Download 光的干涉

1. the Doppler effect
2. the nature of light, wave-particle duality
3. Light as electromagnetic waves
4. Coherent light, Interferences of light
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Geometric Optics
ray model, path reversible
Optics
Wave Optics: Wave model
electromagnetic waves,
Huygens’ principle
Quantum Theory:
particle-wave duality, etc
reflection
refraction
imaging
prism
interference
diffraction
polarization
Photoelectric effect
Compton effect
Blackbody radiation
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Interference of Light
（光的干涉）
Conditions for Interference （干涉条件）
① identical wavelengths
② constant phase difference
③ vibrating in parallel direction
Yes
coherent
Conditions for interference fulfilled?
No
incoherent
Again, to observe obvious interference effects, the intensity
difference between the individual waves can’t be too large .
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Optical Path Length
（光程）
f
light
Path length:
r   ni ri
i


0 2
r
0 is the wavelength of light in vacuum.
4
Young’s Double-Slit Experiment
（杨氏双缝试验）
5
Optical Path Difference in Double-Slit Experiment
  r2  r1
y
d sin   d
L
6
d 2
d 2
2
r2  r1  L  ( y  )  L  ( y  )
2
2
d
d
d
y

y

y

L
2 )2  (
2 )2 ]
 [(
2
for
2
L
L
L
yd

L
2
yd

L
d
y
2
for
L
1
1
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Case 1:
  m , m  0,  1,  2,
(or y  m
L
d
)
interfere constructively
bright fringes
（亮纹）
Case 2:
1
  (m  ) , m  0,  1,  2,
2
1 L
(or y  (m  ) )
2 d
interfere destructively
dark fringes
（暗纹）
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Order Number of Bright Fringes
（亮纹的级数）
  m , m  0,  1,  2,
m is called order number.
（ m 称为级数）
m = 0:
y = 0, central bright fringe （中央亮纹）
zeroth-order maximum （零级极大）
m  1
y = λL/d, first-order maximum
(一级极大)
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Spatial Distribution of the Fringes
（干涉条纹的空间分布）
Bright Fringes
xm  m
xm  xm 1 
Dark Fringes
L
d
d
L
d
1 L
ym  ( m  )
2 d
ym  ym 1 
sin  m  m

L
angular positions
1 
sin  m  (m  )
2 d
d
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Intensity Distribution
of the Double-Slit Interference Pattern
（双缝干涉图样的强度分布）
A
A  A  2 A1 A2 cos ； 
2
1
2
2
I  I1  I 2  2 I1I 2 cos
2


2

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About the Light Source
The position of the bright fringes:
ym  m
L
d
Monochromatic light（单色光）
As discussed above.
White light（白光）
All bright fringes except the central one are chromatic.
（除了中央亮纹，其他亮纹都是彩色的）
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Question
If there exists medium in space, the refraction
index of which is n, what are the positions of the
bright and dark fringes?
nyd
(  n(r2  r1 ) 
)
L
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Lloyd’s Mirror
（劳埃德镜）
  n(r2  r1 ) 

2
Dark fringe is found at p’ due toπ-phase shift.
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Fresnel’s Double-Mirror
（菲涅尔双镜）
M1
M2
Interference pattern can only be observed in dark zone.
（只有阴影区域可以观察到干涉图样）
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Interference in Thin Films
（薄膜干涉）
air
n1 (air)  n2 (film)
film
16
a
a
2n2t

 2t  tan i ' n1 sin i   2n2t cos i '
cos i '
2
2
 2t n  n sin i 
2
2
2
1
2
a
2
Lenses do not influence the optical path difference
（透镜不引起附加的光程差）
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  m
1
or 2n2t cos i '  (m  )
2
1
  ( m  )
2
or 2n2t cos i '  m
interfere constructively
bright fringes
interfere destructively
dark fringes
i  i ' 
interferences of equal inclination
（等倾干涉）
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Pattern
Bright/dark fringes
P
Viewing screen
lens
L
Planar light source
mirror
Thin film
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The Interferences of Equal Inclination
（等倾干涉）
1
  m or 2n2t cos i '  (m  )
2
cos i 'm1  cos i 'm 

2n2t
1. The fringes are rings with a common center
（干涉条纹是同心圆环）
2. The distance between the adjacent fringes is not uniform
（相邻条纹的间距不相等）
3. The order number reaches its maximum at the center.
（中央条纹的级数是最大的）
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Interferences of Transmission
（透射光的干涉）
1
i
  2t n  n sin i
2
2
i
2
1
2
3
2
For a given incident angle, if the reflected light interfere to
produce bright fringes, then the transmitted light produce dark
fringes.
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Interference in a Wedge-shaped Film
22
lens
Light source
microscope
S
mirror

h
l
Wedge with very small θ
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n1
n2
1
n2  n1 ,   2nh  
2
1
n2  n1 ,   2nh  
2
  m
bright fringes
1
  ( m  )
2
dark fringes
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Discussions on Wedge-Shaped Film
Case1: h = 0
1
 
2
dark fringes
1 
Case 2:   m  h  ( m  )
2 2n2
bright fringes
height difference between adjacent bright fringes:
h 

2n2
So, the distance between two adjacent bright fringes is
h

x 

tan  2n2 tan 

2n2
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The total number of bright fringes which can be observed thus can
be obtained as
（在劈尖上能够观测到的亮条纹的条数可以计算如下）
l
N
x
And it is easily to find the fringes are spaced uniformly.
（易得，条纹是均匀分布的）
The interference in a wedge-shaped film is called interference of
equal thickness for the obvious reason.
（劈尖上的干涉被称为等厚干涉）
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Quick Quiz
What if?
(1) What happens to the fringes if the upper (lower) surface of
the wedge-shaped film moves upward a little？
(2) What happens if the angle of the wedge-shaped film increases？
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