大学物理双语奥本汉姆ChapOpticDif
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波传到的任何一点都是子波的波源，各次级子波 在空间某点的相干叠加，就决定了该点波的强度。
The method discussing location of diffraction pattern for a single-slit diffraction is called fresnel’ half-wave-zone method (半波带).
1. Diffraction (衍射) by a single slit
screen
screen
shadow
When the slip wider, light travels in straight line.
When the slip gets narrow, the light produce a diffraction pattern on the screen.
Chapter 31 Diffraction and Polarization
1. Diffraction of Light 2. Diffraction Gratings 3. X-Ray Diffraction 4. Polarized Light
31-1. Diffraction of Light (P703)
is called diffraction of light (P703).
Condition of diffraction: the width of slit (dimension of barrier) is similar to the wavelength a ～λ
Recalling: Hugens-Fresnel’s principle
x
fl
a
1 2
x0
—— half of the central width.
其他明纹宽度为中央明纹宽度的一半
Example:
A slit 1.00 mm wide is illuminated by light of l= 589 nm.
We see a diffraction pattern on a screen 3.00 m away. What is the distance between the first two diffraction minima on the same side of central diffraction maximum?
For central bright fringe: a sin 0
i.e. l a sin l sin tan
Angular-width(角宽度):
0
21
2ቤተ መጻሕፍቲ ባይዱ
l
a
Linear-width:
x0
2f
t an1
2f
l
a
when a
x0
1:半角宽度
For 1-order dark fringe,
2. Locating the diffraction bands (P704)
slit a L
L
S
*
B
a
screen
·P
O
Aδ
f
f
E
Lens doesn’t produce additional light-path difference.
Path difference of A→P & B→P:
max a sin
max a sin
(i) 0， 0 central bright (中央明纹)
(ii) a sin l first dark fringe
Two half-wave-zones can be gotten, and P is first dark fringe (out of phase pairs rays)
When monochromatic (单色) light from a
distant source passes through a narrow slit or
obstacle —— produces a diffraction pattern
(光能绕过障碍物的边缘传播形成具有明暗相间的衍射图样)
In a single-slit diffraction experiment, dark fringes are produced where the path length
differences (a sin ) between the top and bottom rays are equal to l, 2l, 3l,.
a
3. Intensity in single-slit diffraction (P705)
2π (x sin ) See Fig.31-8 in P706 l
(a) The central maximum; (b) Between center and first minimum; (c) The first minimum; (d) Near secondary maximum.
a sin
a tan
a x1 l
f
fl
x1 a
Position of 1th dark fringe一级暗纹坐标
Similarly, for 2-order dark fringe,
x2
2 fl
a
Position of 2th dark fringe
Width of each order of bright fringes:
当 增加,半波带数增加,未被抵消的 半波带面积减少,所以光强I 变小.
i.e. , I
Solution:
Using the condition of minima of diffraction: asin ml
x1 f tan 1 and x2 f tan 2
The separation of the two minima is:
x
x2 x1
f ( 2l
a
l ) 1.77mm
(iii) a sin 3 l
2
first bright fringe
a
sc屏re幕en
P
Conclusion:
a sin
ml
(2m 1)
l
2
m 1,2,3, dark m 1,2,3, bright
opposite to the condition of interference pattern
The method discussing location of diffraction pattern for a single-slit diffraction is called fresnel’ half-wave-zone method (半波带).
1. Diffraction (衍射) by a single slit
screen
screen
shadow
When the slip wider, light travels in straight line.
When the slip gets narrow, the light produce a diffraction pattern on the screen.
Chapter 31 Diffraction and Polarization
1. Diffraction of Light 2. Diffraction Gratings 3. X-Ray Diffraction 4. Polarized Light
31-1. Diffraction of Light (P703)
is called diffraction of light (P703).
Condition of diffraction: the width of slit (dimension of barrier) is similar to the wavelength a ～λ
Recalling: Hugens-Fresnel’s principle
x
fl
a
1 2
x0
—— half of the central width.
其他明纹宽度为中央明纹宽度的一半
Example:
A slit 1.00 mm wide is illuminated by light of l= 589 nm.
We see a diffraction pattern on a screen 3.00 m away. What is the distance between the first two diffraction minima on the same side of central diffraction maximum?
For central bright fringe: a sin 0
i.e. l a sin l sin tan
Angular-width(角宽度):
0
21
2ቤተ መጻሕፍቲ ባይዱ
l
a
Linear-width:
x0
2f
t an1
2f
l
a
when a
x0
1:半角宽度
For 1-order dark fringe,
2. Locating the diffraction bands (P704)
slit a L
L
S
*
B
a
screen
·P
O
Aδ
f
f
E
Lens doesn’t produce additional light-path difference.
Path difference of A→P & B→P:
max a sin
max a sin
(i) 0， 0 central bright (中央明纹)
(ii) a sin l first dark fringe
Two half-wave-zones can be gotten, and P is first dark fringe (out of phase pairs rays)
When monochromatic (单色) light from a
distant source passes through a narrow slit or
obstacle —— produces a diffraction pattern
(光能绕过障碍物的边缘传播形成具有明暗相间的衍射图样)
In a single-slit diffraction experiment, dark fringes are produced where the path length
differences (a sin ) between the top and bottom rays are equal to l, 2l, 3l,.
a
3. Intensity in single-slit diffraction (P705)
2π (x sin ) See Fig.31-8 in P706 l
(a) The central maximum; (b) Between center and first minimum; (c) The first minimum; (d) Near secondary maximum.
a sin
a tan
a x1 l
f
fl
x1 a
Position of 1th dark fringe一级暗纹坐标
Similarly, for 2-order dark fringe,
x2
2 fl
a
Position of 2th dark fringe
Width of each order of bright fringes:
当 增加,半波带数增加,未被抵消的 半波带面积减少,所以光强I 变小.
i.e. , I
Solution:
Using the condition of minima of diffraction: asin ml
x1 f tan 1 and x2 f tan 2
The separation of the two minima is:
x
x2 x1
f ( 2l
a
l ) 1.77mm
(iii) a sin 3 l
2
first bright fringe
a
sc屏re幕en
P
Conclusion:
a sin
ml
(2m 1)
l
2
m 1,2,3, dark m 1,2,3, bright
opposite to the condition of interference pattern