nair sinθi - IYPTsolutions.iypt.org/uploads/2012_KR_Bright_waves_Hyung_Ju_Suh... · Water Surface...
Transcript of nair sinθi - IYPTsolutions.iypt.org/uploads/2012_KR_Bright_waves_Hyung_Ju_Suh... · Water Surface...
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iθ
fθ
airair v
cn =
waterwater v
cn =
fwateriair nn θθ sinsin =
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Change of Surface Curvature!
Unequal Distribution of Light Rays Pattern!
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Theory
Water Surface Modeling
Light Flux Density
Refraction
Experiment Conclusion
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http://www.google.ca/imgres?imgurl=http://imaginezambia.org/wp-content/uploads/splash-water-waves-4565.jpg&imgrefurl=http://imaginezambia.org/2476/training-workshop-moringa-propogation-teams-quick-update/splash-water-waves-4565/&usg=__ouoxefwUL0whvrDUOOQBnp3NR40=&h=324&w=620&sz=42&hl=ko&start=17&zoom=1&tbnid=zsBhBUfaehuTBM:&tbnh=71&tbnw=136&ei=84LyT9G2NcWjiAfnn_C6Aw&prev=/search%3Fq%3Dwater%2Bwaves%26um%3D1%26hl%3Dko%26tbm%3Disch&um=1&itbs=1
http://www.shutterstock.com/pic-3965908/stock-photo-water-waves.html
Actual Waves Different Phenomenon
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Surface of Waves
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ζ
λ
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Patterns of Light
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Too Complex! Light Flux
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http://www.google.ca/imgres?q=caustics&um=1&hl=ko&sa=X&tbs=isz:l&tbm=isch&tbnid=WaBPapCHOju9dM:&imgrefurl=http://etacar.put.poznan.pl/piotr.pieranski//Physics%2520Around%2520Us/Physics%2520around%2520us.html&docid=MXJT4dwA74pQGM&imgurl=http://etacar.put.poznan.pl/piotr.pieranski//Physics%252520Around%252520Us/Caustics%25252004.JPG&w=1280&h=960&ei=Jp_xT8DRAemYiAfck_2xDQ&zoom=1&iact=hc&vpx=93&vpy=105&dur=919&hovh=194&hovw=259&tx=140&ty=94&sig=106441543725892116471&page=2&tbnh=123&tbnw=165&start=8&ndsp=23&ved=1t:429,r:6,s:8,i:120&biw=1120&bih=576
http://www.google.ca/imgres?q=caustics&um=1&hl=ko&sa=X&tbs=isz:l&tbm=isch&tbnid=ZkfOhJ4Ec0ZEgM:&imgrefurl=http://dxbigd.deviantart.com/art/Glass-VRay-Caustics-Test-50302568&docid=Ag6X_5I5UllUkM&imgurl=http://www.deviantart.com/download/50302568/Glass___VRay_Caustics_Test_by_DXBigD.jpg&w=1024&h=768&ei=Jp_xT8DRAemYiAfck_2xDQ&zoom=1&iact=hc&vpx=600&vpy=211&dur=247&hovh=164&hovw=225&tx=123&ty=76&sig=106441543725892116471&page=1&tbnh=161&tbnw=221&start=0&ndsp=8&ved=1t:429,r:2,s:0,i:79&biw=1120&bih=576
Image Source Image Source
Different Concentrations of Light Flux!
