Post on 13-Dec-2015
11
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
22
Overview HypothesisHypothesis
Assumption of Experiment Experimental SetupExperimental Setup
Devices and Process InvestigationsInvestigations
Experimental Results TheoryTheory
The Physics Behind Brilliant Pattern ConclusionConclusion
33
HypothesisEffects of reflection and refraction
Diffraction
Geometrical Optics
Physical Optics
d/2
a
44
Experimental Setup
Laser Pointer
10 mw, 532 nm, Radius: 1.45 mm
1 mm
35 cm
55
Observation: 0o
66
(a) (b) (c)
(a)
(b)
(c)
Observation: 150o ~180o ; -150o~ -180o
42o
51o
77
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
88
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
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
1010
Traveling backwards (180o)
Theory
a
i
1
2
r32d
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)
1212
(a) (b) (c)
(a)
(b)
(c)
0o
42o
51o
Experimental Results
1313
Experimental Video(a)
1414
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
1515
2 cm
4 m
Experiment 2: Physical Optics
Diffraction
1616
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
1717
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
1818
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
1919
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
2020
Theoretical Analysis
4 m
2 cm
0.9 mm
1.2 mm
1.5 mm
2.0 mm
Diameter of water drop:
2121
0.9 mm 1.2 mm 1.5 mm 2 mm
Theoretical AnalysisDiameter of water drop:
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
2323
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
(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