1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe....
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Transcript of 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe....
![Page 1: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/1.jpg)
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Brilliant Pattern
ProblemProblem
Suspend a water drop at the lower end Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop of a vertical pipe. Illuminate the drop using a laser pointer and observe the using a laser pointer and observe the pattern created on a screen. Study and pattern created on a screen. Study and explain the structure of the patternexplain the structure of the pattern
![Page 2: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/2.jpg)
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Overview HypothesisHypothesis
Assumption of Experiment Experimental SetupExperimental Setup
Devices and Process InvestigationsInvestigations
Experimental Results TheoryTheory
The Physics Behind Brilliant Pattern ConclusionConclusion
![Page 3: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/3.jpg)
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HypothesisEffects of reflection and refraction
Diffraction
Geometrical Optics
Physical Optics
d/2
a
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Experimental Setup
Laser Pointer
10 mw, 532 nm, Radius: 1.45 mm
1 mm
35 cm
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Observation: 0o
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(a) (b) (c)
(a)
(b)
(c)
Observation: 150o ~180o ; -150o~ -180o
42o
51o
![Page 7: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/7.jpg)
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TheoryPassing through water drop (0o)
2d
a
ir
'r
o
: angle of incidence i
: angle of refraction (air water)r
' : angle of refraction (water air)r
: angle of divergenceo
: diameter of laserd
: radius of waterdropa
![Page 8: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/8.jpg)
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2d
a
ir
'r
o
sin( ) 2i d a
sin(2 )cos(2 ) 1
tan(2 2r i
r ii r
f a
d f
f
![Page 9: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/9.jpg)
99
2d
a
ir
'r
o
1 sin( ) 1.33 sin( )i r
sin( ) 2i d a
'1.33 sin( ) 1 sin( )r r
'r i
2o i r d o
Snell’s LawSnell’s Law
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Traveling backwards (180o)
Theory
a
i
1
2
r32d
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1111
a
i
1
2
r32d
o42
o51
2
13
1 o
2 42 o
3 51
a
1
2
o3
2
4 2
180 2 6
i
r i
i r
(b) (c)
(b)(c)
![Page 12: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/12.jpg)
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(a) (b) (c)
(a)
(b)
(c)
0o
42o
51o
Experimental Results
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Experimental Video(a)
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Distance between water drop and screen 3 m
Water Droplet Radius: 0.9~2 mm
Laser Pointer Radius: 1.45 mm
Wavelength: 532 nm
Experiment 2: Physical Optics
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2 cm
4 m
Experiment 2: Physical Optics
Diffraction
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Theory Huygens’s Principle
Every point on a propagating wavefront serves as the source of spherical secondary wavelets, wavelets, such that the wavefront at some later time is the envelope of these wavelets
v twavelett tv
wavelet0t
wavelet0t
v
v
v twavelet0t
wavelett t
![Page 17: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/17.jpg)
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R
( , , )X Y Z
y
z
PO
dS
r
x
21
222:
2number wave:
2frequencyangular :
areaunit per source ofstength :
ZYXOPR
k
fA
Theory Huygens’s Principle
Every point on a propagating wavefront serves as the source of spherical secondary wavelets, wavelets, such that the wavefront at some later time is the envelope of these wavelets
( )
( )( )/
Aperature
i t krA
i t kRik Yy Zz RA
dE e dSr
eE e dS
R
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a
O R
y
z
P
q
0( )J u
1( )J u
2( )J u
u
( )2
12 ( ) ( )i t kR
A e R k a qE a J
R k a q R
2
1( ) 2 ( sin )
(0) ( sin )
I J k a
I k a
2 2
2(0)
2A a
IR
Bessel Function22 2
12
2 ( )
( )A a J k a q R
IR k a q R
![Page 19: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/19.jpg)
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0( )J u
1( )J u
2( )J u
u
R
y
z
P
q
( )
( )( )/
out of aperture
i t krA
i t kRik Yy Zz RA
dE e dSr
eE e dS
R
( )
02 ( ' ) ( )i t kR
A e k a qE a a J
R R
2 2
2
02
2 ( ' )( )A a a
I J k a q RR
a
'a
![Page 20: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/20.jpg)
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Theoretical Analysis
4 m
2 cm
0.9 mm
1.2 mm
1.5 mm
2.0 mm
Diameter of water drop:
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2121
0.9 mm 1.2 mm 1.5 mm 2 mm
Theoretical AnalysisDiameter of water drop:
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2222
0.9 mm 1.2 mm
1.5 mm 2 mm
Experimental Results
0.9 mm 1.2 mm
Experimental Results
1.5 mm 2 mm
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ConclusionGeometrical Optics:Geometrical Optics:
– At 0o the light passes through the water droplet and is magnified
– At 180o the light is reflected and refracted by the water droplet; thus, interference is demonstrated
– At other degrees because the light beam has attenuated its energy so patterns are unable to be observed
Wave Optics: Wave Optics: – Due to Huygens’s law, light is diffracted,
so diffraction bands are observable– As water droplets are enlarged the
distance between each band decreases
![Page 24: 1 Brilliant Pattern Problem Problem Suspend a water drop at the lower end of a vertical pipe. Illuminate the drop using a laser pointer and observe the.](https://reader035.fdocuments.us/reader035/viewer/2022062713/56649f535503460f94c773de/html5/thumbnails/24.jpg)
(a)
(b)
(c)
Geometrical Optics:Geometrical Optics: – At 0o the light passes through the water
droplet and is magnified– The light is reflected and refracted by
the water droplet; thus, interference is demonstrated
– At other degrees because the light beam has attenuated its energy so patterns are unable to be observed
Wave Optics: Wave Optics: – Due to Huygens’s principle, light is
diffracted, so diffraction bands are observable
– As water droplets are enlarged the distance between each band decreases
Conclusion