Wave Physics
PHYS 2023
Tim Freegarde
Wave propagation in changing media
• today’s lecture:
• Huygens’ construction
• gradual change:
• refraction
• interface between media:
• refraction; continuity conditions
• obstacles:
• 1-D: boundary conditions
• 2/3-D: diffraction
2
Young’s double slit diffraction

a

x
s
3
Young’s double slit diffraction

2 d

a

 d
x
s
 d
amplitude
intensity
4
Young’s double slit diffraction

2 d

a

 d
x
s
 d
amplitude
intensity
5
Single slit diffraction

y

a

2 a
 a
x
 a
 2 a
amplitude
intensity
s
6
Diffraction grating
y

a
x
d
s

1
m=0
0.8
m=-1
0.6
m=1
0.4
0.2
m=-2
-1.5
-1
m=2
-0.5
0.5
1

1.5
7
Diffraction grating
y

x
d

s
• place secondary sources along wavefront
• ...and trigger when wavefront arrives
• apply to sinusoidal waves by taking into account
the phase with which components arrive
INTERFERENCE
• combine by adding the amplitudes
• contributions may therefore interfere
constructively or destructively
8
Diffraction gratings
y
ad

w
s
newport.com
• diffracted angle
9
Grating spectrometer

scope.pari.edu
10
Diffraction gratings
y
ad

w
s
newport.com
• diffracted angle
• incident angle
11
Phased-array loudspeakers
• Croke Park, Dublin
duran-audio.com AXYS
• incident angle
• phase angle
12
Phased-array radar
• Fylingdales, Yorkshire
• 2560 transducers, 25m diameter, 420-450 MHz
• phase angle
13
Towed array sonar
www.surtass-lfa-eis.com
• typically 100 hydrophones over 300m
• 1500 m.s-1 seawater; 1435 m.s-1 freshwater
• phase angle
14
Spatial light modulators
www.holoeye.com
• 1920 x 1200 pixels, LCD technology
• 8.1 μm pitch
15
Spatial light modulators
www.holoeye.com
• 1920 x 1200 pixels, LCD technology
• 8.1 μm pitch
www.physics.gla.ac.uk/optics
• laser tweezing of 2 μm glass spheres in fluid
• computer-controlled hologram
• projected and viewed through microscope
16
Wave Physics
PHYS 2023
Tim Freegarde
Wave Physics
general wave phenomena
WAVE EQUATIONS &
SINUSOIDAL SOLUTIONS
wave equations, derivations and solution
sinusoidal wave motions
complex wave functions
Huygens’ model of wave propagation
WAVE PROPAGATION
interference
Fraunhofer diffraction
longitudinal waves
BEHAVIOUR AT
INTERFACES
SUPERPOSITIONS
continuity conditions
boundary conditions
linearity and superpositions
Fourier series and transforms
waves in three dimensions
FURTHER TOPICS
waves from moving sources
operators for waves and oscillations
further phenomena and implications
18
http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7
Wave propagation in changing media
• Huygens’ construction
• gradual change:
• refraction
• interface between media:
• refraction; continuity conditions
• obstacles:
• 1-D: boundary conditions
• 2/3-D: diffraction
• place secondary sources along wavefront
• ...and trigger when wavefront arrives
• apply to sinusoidal waves by taking into account
the phase with which components arrive
INTERFERENCE
• combine by adding the amplitudes
• contributions may therefore interfere
constructively or destructively
19
Diffraction grating
y

x
d

s
• interference by division of wavefront
20
Michelson interferometer
• interference by division of amplitude
δx
beamsplitter
detector
source
21
Michelson interferometer
• interference by division of amplitude
δx
δx
beamsplitter
• FTIR: Fourier transform infrared
detector
source
chemistry.oregonstate.edu
optique-ingenieur.org
• sodium doublet
22
Beating
TWO DIFFERENT FREQUENCIES
23
Newton’s rings
beam-splitter
diffuser
r
lens
s
plate
• apply to sinusoidal waves by taking into account
the phase with which components arrive
• combine by adding the amplitudes
www.sciencebuddies.org
• contributions may therefore interfere
constructively or destructively
24