High Light Flux Density High Intensity Low Light Flux Density Low Intensity
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Focal Length
Brightest Point
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Snell’s Law
1θ
2θ
2211 sinsin θθ nn =
Refraction Flux Density Bright Waves Patterns
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)(xfy =
l
'l
Surface Wave Function
n
d
))`
`)(cos(sin())cos(sin( 21 lnlnan
lnlnan
⋅−=
⋅
`ll =)1,( −∂∂
=xfn
xlldx x
y
+= ``
`
Snell’s Law
Normalization
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1x
'1xScreen hy −=
Wave
2x
'2xv
1x
'1x '2x
2x
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x
'x')( xxh =
Displacement
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x
)(' xhVelocity
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400
400
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x
y z
x
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Amplitude: 7
Amplitude: 9 Amplitude: 13
Amplitude: 11
Amplitude and Curvature
A
rFocal Length Decrease
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Theory
Water Surface Modeling
Light Flux Density
Refraction
Experiment Conclusion
Analytical Prediction
Numerical Simulation
Lens Approximation
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Experiment
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Acrylic Wave
Syringe Pump
Laser
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0
0.2
0.4
0.6
0.8
1
1.2
6.8 7.8 8.8 9.8 10.8 11.8 12.8 13.8
Velocity of Final Light (cm/s)
Distance in Incident Light(cm)
Velocity of Final Light
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Experiment in Water
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Screen
Slanted Sponge
Mechanical Oscillator
Slanted Mirror
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Experiment Setting
Spherical light source
(point source)
Wave Generator (Horizontal Push)
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Surface Wave: Amplitude 3.2mm, Wavelength 42.9mm (Incoherent)
5.92cm 5.85cm
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Surface Wave: Amplitude 3.6mm, Wavelength 42.9mm (Incoherent)
5.25cm 5.29cm
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Surface Wave: Amplitude 4.0mm, Wavelength 42.9mm (Incoherent)
4.97cm 5.02cm
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4.9
5.1
5.3
5.5
5.7
5.9
3 3.2 3.4 3.6 3.8 4
Amplitude vs. Pattern Width
Theory
Experiment
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Theory
Water Surface Modeling
Light Flux Density
Refraction
Experiment Conclusion
Analytical Prediction
Numerical Simulation
Lens Approximation
Acrylic Wave – Laser Experiment
Water Waves and Patterns
Bright Wave Pattern Predicted
Relationship between Amplitude & Focal Length
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Actual Waves…?
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http://www.google.ca/imgres?imgurl=http://imaginezambia.org/wp-content/uploads/splash-water-waves-4565.jpg&imgrefurl=http://imaginezambia.org/2476/training-workshop-moringa-propogation-teams-quick-update/splash-water-waves-4565/&usg=__ouoxefwUL0whvrDUOOQBnp3NR40=&h=324&w=620&sz=42&hl=ko&start=17&zoom=1&tbnid=zsBhBUfaehuTBM:&tbnh=71&tbnw=136&ei=84LyT9G2NcWjiAfnn_C6Aw&prev=/search%3Fq%3Dwater%2Bwaves%26um%3D1%26hl%3Dko%26tbm%3Disch&um=1&itbs=1
http://www.shutterstock.com/pic-3965908/stock-photo-water-waves.html
Actual Waves Different Phenomenon
Lip Shape
Interference
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Focal Length Decrease
Amplitude Increase
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A
x
y
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l
'l
n
),( yxfhz +=
)1,,( −∂∂
∂∂
=yf
xfn
)`
`)(sin()sin( 21 lnlnn
lnlnn
⋅−=
⋅
`ll =
`lnnl
×=×
)``
),(,``
),((),( yz
xz
ll
yxfzll
yxfzyx ++=
Snell’s Law
Normalization
Same Plane Condition
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Lip Shape!
Depth Increase
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Theory
Water Surface Modeling
Light Flux Density
Refraction
Experiment Conclusion
Analytical Prediction
Numerical Simulation
Lens Approximation
Acrylic Wave – Laser Experiment
Water Waves and Patterns
Theory
Water Surface Modeling
Light Flux Density
Refraction
Experiment Conclusion
Analytical Prediction
Numerical Simulation
Lens Approximation
Acrylic Wave – Laser Experiment
Water Waves and Patterns
Bright Wave Pattern Predicted
Relationship between Amplitude & Focal Length
Actual Waves Interference
Lip-Shape
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),( txz ζ=
x
z
)21( 2
tugzqp∂∂
+++ ρ
Bernoulli Equation for Unsteady Potential Flow )sin(0 tkxka ω
ωζ −−=
when
d<<<< λζ
λ
ζ
d
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