Major Concepts of Physics PHY102
Lecture #5
How are waves mixed each other?
Interference
February 3rd, 2016
Prof. Liviu Movileanu
http://movileanulab.syr.edu/MajorConceptsPhysics2016.html
lmovilea@syr.edu
Room 211, Physics Bldg., 443-8078
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Lecture objectives
1. Review the quantitative description of waves
 Review quantitative parameters describing waves
 Review periodical expressions describing waves
 Simple Harmonic Motion (SHM)
2. What is the interference?
 Constructive and Destructive Interference
(Hypothesis)
 Young’s double-slit experiment (Experimental
evidence)
 Interference patterns (Interpretation)
3. Lecture demonstration (double-slit interference)
4. Announcements
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Quantitative understanding of waves
Major Concepts of Physics PHY102 – Lecture #5
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Periodicity of waves: time and space
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Simple Harmonic Motion (SHM)
Idea: Any object that is initially displaced slightly from a stable equilibrium
point will oscillate about its equilibrium position. It will, in general,
experience a restoring force that depends linearly on the displacement
x from equilibrium: Hooke's Law:
Fs = - kx
x is the displacement, or the distance of the mass from the equilibrium point
and
k is a constant that depends on the system under consideration.
The equilibrium point is considered at x=0
N
The units of k are: [k] =
m
kx2 mv2
Etot  Ek  E p 

2
2
Total energy=Kinetic energy + potential energy
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Simple Harmonic Motion
Definitions:
•Amplitude (A): The maximum distance that an object moves from its
equilibrium position. A simple harmonic oscillator moves back and forth between
the two positions of maximum displacement, at x = A and x = - A .
•Period (T): The time that it takes for an oscillator to execute one complete
cycle of its motion. If it starts at t = 0 at x = A , then it gets back to x = A after
one full period at t = T .
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Simple Harmonic Motion
Definitions:
•Frequency ( f ): The number of cycles (or oscillations) the object
completes per unit time. f = 1/T
The unit of frequency is usually taken to be 1 Hz = 1 cycle per second.
•Simple Harmonic Oscillator: Any object that oscillates about a stable equilibrium
position and experiences a restoring force approximately described by Hooke's law.
Examples of simple harmonic oscillators include: a mass attached to a spring,
a molecule inside a solid.
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Interference can be observed only with coherent light
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2016Syracuse University
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Constructive interference: amplitudes are added up
When the waves are in-phase, we have constructive
interference.
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Destructive Interference
When the waves are 180 degrees out-of-phase,
we have destructive interference.
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Interference: How does it work?
Maximum
Minimum
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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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.
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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The Thomas Young double-slit experiment
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
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Interpretation of Interference Data
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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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
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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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
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Interference Equations, 4
• The positions of the
fringes can be
measured vertically
from the zeroth
order maximum
• y = L tan θ  L sin θ
• Assumptions
– L>>d
– d>>λ
– tan θ  sin θ
θ is small and therefore the
approximation tan θ  sin θ can
be used
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Interference Equations, Final
• For bright fringes (use sinθ bright=m λ /d)
y bright
L

m m  0,  1,  2 
d
• For dark fringes (use sinθ dark=λ (m + ½)/d)
y dark
L 
1

 m   m  0,  1,  2 
d 
2
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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Announcements
1. Reading materials: Chapter 25th, Sections 25.1, 25.4
Examples 25.1 25.4; pp. 936-939, 948-951.
2. Workshop #2 is scheduled this week! Best of luck with your
Interference experimentation!
3 Homework #2 for the next week (on paper): Please pick up the
print outs or download the file using the web site of the PHY 102
class.
4. Do you want to be challenged? More MCAT preps? See on our PHY
102 website.
Please prioritize conceptual examples 25.1, 25.4, and 25.5
Major Concepts of Physics PHY102 – Lecture #5
2016Syracuse University
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