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?
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)
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:
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.
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
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).
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)
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:
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.
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
(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
For central bright fringe: a sin 0
i.e. l a sin l sin tan
Angular-width(角宽度):
0
21
2
ቤተ 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,
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
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,.
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)