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