Chapter 25
Electromagnetic Waves
Outline
25-1
The production of Electromagnetic Waves
25-3
The Electromagnetic Spectrum
25-4
Energy
gy and momentum in Electromagnetic
g
Waves
25-5
Polarization
25-5
Polarization
Natural
N
t l white
hit lilight
ht iis non-polarized,
l i d since
i
th
the itits E vector
t off th
the
electromagnetic wave vibrates randomly in any direction.
If the E vector vibrates only in one direction, the wave is said to be
polarized --- linearly polarized.
The electric field defines the polarization direction.
Figure 25-11
25 11
Polarization of Electromagnetic Waves
Representation of Polarization
Figure 25-12
Fi
25 12
Polarized Versus
Unpolarized Light
Light Passing through Polarizer
The polarizer is made of special material, and it allows light go through
along one direction – called transmission axis.
Figure 25-13
A Mechanical Analog of a
Polarizer
The Law of Malus (Transmission of Polarized Light Through a Polarizer)
I = I 0 cos 2 θ
(25 − 13)
Where θ is the angle of the polarization direction of the linear polarized
input light and the polarizer transmission axis
Figure 25-14
Transmission of Polarized
Li ht Through
Light
Th
h a Polarizer
P l i
Exercise 25-5
Vertically polarized light with an intensity of 515 W/m2 passes through
a polarizer oriented at an angle θ to the vertical (transmission axis of a
polarizer). Find the transmitted intensity of the light for (a) θ=10.0º and
(b) θ=45.0º,
4 0º and
d (c)
( ) θ=90.0º.
90 0º
Solution
( )
(a)
I = I 0 cos 2 θ = (515W / m 2 ) cos 2 10.0° = 499 W / m 2
(b)
I = I 0 cos 2 θ = (515W / m 2 ) cos 2 45.0° = 258 W / m 2
(c)
I = I 0 cos 2 θ = (515W / m 2 ) cos 2 90.0° = 0 W / m 2
Transmission of an un-polarized light
Figure 25-15
Transmission of Unpolarized Light
Through a Polarizer
Transmission of an un-polarized light
1
I = I0
2
It is independent to the angle θ.
(25 − 14)
A common experiment
Figure 25-16
A Polarizer and an Analyzer
Example 25-5
In the polarization shown in the sketch
sketch, the final intensity of the beam
is 0.200 I0. What is the angle θ between the transmission of the
analyzer and polarizer?
Example 25-5
Analyze This
Active Exercise
Calculate
C
l l t th
the ttransmitted
itt d iintensity
t
it ffor th
the ffollowing
ll i cases: [(
[(a)) A
vertically polarized beam of intensity I0 passes through a polarizer
with its transmission axis at 60º to the vertical (transmission axis )].
(b) a vertical
ti l polarized
l i db
beam off iintensity
t
it I0 passes through
th
h ttwo
polarizers, the first with its transmission axis at 30º to the vertical,
and the second with its transmission axis at 60º to the vertical.