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Lecture 22: July 15th 2009
Physics for Scientists and Engineers II
Physics for Scientists and Engineers II , Summer Semester 2009
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Momentum and Radiation Pressure
Electromag netic radiation carries energy TER and momentum p per unit time.
If TER is totally absorbed by a surface perpendicu lar to S, the momentum p
transporte d to the surface has a magnitude :
T
p  ER
(complete absorption )
c
 A pressure P is exerted on the surface by the radiation (" radiation pressure" )
 dTER 
dt  Savg I
F 1 dp 1 d  TER  1 
P 



(complete absorption )


A A dt A dt  c  c
A
c
c
(Note : P here is pressure, not power)
2Savg 2I
2T
For complete reflection : p  ER
and P 

c
c
c
Physics for Scientists and Engineers II , Summer Semester 2009
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Antennas
Stationary charges : Produce constant electric fields
Constant currents : Produce constant magnetic fields
Maxwell' s equations tell us that we need time - varying fields
to produce electromag netic radiation.
 Accelerate d charges needed to produce time - varying fields.
Whenever a charged particle accelerate s, it radiates energy (em radiation) .

4
+
+
The Half Wave Antenna
+
+
Source of alternating
voltage having
frequency f = c / 
Conducting rods

4
-
-
Physics for Scientists and Engineers II , Summer Semester 2009
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Driving the resonance frequency of the antenna ----???
You can create a driven oscillatio n by applying an alternatin g voltage with
c
a frequency equal to the self - oscillatio n frequency of the antenna (f 
).
2L
 Resonance occurs with higher amplitudes (greater electric fields, greater current).
Snapshot in time:
+
+
+
S
B
I
E I
+
-
B
S
Separation of charges creates an electric
field like that of a dipole:
 Given the name “Dipole antenna”
E
-
-
B  E at all points in space and time.
Physics for Scientists and Engineers II , Summer Semester 2009
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Driving the resonance frequency of the antenna
+
+
Snapshot in time:
+
S
B
I
+
B
S (indicatin g the direction
E I
-
E
in which energy flows)
-
B  E at all points in space and time.
E and B are 90 out of phase (e.g., when I  0, the charges
at the outer ends of the rods are at a maximum).
Physics for Scientists and Engineers II , Summer Semester 2009
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Voltage and Current Distribution
V I
V I
V I
V I
Physics for Scientists and Engineers II , Summer Semester 2009
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Driving the resonance frequency of the antenna
V I
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The “near field” (dipole field) behavior
+
+
+
+
+
+
S
B
I
E I
+
-
B
S
B
I
S
E I
E
-
+
-
B
E
-
-
Shortly th ereafter, the current reverses :
 Poynting vector reverses direction
 Energy flowing inward
 no net flow of energy ??? No! The dipole field (near field)
falls of proportion al to
1
and quickly becomes insignific ant.
3
r
Physics for Scientists and Engineers II , Summer Semester 2009
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The “far field” behavior
At larger distances time - varying electric fields induce time varying magnetic field and vice versa according to
 E  ds  
d B
dt
Faraday' s law 
d E
Ampere - Maxwell law 
dt
The magnetic and electric fields produced in this manner are in phase.
1
E and B are proportion al to
r
1
 radiation looses intensity proportion al to 2
r
 B  d s   0  I  I d    0 I   0 0
Physics for Scientists and Engineers II , Summer Semester 2009
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Angular dependence of radiation intensity

