PA2001: Time and Energy
Waves and Interference
• Light as a wave
• Fermat’s principle
• Reflection
• Refraction
• Thin Film interference
• Single slit diffraction
• Young’s double slit experiment
http://www.le.ac.uk/ph/mr6/lectures.html
Tipler Chapters 16,33,35
Dr Mervyn Roy, S6
Waves and Interference
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The Electromagnetic Spectrum
1000 m
Long-waves
10 m
Radio, TV
Wavelength
10 cm
Microwaves
700 nm
Infra-red
600 nm
1 mm
10 mm
100 nm
Visible
500 nm
1 nm
X-rays
0.1 nm
Gamma rays
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400 nm
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Fermat’s principle
The path taken by light in travelling from one point to another is
such that the time of travel is a minimum.
Explains the law of reflection:
Euclid
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Phase changes
wave incident on a barrier
incident wave:
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Phase changes
wave incident on a barrier
incident wave:
reflected wave:
phase change of  upon reflection
(note: phase change of  only for reflection at rare/dense interface)
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Refraction
some reflection
rare medium (air)
some reflection
dense medium (glass)
note: phase change of  only at rare /
dense interface
Snell’s Law
- derived using Fermat’s principle – shortest path is not the fastest as v < c
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Refraction
some reflection
phase change 
rare medium (air)
some reflection
no phase change
dense medium (glass)
note: phase change of  only at rare /
dense interface
Snell’s Law
- derived using Fermat’s principle – shortest path is not the fastest as v < c
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Refraction 2
Or, why shooting fish in a barrel isn’t easy
nwater = 1.3
Fish are always deeper than you think
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Dispersive media
- waves of different wavelength travel at different velocity and
therefore refract differently
Newton’s prism
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Interference
Add coherent harmonic waves with phase difference

0, 2
/2
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Interference
Add coherent harmonic waves with phase difference

0, 2
/2
Waves and Interference
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Interference
Add coherent harmonic waves with phase difference

0, 2
/2
Waves and Interference
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Interference
Add coherent harmonic waves with phase difference

0, 2
/2
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Interference 2
Add coherent harmonic waves with phase difference
Intensity,
With constant amplitude as before,
In general (Hecht, Optics 2nd Ed. 9.1),
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Interference 3
Add coherent harmonic waves with path difference,
Phase difference is related to path difference
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Thin film interference 1
travels further than
difference in path length introduces phase
difference
interferes with
type of interference depends on
To find type of interference:
Calculate path and phase difference, then:
Note: have to be careful with possible phase changes of  at each interface
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Thin film interference 2
travels further than
difference in path length introduces phase
difference
interferes with
type of interference depends on
At normal incidence:
Maximum in the intensity if
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Thin film interference 3
At normal incidence see interference
fringes with films of varying thickness
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B
Thin film interference 4
D
C
D
C
A
B
combine
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A
A
D
with Snell’s law
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Thin film growth
In-situ monitoring of film thickness
At fixed, angle of incidence,
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Diffraction (single slit)
Water wave
slit width, a
screen
• aperture size ~ wavelength
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Diffraction (single slit)
Laser light
slit width, a
screen
Screen
Intensity
-2/a
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-/a
/a
2/a
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Young’s slits
slit separation, d
Laser light
Interference
fringes
Screen far away, rays ~ parallel
d
Path difference,
Constructive interference:
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Diffraction gratings
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Angle of maxima is wavelength
dependent:
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