Wave Physics PHYS2023

Wave PhysicsPHYS 2023

Tim Freegarde

08 Huygens construction2020-21

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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:

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Wave propagation in 2D & 3D

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Spherical waves

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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

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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

• two point sources

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Huygens’ wave construction

• five point sources• two point sources

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Huygens’ wave construction

• 21 point sources• five point sources

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Huygens’ wave construction

• propagation from a point sourceChristiaan Huygens (1629-1695)

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Huygens’ wave construction

• reflection at a plane surfaceChristiaan Huygens (1629-1695)

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Huygens’ wave construction

• refraction at a plane surfaceChristiaan Huygens (1629-1695)

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Huygens’ wave construction

• refraction at a plane surfaceChristiaan Huygens (1629-1695)

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Snell’s law, following Huygens

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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

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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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Snell’s law, following Fermat

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Phasors

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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

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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

Wave PhysicsPHYS 2023

Tim Freegarde