Transcript electromagnetic wave

Electric and magnetic fields
fluctuating together can form a
propagating electromagnetic
wave.
An electromagnetic wave
is a transverse wave, the
electric and magnetic fields are
perpendicular to the direction
the wave travels.
Electromagnetic waves can
travel through a vacuum or
a material substance. The
speed of light in a vacuum
8
is c = 3.00 x 10 m/s.
This speed is generally
slower in other materials.
AM radio waves have frequencies
between 545 and 1605 kHz.
FM is between 88 and 108 MHz.
TV channels 2-6 are from
54 to 88 MHz, channels
7-13 use 174 to 216 MHz.
An electromagnetic wave,
like any wave, follows this
equation: v = fl.
In the case of EM waves:
c = fl.
EM waves range from
4
less than 10 Hz to
22
greater than 10 Hz.
Since c is constant,
c = fl may be used
to find the range of
wavelengths:
4
from over 10 m to
-16
10 m.
The parts of the spectrum
are: radio waves,
infrared (heat waves),
visible light (roygbiv),
ultraviolet (electric arc),
x-rays, and
gamma rays (nuclear decay).
Higher frequency (shorter
wavelangth) radio waves are
called microwaves.
Red martians invaded
venus using x-ray guns.
Radio waves, microwaves,
infrared, visible, ultraviolet,
x-rays, gamma rays.
The spectrum ranges
from long wavelengths
with low frequency and
low energy to short
wavelengths with high
frequency and high
energy.
Visible light has a frequency
range of about 4.0 x 1014 Hz
to 7.9 x 1014 Hz. This
corresponds to extremely small
wavelengths that are usually
expressed in nanometers (nm)
1 nm = 10-9 m. An angstrom
(10-10 m) is an occasionally
used but obsolete unit.
Ex. 1 - Find the range in
wavelengths (in vacuum)
for visible light in the
frequency range between
14
4.0 x 10 Hz (red light)
14
and 7.9 x 10 Hz (violet
light). Express the answers
in nanometers.
Ex. 2 - Diffraction is the ability
of a wave to bend around an
obstacle or the edges of an
opening. Would you expect
AM or FM radio waves to
bend more readily around an
obstacle such as a building?
The most accurate
measurements of the speed
of light before modern day
measurements were made by
Albert Michelson using an
rotating mirror in 1926. Today
the speed of light is set at
299 792 458 m/s.
When we look at
stars, we see them
as they were
thousands or
more years ago.
Maxwell determined that EM
waves travel through a vacuum at
a speed given by: c = 1/ (√e0µ0).
e0 is the electric permittivity of
free space,
e0 = 8.85 x 10-12 C2/(N•m2),
µ0 is the magnetic permittivity
of free space,
µ0 = 4π x 10-7 T•m/A.
Maxwell determined this
formula theoretically, but
when the values for e0 and
µ0 substituted, the result
8
obtained is 3 x 10 m/s;
which fits experimental
evidence.
The energy of an EM wave u is
carried by the electromagnetic
and magnetic fields that
comprise the wave. The total
amount of energy per volume is
found by adding the electric
energy density and the
magnetic energy density.
u = e0
2
E /2
+
2
B/
2µ0
Since the electric field and
magnetic field carry equal
amounts of energy, this
equation reduces to:
u = e0
2
E/
=
2
B /µ
0
The electric and magnetic
fields are related by E =
cB. The values of E and B
fluctuate. If an average
value for u is needed,
average values for
2
2
E and B must be found.
We use rms values
for E and B in this
case.
Erms = E0/ √2
Brms = B0/ √2
Ex. 4 - Sunlight enters the top of
the earth’s atmosphere with an
electric field whose rms value is
Erms = 720 N/C. Find (a) the
average total energy density of
this electromagnetic wave and
(b) the rms value of the
sunlight’s magnetic field.
The intensity is found by
multiplying the speed of light
by the total energy density
of the wave: S = cu.
From previous equations:
2
2
S = cu = c e0E = c B /µ0
Using rms values gives average intensity.
Ex. 5 - A neodymium-glass
laser has an electric field with
an rms value of Erms=
2.0 x 109 N/C. Find the
average power of each pulse
that passes through a
-5
2
1.6 x 10 m surface that is
perpendicular to the laser
beam. (P = SA)
The single equation for
the doppler effect is:
f’ = f(1 ±u/c) if u<<c.
f’ is observed frequency
f is emitted frequency
u is relative speed
c is speed of light
Electromagnetic waves are
transverse, and can therefore
be polarized. Polaroid material
only allows transmission along
the transmission axis. A filter
such as this absorbs 1/2 of the
intensity of the unpolarized
light.
A polarized filter
absorbs as much
of the electric
(and magnetic)
field as it emits.
When two
polarizing filters are
used, the first is
called the polarizer
and the second
the analyzer.
If the transmission axis
of the analyzer is
oriented at an angle θ
to the transmission axis
of the polarizer, the
electric field strength is
E cos θ.
Intensity S is proportional
2
to cos θ.
Therefore:
2
Savg = S0 avg cos θ
S0 avg is average light intensity
entering the analyzer.
This is Malus’ Law.
Ex. 7 - What value of θ
should be used so the
average intensity of light
leaving the analyzer is
one-tenth the average
intensity of the
unpolarized light?
When θ is 90°,
the polarizer and
analyzer are said to
be crossed, and no
light is emitted by the
combination.
Ex. 8 - No light is emitted from
a crossed polarizer-analyzer
combination. Suppose a third
piece of polarizing material is
inserted between the
combination at an axis angle of
45°. Is light now emitted from
the combination?