S
Intensity of Radiation : I  S avg
sin 2 

r2
Similarly, when using an antenna to receive radiation, orientatio n matters equally.
S
Physics for Scientists and Engineers II , Summer Semester 2009
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Angular dependence of radiation intensity
Similarly, when using an antenna to receive radiation, orientatio n matters equally.
E
S
B
Sender
Good reception
S
Sender
No reception
S
B
Sender
No reception
E
E should be parallel to antenna
Physics for Scientists and Engineers II , Summer Semester 2009
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Electromagnetic Spectrum
Physics for Scientists and Engineers II , Summer Semester 2009
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The Nature of Light
Newton: Light = Stream of Particles (can explain reflection and refraction)
1678 Christian Huygens : Showed that a wave model of light can also explain
reflection and refraction.
1801 Thomas Young: Experimental demonstration of the wave nature of light
(Double slit experiment  “Interference” effects)
Maxwell: Light = high frequency electromagnetic wave
Hertz: Confirms existence of electromagnetic waves
…..but also discovers the photoelectric effect (contradicts the wave model,
which predicts: more light intensity = more energy transferred to electrons)
Einstein 1905: Proposes that energy of light wave is present in particles called
photons. E=hf is the energy of a photon (explains photoelectric
effect).
Physics for Scientists and Engineers II , Summer Semester 2009
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Measuring the speed of light
Galileo: Using lanterns between mountains didn’t work. The light is too fast.
1675: Ole Roemer found that the period of revolution of the moon Io around
Jupiter depends on whether the earth is receding from or moving towards
Jupiter (longer period when earth is receding).
From these data Huygens calculated c > 2.3 x 108 m/s
1849: Fizeau’s method (toothed wheel): c = 3.1 x 108 m/s
Currently accepted value: c = 2.997 9 x 108 m/s
Physics for Scientists and Engineers II , Summer Semester 2009
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Eclipse Time Delay of Io in the shadow of Jupiter
Roemer’s method
Jupiter
Io
being
eclipsed
by Jupiter
2  Rsunearth
c
tdelay
Sun
In this position, the time of the eclipse
is delayed by many minutes
compared to the opposite position
of the earth.
Physics for Scientists and Engineers II , Summer Semester 2009
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Ray Approximation in Geometric Optics
Geometrical Optics
The study of the propagation of light under these assumptions:
1) In a uniform medium light travels in a straight line.
2) Light changes direction in a medium with non-uniform optical properties,
or at the interface between two media.
The “Ray approximation”:
Wave moving through a medium
travels in a straight line in the
direction of it’s rays.
Rays
Physics for Scientists and Engineers II , Summer Semester 2009
Wave fronts
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Ray Approximation in Geometric Optics
Encountering barriers (like an opening in a wall):
The ray approximation is valid if  << d, where d is the size of the opening.
  d
Wave continues in a straight line
  d
Diffraction occurs
Opening acts like a point source of a wave.
Physics for Scientists and Engineers II , Summer Semester 2009
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Reflection of Light/Wave
Incident Ray
Normal
1
Reflected Ray
1'
1'  1
Angle of reflection  Angle of incidence
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Specular and Diffuse Reflection
Specular reflection
“Smooth surface”
Variations in surface  
Diffuse reflection
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The Wave under Refraction
Incident Ray
Normal
1   2
1'
v1
Air
Glass
v2  v1
2
Angle of Refraction
Physics for Scientists and Engineers II , Summer Semester 2009
Reflected Ray
Refracted Ray
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The Wave under Refraction
Incident Ray, Reflected Ray, and Refracted ray are all in one plane.
sin  2 v2 Speed of light in medium 2
 
sin 1 v1 Speed of light in medium 1
Physics for Scientists and Engineers II , Summer Semester 2009
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The Wave under Refraction
Incident Ray
Normal
1
Reflected Ray
1'
v1
Glass
Air
v2  v1
 2  1
Angle of Refraction
Physics for Scientists and Engineers II , Summer Semester 2009
Refracted Ray
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Index of Refraction – not yet covered in class but needed for HW 16
Index of Refraction : n 
speed of light in vacuum
c

speed of light in a medium v
n vacuum  1
For vacuum :
All other media :
n 1
When light enters a medium :
frequency remains constant, but wavele ngth changes.
f1  f 2  f
v1  1 f
v2  2 f
v1

c
1
v
n1 n2
f

 1 

v
c
2
v2
n1
2
f

 n
n
 1n1  2 n2
n2
Wavelength in vacuum
n  
Wavelength in medium
Physics for Scientists and Engineers II , Summer Semester 2009
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Snell’s Law of Refraction – not yet covered in class but needed for HW 16.
sin  2 v2 n1
 
sin 1 v1 n 2

n1 sin 1  n 2 sin  2
Snell’s Law of Refraction
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