Chapter 33:
Interference and Diffraction
Homework: 17, 31, 37, 55
Cover Sections: 1, 2, 3, 4, 6, 7
Omit Sectons: 5, 8
1
Outline:
 Phase Difference and Coherence
 Interference in Thin Films
 Single Slit Diffraction Pattern
 Two Slit Interference
 Fraunhofer and Fresnel Diffraction
 Diffraction and Resolution
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3
33-1
Phase Difference and Coherence
Phase Difference: The fractional part of a period
which represents the offset in peak positions of
waves.
Coherence: The existence of a correlation between
the phases of two or more waves such that
interference effects can be observed.
Interference: The variation with distance or time of
the amplitude of a wave which results from the
superposition of two or more waves.
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5
33-2
Interference in Thin Films
6
7
Change in Wavelength
c f
v 
 f 
n n
 

n
n = index of refraction
8
p
p
9
10
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Condition: Ray 1 and 2 will be out of phase by p
radians for 589nm light.
Path difference = 2t.
2t

2p  p
9
589 10 m / 1.33
9
5.32t  589 10 m
t  110nm  0.110m
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33-3
Two-Slit Interference Pattern
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14
y-axis
bright/dark are
symmetric
m = 2 bright fringe
L
m = 1 bright fringe
central max
m = 1 dark fringe
m = 2 dark fringe
m = 3 dark fringe
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16
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Example: slit-separation d = 1.5mm. Light  = 589nm.
Bright fringes occur at:
1  sin 1 (1)(589 109 m) / 1.5 103 m  0.0224
 2  sin 1 (2)(589 109 m) / 1.5 103 m  0.0449
 3  sin 1 (3)(589 10 9 m) / 1.5 10 3 m   0.0674
etc.
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Example: L = 3m. slit-separation d = 1.5mm. Light  =
589nm.

 (3)(589 10

m   3.53mm
y2  (2) (589 109 m)(3m) / 1.5 103 m  2.36mm
y3
9
m)(3m) / 1.5 10 3
Bright fringe spacing = y3 – y2 = 1.17 mm
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Example: slit-separation d = 1.5mm. Light  = 589nm.
2nd Dark fringe occurs at:
 2  sin 1 (2  12 )(589 10 9 m) / 1.5 10 3 m   0.0337
The 2nd Dark fringe should occur between 1st and 2nd
Bright fringes:
0.0224  0.0449
2 
 0.0337
2
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33-4
Diffraction Pattern of
a Single Slit
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23
a = Slit-Width
(a ≠ d)
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25
Example: slit-width a = 0.200mm. Light  = 589nm.
Dark fringes occur at:
1  sin 1 (1)(589 109 m) / 0.200 103 m  0.168
 2  sin 1 (2)(589 109 m) / 0.200 103 m  0.337
etc.
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(Omit)
33-5
Using Phasors to
Add Harmonic Waves
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33-6
Fraunhofer and Fresnel
Diffraction
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Fraunhofer and Fresnel Diffraction
Patterns
• Fresnel Pattern: observed near obstacle
causing diffraction.
• Fraunhofer Pattern: observed far from away
from the obstacle.
• The criterion for determining near and far is
the convergence angle of the light which
makes up the pattern.
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33-7
Diffraction and Resolution
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First Diffraction Minimum of a
Circular Aperture
  1.22

D

31
Rayleigh Criterion
…occurs when two point sources of light are close enough
together that light coming from them passes through a circular
aperture so that the 1st minimums of the diffraction patterns fall
on the central maximum of the other. A single ellipsoid is seen
instead of two separate objects.
32
Rayleigh Criterion Formula
…is a condition for the angle of convergence of rays
emanating from the objects that pass through the aperture.
This angle is called “alpha”, and occurs when:
 c  1.22

D
33
Summary:
• Phase Difference and Path Difference
• Coherence defined
• Interference in Thin Films
• Single Slit and Two Slit Patterns
• Fraunhofer and Fresnel Diffraction
• Diffraction limits ultimate resolution
34
Omit
33-8
Diffraction Gratings
End of 33
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