transmission axis of the polarizer and that of
the analyzer.
Example
Find the intensity of the transmitted beam when θ1 = 19°, θ2 =
55°, and θ3 = 100.0° if the initial intensity is 1260 w/m2.
Polarized light exists in nature when unpolarized light is
reflected or scattered. The intensity of reflections off of
horizontal surfaces is reduced by wearing sunglasses with
vertically polarized lenses. Also the sky will appear different
when wearing polarized sunglasses due to the elimination of
horizontally polarized light.
P 744 Questions 1, 3, 6, 7, 9, 10, 11
P 745 Problems 5, 7, 11, 12, 15, 17, 21, 25, 31, 34, 36, 47