Transcript EM Waves - UCF Physics

Chapter 23
Electromagnetic Waves
Formed from an electric field and magnetic field orthonormal to each other,
propagating at the speed of light (in a vacuum).
• The fundamental sources of all electromagnetic radiation are electric
charges in accelerated motion.
• All objects emit electromagnetic radiation as a result of thermal motion
of their molecules; this radiation, called thermal radiation, is a mixture of
different wavelengths.
24.1 The Nature of Electromagnetic Waves
The speed of an electromagnetic wave in a vacuum is:
c  3.00 108 m s
Characteristics of electromagnetic waves in vacuum


1. The wave is transverse: Both E and B are perpendicular to the
direction of propagation of the wave and to each other.


2. There is a definite ratio between magnitudes of E and B :
E= cB.
3. The wave travels in vacuum with a definite and unchanging speed
c (c = 3.00 x 108 m/s).
4. Unlike mechanical waves, which need the oscillating particles of a
medium such as water or air to be transmitted, electromagnetic
waves require no medium. What’s “waving” in an electromagnetic
wave are the electric and magnetic fields.
The electromagnetic Spectrum
All these electromagnetic waves have the general characteristics,
including the common propagation speed c = 3.00 x 108 m/s (in
vacuum). All are the same in principle; they differ in frequency f
and wavelength  , but the relation c  f holds for all.
• A special light source that has attained prominence in the last
50 years is the laser, which can produce a very narrow beam
of enormously intense radiation.
• A significant characteristic of laser light is that it is much
more nearly monochromatic, or single frequency, than light
from any other source.
The Energy Carried by Electromagnetic Waves
Electromagnetic waves, like water waves or sound waves,
carry energy.
The energy is carried by the electric and magnetic fields
that comprise the wave.
The total energy density u of an electromagnetic Wave:
Total energy 1
1
u
 E 
B
Volume
2
2
2
2
o
o
Electric
energy
density
Magnetic
energy
density
In an electromagnetic wave propagating through a vacuum or
air, the electric field and the magnetic field carry equal
amounts of energy per unit volume of space.
1
1
E 
B
2
2
2
2
o
o
It is possible to rewrite the equation for total energy density,
1
1
u  E 
B , in two additional, but equivalent, forms:
2
2
o
2
2
o
u  E
2
o
u
1

o
B
2
The fact that the two energy densities are equal implies that the electric
and magnetic fields are related. To see how, we set the electric energy
density equal to the magnetic energy density and obtain
1
1
E 
B
2
2
1
or E 
B
2
2
o
o
2

o
2
1
o
In 1865, Maxwell determined theoretically that electromagnetic waves
propagate through a vacuum at a speed given by
c
1

o
.
o
Hence, from equation (1) it follows that
E c B
2
2
or E  cB
2
As an electromagnetic wave moves through space, it
carries energy from one region to another. This energy
transport is characterized by the intensity of the wave.
For an electromagnetic wave, the intensity is the
electromagnetic power divided by the area of the surface
P
S
A
Total energy

tA
24.4 The Energy Carried by Electromagnetic Waves
P Total energy uctA
S 

 cu
A
tA
tA
Thus, the intensity and the energy density are related by the
speed of light, c.
Intensity of an electromagnetic wave depends on the
electric and magnetic fields according to the following
equivalent relations:
1
c
S  cu  c E 
B
2
2
2
0
0
S  c E
2
0
S
c

0
B
2
2
Polarization
• Polarization occurs with all
transverse waves (e.g., wave on a
string).
• When a wave has only y
displacements, we say that it is
linearly polarized in the y direction ;
similarly, a wave with only z
displacements is linearly polarized
in the z direction.
• For mechanical waves, we can
build a polarizing filter that permits
only waves with a certain
polarization direction to pass.
• In figure c, the string can slide
vertically in the slot without friction,
but no horizontal motion is possible.
An electromagnetic wave is a transverse wave: The fluctuating
electric and magnetic fields are perpendicular to the direction of
propagation and to each other. We always define the direction of
polarization of an electromagnetic wave to be the direction of the
electric-field vector, not the magnetic-field vector, because most
common electromagnetic-wave detectors (including the human
eye) respond to the electric forces on electrons in materials, not
the magnetic forces.
24.6 Polarization
POLARIZED ELECTROMAGNETIC WAVES
Linearly polarized wave
on a rope.
24.6 Polarization
In polarized light, the electric field
fluctuates along a single direction.
24.6 Polarization
Polarized light may be produced from unpolarized light with
the aid of polarizing material.
24.6 Polarization
MALUS’ LAW
S  S o cos 
2
intensity after
analyzer
intensity before
analyzer
24.6 Polarization
Example 7 Using Polarizers and Analyzers
What value of θ should be used so the average intensity of the polarized
light reaching the photocell is one-tenth the average intensity of the
unpolarized light?
24.6 Polarization
1
10
S o  12 S o cos 2 
1
5
 cos 2 
cos  
1
5
  63.4
24.6 Polarization
Conceptual Example 8 How Can a Crossed Polarizer and
Analyzer Transmit Light?
Suppose that a third piece of polarizing material is inserted
between the polarizer and analyzer. Does light now reach the
photocell?