Text book
Physics; John D. Cutnell and Kenneth W. Johnson;
7th edition; Wiley; 2007.
Electromagnetic Waves
Each of the beautiful colors in this dancer’s carnival outfit corresponds to a different wavelength
in the visible region of the spectrum of electromagnetic waves. (Sylvain Grandadam/Getty
Images, Inc.)
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An electromagnetic wave is a transverse wave because the electric
and magnetic fields are both perpendicular to the direction in which
the wave travels.
An electromagnetic wave, does not require a medium in which to
propagate. Electromagnetic waves can travel through a vacuum or a
material substance, since electric and magnetic fields can exist in
either one.
Electromagnetic waves can be produced in situations that do not
involve a wire antenna. In general, any electric charge that is
accelerating emits an electromagnetic wave, whether the charge is
inside a wire or not.
All electromagnetic waves move through a vacuum at the same speed
‘c’ . This speed is called the speed of light in a vacuum is equal to 3.00
x 108 m/s . In air, electromagnetic waves travel at nearly the same
speed as they do in a vacuum, but, in general, they move through a
substance such as glass at a speed that is substantially less than c.
Cochlear implants:
Cochlear implants use the broadcasting and
receiving of radio waves to provide assistance to
hearing-impaired people who have auditory nerves
that are at least partially intact.
Wireless capsule endoscopy:
The broadcasting and receiving of radio waves is also now
being used in the practice of endoscopy. In this medical
diagnostic technique a device called an endoscope is used to
peer inside the body. For example, to examine the interior of
the colon for signs of cancer, a conventional endoscope
(known as a colonoscope) is inserted through the rectum.
As the capsule moves through the intestine,
the transmitter broadcasts the images to an
array of small receiving antennas attached to
the patient’s body. These receiving antennas
also are used to determine the position of the
capsule within the body.
An electromagnetic wave, like any periodic wave,
has a frequency f and a wavelength that are related to
the speed v of the wave by v = f λ.
For electromagnetic waves traveling through a
vacuum or, to a good approximation, through air, the
speed is v=c, so . c = f λ
An ear thermometer, like the pyroelectric
thermometer shown in the figure, determines the
body’s temperature by measuring the amount of
infrared radiation that emanates from the eardrum
and surrounding tissue.
Find the range in wavelengths (in vacuum) for visible
light in the frequency range between 4.0 x 1014 Hz (red
light) and 7.9 x 1014 Hz (violet light). Express the
answers in nanometers.
Solution:
c 3.00 108 m / s
7
 

7
.
5

10
m  750 nm
14
f
4.0 10 Hz
Since 1 nm = 10-9 m
c 3.00 108 m / s
7
 

3
.
8

10
m  380 nm
14
f
7.9 10 Hz
1/2746) (a) Neil A. Armstrong was the first person to walk on the moon.
The distance between the earth and the moon is 3.85 x 108 m. Find the
time it took for his voice to reach earth via radio waves. (b) Someday a
person will walk on Mars, which is 5.6 x 1010 m from earth at the point
of closest approach. Determine the minimum time that will be required
for that person’s voice to reach earth. (1.28 s, 1.9 x 102 s)
2/2746) During a flare-up from a sunspot, X-rays (electromagnetic
waves) are emitted. If the distance between the sun and the earth is 1.50 x
1011 m, how long (in minutes) does it take for the X-rays to reach the
earth? (8.3 min.)
3/2746) In astronomy, distances are often expressed in light-years. One
light-year is the distance traveled by light in one year. The distance to
Alpha Centauri, the closest star other than our own sun that can be seen
by the naked eye, is 4.3 light-years. Express this distance in meters. (4.1
x 1016 m)
7/2747)
A truck driver is broadcasting at a frequency of 26.965
MHz with a CB (citizen’s band) radio. Determine the wavelength of the
electromagnetic wave being used. (11.125 m)
10/2747)
Magnetic resonance imaging, or MRI, and positron
emission tomography, or PET scanning, are two medical diagnostic
techniques. Both employ electromagnetic waves. For these waves, find
the ratio of the MRI wavelength (frequency = 6.38 x 107 Hz) to the PET
scanning wavelength (frequency = 1.23 x 1020 Hz)
(λ PET = 5.18 x 10 -13 λ MRI)
11/2747)
The human eye is most sensitive to light having a
frequency of about 5.5 x 1014 Hz, which is in the yellow-green region of
the electromagnetic spectrum. How many wavelengths of this light can
fit across the width of your thumb, a distance of about 2.0 cm?
(36666.66)
The Reflection of Light: Mirrors
The reflection of light from the plane surface of the water acts to double the presence of this
white ibis. This chapter discusses the images formed by the reflection of light from plane and
spherical mirrors. (Darrell Gulin/The Image Bank/Getty Images)
(a)
(b)
Portions of two spherical wave fronts are
shown. The rays are perpendicular to the
wave fronts and diverge.
For a plane wave, the wave fronts are flat
surfaces, and the rays are parallel to each
other.
Law of Reflection
The incident ray, the reflected ray, and the normal to the surface
all lie in the same plane, and the angle of reflection θr equals the
angle of incidence θi:
θr = θi
(a)
(b)
The drawing shows specular reflection from a polished
plane surface, such as a mirror. The reflected rays are
parallel to each other.
A rough surface reflects the light rays in all directions;
this type of reflection is known as diffuse reflection.
The properties of the images formed by plane mirrors:
1. The image is upright.
2. The image is virtual.
3. The image is the same size as you are.
4. The image is located as far behind the mirror as you
are in front of it.
5. The image of yourself in the mirror is also reversed
right to left and left to right.
5/2820)
Two plane mirrors are separated by 120°, as the
drawing illustrates. If a ray strikes mirror M1 at a 65° angle of
incidence, at what angle does it leave mirror M2?
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4/2820)
The drawing shows a laser beam shining on a
plane mirror that is perpendicular to the floor. The beam’s
angle of incidence is 33.0°. The beam emerges from the laser at
a point that is 1.10 m from the mirror and 1.80 m above the
floor. After reflection, how far from the base of the mirror does
the beam strike the floor?
(a) When a ray of light is
directed from air into
water, part of the light is
reflected at the interface
and the remainder is
refracted into the water.
The refracted ray is bent
toward the normal (θ2 <
θ1).
(b) When a ray of light is
directed from water into
air, the refracted ray in air
is bent away from the
normal (θ2 > θ1).
Snell’s Law of Refraction
When light travels from a material with refractive
index n1 into a material with refractive index n2, the
refracted ray, the incident ray, and the normal to the
interface between the materials all lie in the same
plane. The angle of refraction θ2 is related to the
angle of incidence θ1 by:
n1 sin θ1 = n2 sin θ2
(a) When light travels from a higher-index medium (water)
into a lower-index medium (air), the refracted ray is bent
away from the normal. (b) When the angle of incidence is
equal to the critical angle θc, the angle of refraction is 90°.
(c) If is greater than θ1, there is no refracted ray, and total
internal reflection occurs.
(a) Light can travel with little loss in a curved optical fiber,
because the light is totally reflected whenever it strikes the
core–cladding interface and because the absorption of light
by the core itself is small.
(b) Light being transmitted by a bundle of optical fibers.
(PhotoDisc, Inc./Getty Images)
A doctor is using an endoscope to collect samples of tissue
and fluid from the lung of a patient who has a history of
asthma and allergies. Subsequently, the samples are
examined under a microscope to obtain a diagnosis. (James
King-Holmes/SPL/Photo Researchers, Inc.)