View
20
Download
0
Category
Preview:
Citation preview
1
CHAPTER 23
ELECTROMAGNETIC WAVES
BASIC CONCEPTS
PROPAGATION OF LIGHT
ELECTROMAGNETIC SPECTRUM
ENERGY IN ELECTROMAGNETIC WAVES -
THE POYNTING VECTOR
2
MAXWELL’S EQUATIONS
Describe electromagnetic waves.
3
Maxwell used these equations to predict
the propagation of electromagnetic waves,
light.
We have from Faraday’s Law
� = ��
We have from Ampere’s Law
� = ������
Thus we get (putting the second in the first)
� = ��������
� = 1����
4
And
� = �����
The E-M Wave will travel in the � direction
at a speed of � (where� = ������).
������������� !�"#� and no
components in the � direction.
5
ELECTROMAGNETIC WAVES
6
The equations for �!��� can be written.
They are
�$��, " = �&'(�#��)� − +"
And
�,��, " = �&'(cos�)� − +"
Defining the wave
7
The wavelength �0 is the distance along
the wave from a point to the next point
where the waves starts to repeat.
The frequency �1 is the number of times
per second a point on the wave passes
through a cycle.
8
The spectrum
What are electromagnetic waves?
9
Energy in E-M Waves
Remember Energy Density in Electric Field
�2 = 12 ���
And
Energy Density in Magnetic Field
�4 = 12�� �
10
Thus for a region with both fields
� = 12 ��� + 1
2�� �
Using
� = 26 = ������
we can simplify
� = 12 ��� + 1
2�� 7������8
� = 12 ��� + 1
2�� �����
11
� = 12 ��� + 1
2 ��� = ���
Energy density for E-M Wave
� = ���
Consider region of space where E-M wave
propagating in ������"�#�.
12
replace d with Δ in figure
Energy in region defined by 9 by �Δ" will be
energy that passed through area 9
13
Energy in region is energy density multiplied
by volume.
Δ; = �Δ< = ����9�Δ"
The energy per unit time through 9 will be
Δ;Δ" = ����9�
And the energy per unit time per unit area
will be
Δ; Δ"=A = �����
14
� = ; 9=
Δ�Δ" = �����
We will call this ?.
? = �����
Using
� = 1�����
�
We get
15
? = ������ = @��� 1�����
�A �
? = �������
�� 1�����
= ������ ��
? = ����
The energy per unit area per unit time
passing through an area with an E-M wave.
?'BC = �&'(�&'(2��
Or since �D&E = 2FGH√ !���D&E = 4FGH
√
JKLM = NOPQROPQ��
16
Measuring the Speed of Light
TWO NEW SCIENCES
By
GALILEO
Simplicio: Everyday experience shows that the
propagation of light is instantaneous; for when
we see a piece of artillery fired, at a great
distance, the flash reaches our eyes without
lapse of time; but the sound reaches the ear
only after a noticeable interval.
Sagredo: Well, Simplicio, the only thing I am
able to infer from this familiar bit of experience
is that sound, in reaching our ear, travels more
slowly than light; it does not inform me
whether the coming of the light is
instantaneous or whether, although extremely
rapid, it still occupies time.
17
� = 6�10��U38U�60 � U⁄ = 2.76�10[U/�
Distance Earth-Jupiter 6x1011
m
Observe image 38 min late.
18
19
SPEED OF ELECTROMAGNETIC WAVES
In vacuum � = 2.99792458�10[U/�
But only in vacuum
In air 2.9970�10[U/� Water 2.2541�10[U/�
Glass 1.8974�10[U/�
Diamond 1.2388�10[U/�
Use these values to define Index of
Refraction, n.
�&'`CDa'b = ���������c!���Uc��������U!"���!
20
Air � = 6.dde�(��f = 1.0003
Water � = 6.gh�(��f = 1.33
Glass � = 6�.[deh(��f = 1.58
Diamond � = 6�.i[[(��f = 2.42
We will use these values when we discuss
refraction.
21
22
Law of reflection
Angle of Incidence = Angle of Reflection
j' =jD
23
Law of Refraction (Snell’s Law)
�'���j' =�k���jk
24
25
Total Internal Reflection
�k < �'
26
Use Snell’s Law
�'���j' =�k���jk
�'�k ���j' = ���jk
Total internal reflection occurs when the
refracted ray is parallel to the surface or
jk = 90�
�'�k ���j' = ���90� = 1
27
���j' = �k�'
And j' = !����� mnmG
Is the smallest angle of incidence for total
internal reflection and is called the critical
angle, j6Da`.
Thus ���j6Da` = mnmG
28
Dispersion and the Rainbow
The index of refraction varies depending on
the wavelength of the radiation.
29
Send radiation through a material of the
right shape and the radiation is broken into
its different wavelengths or colors.
That is what is happening with a rainbow.
30
31
Polarization
Look back at our diagram of the
electromagnetic wave.
32
In general the E vector points in all
directions in the plane perpendicular to the
direction of motion of the wave. But if the
E vector is only oscillating in one direction
as shown here, the wave is said to be
polarized.
There are materials that will filter out the E
vector in all directions except the one
direction.
33
34
o = o&'(�#�p
35
Some of you wear sunglasses that polarize
the light.
Intensity through crossed polarizers is
Recommended