wave physics phys2023
TRANSCRIPT
2
Wave propagation in changing media
• Huygens’ construction
• gradual change: • refraction
• refraction; continuity conditions
• obstacles: • 1-D: boundary conditions
• 2/3-D: diffraction
• today’s lecture:
• interface between media:
5
Wave propagation
waves are
• collective bulk disturbances, in which
• motion is a delayed response
• to neighbouring motions
• the amplitudes are added
when propagation follows multiple routes
• waves propagate via all possible routes
6
Huygens’ wave construction
• wavefronts propagate from initial disturbancein all directions
Christiaan Huygens (1629-1695)
• each point on the wavefront acts as asecondary source
• further wavefronts propagate from the secondary sources in the same fashion
• where wavefronts coincide (strong constructive interference), a new wavefront is formed
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Huygens’ wave construction
• mirages by refraction in the atmosphereChristiaan Huygens (1629-1695)
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Huygens’ wave construction
Christiaan Huygens (1629-1695)
• ocean waves parallel to shore
http://www.uwgb.edu/dutchs/EarthSC202Slides/COASSLID.HTM
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Huygens’ wave construction
Christiaan Huygens (1629-1695)
http://geographyfieldwork.com/WaveRefraction.htm
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Huygens’ wave construction
Christiaan Huygens (1629-1695)
http://www.smccd.edu/accounts/bramalln/documents/waterwaves.pdf
http://www.dorsetphotos.co.uk
Google Earth
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Fermat’s principle of least time
• refraction at a plane surfacePierre de Fermat (1601-1665)
x0 L
a
b
A B C
S
P
S
P
x
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Fermat’s principle of least time
• refraction at a plane surfacePierre de Fermat (1601-1665)
x0 L
a
b
S
P
x
• light rays follow the path of least timebetween two points
S
P
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Snell’s law of refraction
• refraction at a plane surface
x0 L
a
b
S
P
x
• light rays follow the path of least timebetween two points
Willebrord Snel van Royen(Leiden, 1580-1626)
S
P
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Huygens’ wave construction
• Fresnel integral
• phasors shorter / rotate more quickly at distance to give spiral
• phasors equivalent to complex numbers on Argand diagram
26
Wave propagation
waves are
• collective bulk disturbances, in which
• motion is a delayed response
• to neighbouring motions
• the amplitudes are added
when propagation follows multiple routes
• waves propagate via all possible routes