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CHAPTER 23

ELECTROMAGNETIC WAVES

BASIC CONCEPTS

PROPAGATION OF LIGHT

ELECTROMAGNETIC SPECTRUM

ENERGY IN ELECTROMAGNETIC WAVES -

THE POYNTING VECTOR

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MAXWELL’S EQUATIONS

Describe electromagnetic waves.

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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����

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And

� = �����

The E-M Wave will travel in the � direction

at a speed of � (where� = ������).

������������� !�"#� and no

components in the � direction.

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ELECTROMAGNETIC WAVES

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The equations for �!��� can be written.

They are

�$��, " = �&'(�#��)� − +"

And

�,��, " = �&'(cos�)� − +"

Defining the wave

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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.

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The spectrum

What are electromagnetic waves?

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Energy in E-M Waves

Remember Energy Density in Electric Field

�2 = 12 ���

And

Energy Density in Magnetic Field

�4 = 12�� �

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Thus for a region with both fields

� = 12 ��� + 1

2�� �

Using

� = 26 = ������

we can simplify

� = 12 ��� + 1

2�� 7������8

� = 12 ��� + 1

2�� �����

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� = 12 ��� + 1

2 ��� = ���

Energy density for E-M Wave

� = ���

Consider region of space where E-M wave

propagating in ������"�#�.

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replace d with Δ in figure

Energy in region defined by 9 by �Δ" will be

energy that passed through area 9

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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 = �����

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� = ; 9=

Δ�Δ" = �����

We will call this ?.

? = �����

Using

� = 1�����

�

We get

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? = ������ = @��� 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��

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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.

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� = 6�10��U38U�60 � U⁄ = 2.76�10[U/�

Distance Earth-Jupiter 6x1011

m

Observe image 38 min late.

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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!"���!

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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.

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Law of reflection

Angle of Incidence = Angle of Reflection

j' =jD

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Law of Refraction (Snell’s Law)

�'���j' =�k���jk

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Total Internal Reflection

�k < �'

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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

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���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

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Dispersion and the Rainbow

The index of refraction varies depending on

the wavelength of the radiation.

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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.

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Polarization

Look back at our diagram of the

electromagnetic wave.

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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.

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o = o&'(�#�p

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Some of you wear sunglasses that polarize

the light.

Intensity through crossed polarizers is