Major Concepts of Physics PHY102 Spring 2005

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Major Concepts of Physics PHY102 - 2006Lecture
3 January 24th
Waves and Interference
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Major Concepts of Physics PHY102 Lecture 3
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Homework - E-mail address
Go to http//www.physics.syr.edu/lmovilea/spring
2006longschedule.pdf Identify your section, so
your TA The Tas e-mail accounts are the
following Ganesh Srinivasan gsriniva_at_physics.s
yr.edu Earnest Akofor eakofor_at_syr.edu Levon
O Vogelsnag lovogels_at_syr.edu

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Announcement Workshops
Workshops They begin this week! Subject of
either the Wednesday or the Friday
workshop Workshop 1 Waves and
Interference Labs meet in Room 110. The
Workshop schedule will be posted on line
at Timetable/Miscellaneous PHY 102
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UpdateTime is Flying
Tues., January 17th Lecture 1 Introduction to
Course. Thurs., January 19th Lecture 2 Waves
and the Concepts Describing Them Tues., January
24th Lecture 3 Interferences of Waves Youngs
Experiment Thurs., January 26th Lecture 4
Traveling Waves Longitudinal vs. Transverse
Waves Tues., January 31st Lecture 5
Diffraction a close look Thurs., February 2nd,
Lecture 6 Electromagnetic Waves Tues., February
7th Lecture 7 Review Meeting, Part I Thurs.,
February 9th Exam 1

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Outline Lecture Objectives
  1)         Review of the basic concepts of
waves.   2)       The nature of
interference.   3)       The Thomas Young
Experiment of 1801.  
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Review fundamental wave concepts
 
1. The frequency f This is the number of full
cycles per time, performed by the wave. Note
The location (along the wave direction) is
fixed.   2. The wavelength ? This is the
distance for a full cycle. It is taken along the
wave direction. Note Time is fixed.   3. The
wave-speed v.   We allow both location and time
to vary, now. The wave-speed v is the speed of
the crests. Recall A crest occurs when the
wave-value is maximum.                  
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The Wave Relation
 
The Wave Relation   This relation connects these
three quantities v, f and ?. It states   v
f?.   So, if we know any two of these quantities,
we can compute the third quantity.
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Interference a way to detect waves
Detection of Waves   Interference is a way to
detect waves   Interference   Suppos
e that more than one wave occupies the same space
at the same time.   Then, the wave values
add.   This is the superposition principle.  
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First Example
We have two waves. Suppose that the crest of the
first wave overlaps the crest of the second wave.
Then, the effect is that the net wave has
increased amplitude at this point and time. This
is constructive interference. d sin ? m?,
m 0, 1, 2, 3, dthe distance
between slits

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Second Example
Suppose the crest of the first wave overlaps the
valley of the second wave. Then, the net wave
has its amplitude reduced. This is destructive
interference.  d sin ? (m1/2)?, m 0, 1, 2,
3,
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Demonstration of Interference
The interference model.   Two sinusoidal waves
superpose on each other.   When the waves are
in-phase, we have constructive interference.
  When the waves are 180 degrees out-of-phase,
we have destructive interference.
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Wavelength
The issue was settled in 1801 by the experiment
of Thomas Young. Light passes through two
holes. Demonstration The Young
Experiment Observe Some places light adds, at
other places it cancels. This would not happen
if light is a particle.  If so, the intensity
would always add.
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The wave-speed
Controversy Is light a particle or a
wave?   Newton Particle   Descartes Wave   
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The Thomas Young double-slit experiment
Thomas Young first demonstrated interference in
light waves from two sources in 1801. Light is
incident on a screen with a narrow slit, So.
The light waves emerging from this slit arrive
at a second screen that contains two narrow,
parallel slits, S1 and S2. The narrow slits, S1
and S2 act as sources of waves. The waves
emerging from the slits originate from the same
wave front and therefore are always in phase.

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Resulting Interference Pattern
The light from the two slits form a visible
pattern on a screen The pattern consists of a
series of bright and dark parallel bands called
fringes Constructive interference occurs where a
bright fringe occurs Destructive interference
results in a dark fringe
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Interference Patterns

• Constructive interference occurs at the center
  point
• The two waves travel the same distance
• Therefore, they arrive in phase

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Interference Patterns, 2

• The upper wave has to travel further than the
  lower wave
• The upper wave travels one wavelength further
• Therefore, the waves arrive in phase
• A bright fringe occurs

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Interference Patterns, 3

• The upper wave travels one-half of a wavelength
  farther than the lower wave
• The trough of the bottom wave overlaps the crest
  of the upper wave (180? phase shift)
• This is destructive interference
• A dark fringe occurs

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Interference Equations

• The path difference, d, is found from the
  triangle
• d r2 r1 d sin ?

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Interference Equations, 2

• This assumes the paths are parallel
• Not exactly, but a very good approximation
  (Lgtgtd)

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Interference Equations, 3

• For a bright fringe, produced by constructive
  interference, the path difference must be either
  zero or some integral multiple of of the
  wavelength
• d d sin ?bright m ?
• m 0, 1, 2,
• m is called the order number
• When m 0, it is the zeroth order maximum
• When m 1, it is called the first order maximum

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Interference Equations, 4

• When destructive interference occurs, a dark
  fringe is observed
• This needs a path difference of an odd half
  wavelength
• d d sin ?dark (m ½) ?
• m 0, 1, 2,

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Interference Equations, 5

• The positions of the fringes can be measured
  vertically from the zeroth order maximum
• y L tan ? ? L sin ?
• Assumptions
• Lgtgtd
• dgtgt?
• tan ? ? sin ?

? is small and therefore the approximation tan ?
? sin ? can be used
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Interference Equations, Final

• For bright fringes (use sin? brightm ? /d)
• For dark fringes (use sin? dark? (m ½)/d)

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Summary

• Youngs Double Slit Experiment provides a method
  for measuring wavelength of the light (Ex. 24-3
  from pp. 670-671.
• This experiment gave the wave model of light a
  great deal of credibility
• It is inconceivable that particles of light could
  cancel each other

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Homework/Textbook
Textbook, Chapter 24, 24-3, pp. 668-669 No
Homework for the next week, Take a look at
Examples 24-1 through 24-3 From textbook, pp.
670-671
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Major Concepts of Physics PHY102 Lecture 3
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