Download Physics 200 Class #1 Outline

Physics 200 Class #5 Notes
September 21, 2005
Reading Assignment Text: Chapter 3,4 pp. 59-94
 Continuation of Chapter 2
 Class Exercises
 Introduction to Chapter 3
Chapter 2 Newton’s particle Theory May or may not be covered in class, depending on timing.
It's interesting in that it presents a hypothesis being made and being tested.
(pp. 33-47; 47-56 is an interesting historical perspective on Newton)
Chapter 3
A wave theory of light
3.1 Waves
Whatever the nature of light may be, light is not like a tiny baseball.
What else travels through space carrying information (energy)?


A wave is a pattern, not a thing (like a ball).
Usually a wave is a moving, changing pattern.
or
A wave is a disturbance that carries information (energy) from one point in space to another
without the net motion of matter.
What is the nature of the disturbance?
In Chapters 3 and 4, we explore the properties of waves and learn that light has a wave-like
character. In Chapter 5, we address the nature of the disturbance in the light wave.
There are two extremes for wave motion:
Transverse waves: The vibration is at right angles to the direction in which the wave is moving.
(String waves, water waves, light)
Compressional (Longitudinal) waves: The vibration is parallel to the direction in which the wave is
moving.
(Sound)
3.2 Some general properties of waves
Reflections and variation in speed
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Superposition
The superposition principle:
To get the resultant pattern during overlap, add the original patterns algebraically
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Periodic Waves
The basic type of wave motion that we shall study is a periodic wave based on Simple Harmonic
Motion.
If we look at the individual elements in time, we get the following behavior (for example, the
motion of a mass on a spring):
Period (T): The time for one complete vibration.
Frequency ( f ): Number of vibrations per second (oscillations per second or Hertz)
If each point of the wave oscillates with this simple harmonic motion of Period T
(frequency f  1/ T ), then a snapshot picture of the wave in space is shown in Figure 3.6.
Then the wave moves a distance λ during a time of one period (T). The speed of the wave is:

1
v
or since f 
v f
NOTE
T
T
following figure from http://eosweb.larc.nasa.gov/EDDOCS/Wavelengths_for_Colors.html#red
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Some common frequencies and wavelengths. Given the wavelengths, what are the frequencies and
vice-versa? Use v = 3 x 108 m/s as the velocity of light (also denoted "c"): c = f
Microwaves: ~1 cm
FM Radio: 100 MHz
AM Radio: 100 kHz (The same percentage bandwidth (say plus or minus 1 percent) is a much
smaller frequency range. Less information can be transmitted. Do you notice the difference in
sound quality?)
Visible light: Violet: 400 nm, Red: 650 nm
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What a python or rattlesnake may see!
Infrared view: http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Intro/ProfinIR.gif
Flower markings on coneflowers (a) in ordinary light and (b) in ultraviolet light. (From Stern,
Introductory Plant Biology, 8th ed., ©2000 McGraw-Hill Companies, Inc.)
What a bee may see. Ultraviolet view
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How do we transport energy?
Particles: A particle is a discrete (localized mass) that can transport energy from one point to
another;
{Later, we will show: KE  12 mv 2 }
Waves: A wave is a disturbance that carries energy (and momentum) from one point in space to
another point in space without the net motion of mass from one point to another.
There are two extreme types of waves: Transverse (strings and light) and longitudinal or
compressional (sound). Later we will verify that light is a transverse wave (polarization).
On the internet, see http://www.geocities.com/CapeCanaveral/Hall/6645/lontra_e/lontra_g.htm
for example
Guiding Principles:
I
Waves move at a constant velocity that is determined by the medium that supports them,
rather than the waves themselves. (Note: light propagates in a vacuum and the speed depends on
the electric and magnetic properties of free space.)
II
Waves obey a superposition principle. If two or more waves arrive simultaneously at the
same point in space, the resulting effect is simply the sum of the effects of each of the waves.
We look at examples of the latter in Chapter 4.
If each point of the wave oscillates with this simple harmonic motion of Period T
(frequency f  1 / T ), then a snapshot picture of the wave in space is:
Then the wave moves a distance λ during a time of one period (T). The speed of the wave is:

1
v
or since f 
v f
T
T
We usually reserve the symbol c for the speed of light.
Aside
Note: The description of the wave in the previous figure can be written mathematically as:
 2 
y  A sin 
x
  
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For sound waves, we generally associate f with pitch. For light, this corresponds to color. We
will eventually concentrate on the electromagnetic spectrum (light).
3.3 Light as a wave?
This Section is best done by observing the phenomena using a ripple tank.
3.4 Refraction quantitatively
inc
vregionof incident wave

f inc
sin i
 AB  inc 

sin r refr refr
f refr vregionof refracted wave
AB
Comparison with light
v
sin i
 air
sin r vwater
Foucault showed: vwater  vair but didn't know value
vair
 1.33
vwater
Angle measurements confirm the wave prediction (and speed measurements)!
But there is more!
Michelson (1883) showed:
We know that waves participate in interference and diffraction phenomena. The question we need
to address is whether or not light participates in these phenomena.
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