Download K = 1

§Chapter 3 Wave Optics
§ 3-1 Light & light interference
Light is a kind of electromagnetic wave.
Light & electromagnetic wave
Light is transverse wave.
Light speed in vacuum:
c
1
 0 0
 299796458m / s
c
c
in transparent medium: v  
n
 r r
Wavelength of light
40
UV
400
visible
760 IR 1000 μm
nm
nm: nanometer 1nm＝10-9m
1nm＝10 Å
Å: angstrom
1 μm ＝10-6m
Å＝10-10m
frequency of light
frequency Hz
f 
c

frequency of visible light
7.5  10 ~ 3.9  10 Hz
14
14
geometric optics
Reflection, refraction; image
optics
wave optics
Interference, diffraction
physical optics polarization
quantum optics
The phenomena and rules when light interacts with
other particles
The nature of light
1) Particle model / corpuscular theory of light
Light was a stream of particles emitted by a light source
Isaac Newton
2) wave model / undulatory theory of light
Light had wave-like properties.
Huygens;
Thomas Yong; Augustin Fresnel
James C. Maxwell
Photoelectric effect
Dual nature
In some cases light acts like a wave and in others it
acts like a particle.
Interference of light Coherent light
The necessary conditions for light interference
1. parallel vibration directions
2. identical frequency
3. constant phase difference
The additional conditions for obvious light interference
1. The intensity difference of two streams of coherent
lights can not be too large
2. The phase difference of two streams of coherent
lights can not be too large
Interference of light
Recall: Interference of wave
y  y1  y2  A cos( t   )
Where:
A  A  A  2 A1 A2 cos 
2
2
1
2
2
  ( 2  1 ) 
2
(r2  r1 )

I  I1  I 2  2 I1I 2 cos 
Intensity of superposed light
I  I1  I 2  2 I1I 2 cos 
If
I1  I 2 I max  I1  I 2  2 I1I 2  I1
Can not observe obvious interference of light.
Interference of waves
  ( 2  1 ) 
2k
=
2

Path length
(r2  r1 )
Interference constructively
A  Amax  A1  A2
(2k  1)
Interference destructively
A  Amin | A1  A2 |
Interference of light
Light can travel in the vacuum, which is different from
mechanical waves.
r
niri ni: reflection index of the medium
r1 r2
r3
i
 i   ni ri
1
n1 n2
n3
i
j
0
0
   ni ri   n j rj
Interference of light
  ( 2  1 ) 
2k
=
2


Bright fringe
A  Amax  A1  A2
(2k  1)
Dark fringe
A  Amin | A1  A2 |
Optical path length difference
2  1  2k ,
if
k  0,1,2,...
k 
i
j
   ni ri   n j rj =
0
Bright fringe
0
(2k  1)

2
Dark fringe
§4-2 Young’s Double slit experiment
Experimental set-up
Schematic diagram
S1
S
S2
Huygens principle
Viewing screen
Results of this experiment
1) For monochrome light 单色光
The bright and dark fringes lay parallel with the slit.
The width of each fringe and the distance between
adjacent bright/dark fringes are identical, respectively.
x1
x
x 0
O
2) For lights with different wavelengths
The width of each fringe and the distance between
adjacent bright/dark fringes are different
3) For white light as external light source
x
O
4) Intensity distribution
Intensity
-λ
0
λ
Discussion

S1
S
d O’
S2
P
r1
r2
x
O
D
  ni ri  n j r j
In air
Phase difference
S1
P
r1
r2
d
D
S2
x
O
d is very small
(r2  r1 )  2D
 r2  r1  r2  r1   2dx
dx
(r2  r1 ) 
D
Optical path difference
dx
  (r2  r1 ) 
D
S1
P
r1
r2
d
D
S2
x
O
If the reflection index n is considered,
Optical path difference
ndx
  n  r2  r1  
D
According to light interference
k Bright fringe

k  0,1,2...
=
(2k  1)

2
Dark fringe
k 
nd x
  n( r2  r1 ) 
=
D
Bright fringe
k  0,1,2...
(2k  1)

2
Dark fringe
The positions of bright fringes and dark fringes
Bright fringes x   D K K = 0，1，2，...
nd
When k=0, corresponding
to middle bright fringe
When k=1, corresponding to
the first bright fringe
x
K=1
O K=0
K=-1
The distance between adjacent two bright/ dark fringes
D
K
Bright fringes x  
nd
D
x  xk 1  xk 

nd
The distance is related to the
wavelength of the used light.
The positions of dark fringes
D

2 K  1
x
nd
2
K = 1，2，...
x
K=1
K=-1
O
The distance between two adjacent dark fringes
D

2 K  1
x
nd
2
D
x  xk 1  xk 

nd
For bright fringes
D
x
K
nd
x
K = 0，1，2，...
For an identical K, x varies with different
wavelengths of used lights.
O
For an identical K, the position of the light with smaller
wavelength is lower than that with larger wavelength.
overlap
D
K
The positions of bright fringes: x  
nd
when
  ki 1  k j 2
overlap
O
x
Other experiments of light interference
1) Fresnel double mirrors
S
Virtual light sources
of S1 and S2 are
coherent light sources
S1
d
S2
光栏
W
M1
M2
L
x
O
W'
2) Lioyd mirror
光栏
S
d
A
p
p'
Q'
M
B
Q
S'
L
Half-wavelength loss
Point B: dark fringe
W