Download THE NATURE OF ELECTROMAGNETIC WAVES

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THE NATURE OF ELECTROMAGNETIC WAVES
Light consists of electromagnetic waves moving through space. Figure 4 is a
representation of a plane-polarized electromagnetic wave at one instant in
time. The concept of polarization is discussed in detail in a later section of
this module.
Fig. 4 Three-dimensional model of plane-polarized EM waves
This wave consists of variations in two types of fields in space. In this case,
the electric field (E) always oscillates vertically to form an electric wave;
the magnetic field (B) always oscillates horizontally to form a magnetic
wave. The two fields are perpendicular to each other, and both are
perpendicular to the direction of propagation of the wave. All
electromagnetic waves have this same basic composition. They differ only
in frequency and wavelength.
THE ELECTROMAGNETIC SPECTRUM
The span of frequencies and wavelengths covered by electromagnetic
radiation is indicated by portion A of Figure 4. Devices that produce or
detect electromagnetic waves must be designed to operate at the frequency
of the waves they emit or receive. Radio transmitters and receivers operate
at frequencies in the 103- and 107 -Hz range and are designed to emit or
respond to these frequencies. X-ray tubes and films are designed for use in
the 1017- to 10l9-Hz frequency range. Lasers produce coherent light in the
frequency and wavelength range indicated by portion B of Figure 4. This
range includes the spectral regions commonly identified as the infrared,
visible, and ultraviolet regions. The human eye responds to the visible
spectrum given in portion C of Figure 5.
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Fig. 5 The electromagnetic spectrum
The most important ideas summarized in figure 5 are:
1. Electromagnetic waves span over many orders of magnitude in wavelength (or
frequency).
2. The frequency of the electromagnetic radiation is inversely proportional
to the wavelength.
3. The visible spectrum is a very small part of the electromagnetic spectrum.
4. Photon energy increases as the wavelength decreases. The shorter the
wavelength, the more energetic are its photons
Table 1 characterizes the spectral regions within which laser emissions and
identifies that portion of the eye that is most susceptible to damage by each
type of emission.
TABLE 1. SPECTRAL REGIONS OF LASER OUTPUTS AND
PARTS OF THE EYE MOST SUSCEPTIBLE TO DAMAGE
Wavelength
(nanometers)
Frequency
(x 1014 Hz)
FAR-MID UV
20–320
150–9.4
Eye part
susceptible to
damage
Cornea
NEAR UV
320–390
9.4–7.7
Lens, Cornea
Spectral
Region
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VISIBLE
390–750
7.7–4.0
Retina
NEAR IR
750–1400
4.0–2.1
Iris, Retina
NEAR-MID IR
1400–3000
2.3–1.0
Cornea, Retina
3000–500,000
1.0–0.006
MID-FAR IR
Cornea
Examples for elecromagnetic waves are:
1. Radio-waves which have wavelength of the order of meters, so they need
big antenas (The dimensions of an antena are of the same order of magnitude
as the wave).
2. Microwaves which have wavelength of the order of centimeters. As an
example: in a microwave oven, these wavelengths can not be transmitted
through the protecting metal grid in the door, while the visible spectrum
which have much shorter wavelength allow us to see what is cooking inside
the microwave oven through the protecting grid.
3. x-Rays which are used in medicine for taking pictures of the bone structure
inside the body.
4. Gamma Rays which are so energetic, that they cause ionization, and are
classified as ionizing radiation.
INDEX OF REFRACTION
All electromagnetic waves travel through a vacuum at the constant speed of
c = 3 10‫נ‬8 m/sec. When these waves travel through a transmitting material,
however, their speed is reduced. The index of refraction of a material is the
ratio of the speed of light in a vacuum to its speed in that material and is
given by Equation 8.
Equation 8
where: n = Index of refraction.
V = Speed of light inside material.
The frequency of a light wave does not change when it enters a material,
but its wavelength is reduced (Figure 6). The index of refraction is also the
ratio of wavelength in vacuum to the wavelength in the material (Equation
9).
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Equation 9
where: 0 = Wavelength in vacuum.
i = Wavelength in material.
Fig. 6 Wavelength reduction in material
When light leaves a material and enters a vacuum, it returns to speed c and
to wavelength 0? The index of refraction of air is about 1.0003, but is
assumed to be 1.0 in most applications.
Examples D and E illustrate the application of Equations 8 and 9.
EXAMPLE D: INDEX OF REFRACTION OF
RUBY
Given:
Light travels through a ruby laser rod at a
speed of 1.74 10‫נ‬8 m/sec.
Find:
Index of refraction of ruby.
Solution:
EXAMPLE E: SPEED AND WAVELENGTH OF
LIGHT IN GLASS
Given:
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A HeNe laser beam ( = 633 nm) travels
through a glass window with an index of
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refraction of 1.65.
Find:
Speed and wavelength inside the glass.
Solution:
We saw that the velocity of light in matter is slower than in vacuum. This slower
velocity is associated with reduced wavelength: = 0/n , while the frequency
remains the same (see figure 7).
Figure 7 Change of wavelength in matter
Example
The velocity of Red light (= 0.6[m]) in a certain medium is 1.5*108 [m/s].
What is the wavelength of this light in this material?
Solution to example 1.1:
First find the index of refraction:
Using n, calculate the wavelength in the material:
Conclusion: The wavelength of Red light in a material with an index of
refraction of 2.0, is 0.3 [m]
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H.W
Wavelength
Color
Frequency (Hz)
Angstrom
M
Violet
Blue
Green
Yellow
Red
1. The indices of refraction of several materials situated in air are given
below. Calculate the velocity of light in each .
a. Fused quartz at 643 nm: n = 1.457.
b. Zinc crown glass at 434 nm: n = 1.528.
c. Fused quartz at 397 nm: n = 1.471.
2-The wavelengths given in Problem 1 are in vacuum. Calculate the wave
lengths inside the materials.
3-Calculate the wavelengths of the following frequencies of light.
1. a. 1.34 10‫נ‬14 Hz.
b. 260.8 THz.
c. 5.83 10‫נ‬l4 Nz.
4-Calculate the periods of the waves in Problem3
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