第12章 波动光学

0, 2 , 4 ,...
I max 4I1 I min 0
Destructive 干涉相消
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0, , 3 ,...
§12-1 Optics Source and the Coherence of Light
4. Obtain of Coherent Light
3. Interference of Light
The critical quantity in optical vibration is the electric vector E, not the magnetic vector H. Vector E is called light vector.
2 0 2 10 2 20
2 01
2 02
Average light intensity:
1 I E E E 2 E10 E20 cos dt t 0
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t
where E0 is determined by Δφ, while Δφ is given by
1 I E E E 2 E10 E20 cos dt t 0
The lack of lights from common sources is due to the fact that the emitting atoms in such sources act independently rather than cooperatively. So these lights have not the same frequency, vibration direction and phase difference, and they are not coherent light.
-3 -2 -1 1 2 3 k=±1: first-order dark fringes;
k=±2: second-oHale Waihona Puke Baiduder dark fringes;
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Features:
(1) The central distance between two adjacent bright (or dark) fringes is:
(1) Shiny objects is called light source. (2) Common mechanism of luminescence(发光).
能级跃迁辐射 波列
ν=E2-E1/h
L =t c
Luminescence of light source is due to molecules or atoms transit from the high energy level to low energy level, when the corresponding energy is released simultaneously.
2 0 2 10 2 20
t
r2 r1 02 01 u
=0
Generally φ02-φ01 varies with t, so the integration will be 0.
incoherent superposition(非相干叠加 ) vary with t, the total intensity Only when φ02-φ01 does not
red orange yellow green wavelength turns shorter cyan blue purple
frequency turns higher 5
2. light source
§12-1 Optics Source and the Coherence of Light
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(3) If two beams (λ1,λ2) pass the slits at the same time
Two kinds of interference pattern
Features:
•中央明条纹重叠； •波长短的靠近中央； •其它级次可能会重叠：
E E1 E2 E0 cos(t 0 )
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Where:
E E1 E2 E0 cos(t 0 )
E0 E E 2 E01 E02 cos
r2 r1 02 01 u E10 sin 1 E20 sin 2 tg0 E10 cos1 E20 cos 2
1. electromagnetic wave and light:
(1) The source of electromagnetic wave:
All vibrating charges(振动电荷) or vibrating charge systems is the source that emit(发射) electromagnetic waves.
r E (r , t ) E 0 cos (t ) u
r H (r , t ) H 0 cos (t ) u
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(3) Characteristics of electromagnetic wave: ①在任意给定点上，E和 H 同时存在，具有相同的相位和速
①Vibrating in the same direction(振动方向相同) ②have the same frequency(频率相同) ③have the invariable phase difference(相差恒定)
Results of interference
①stable interference pattern(稳定的干涉花样) Constructive 干涉相长 ②about the light intensity
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(4) Visible light and electromagnetic wave:
Light is a kind of electromagnetic wave, which has a velocity of c=3×108m/s . Visible light(可见光) can cause the sense of sight(视觉), which is due to the electric field vector and is called light vector. The wavelength of visible light is 400—760nm, whose color corresponding different wavelength(frequency):
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§12-1 Light Source and the Coherence of Light §12-2 Optical Distance and Optical Path Difference §12-3 Film Interference §12-4 Michelson’s Interferometer §12-5 Diffraction of Light, Huygens-Fresnel’s Principle
k=±1: first-order bright fringes; k=±2: second-order bright fringes;
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Discussions:
(2)When δ=(2k-1)•λ/2, →I=Imin
干涉相消，形成暗纹。
dark fringe
D x ( 2 k 1) , k 1,2,3 ... 2d
interference pattern
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1 Young’s Double-Slits Experiment 杨氏双缝实验
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1 Young’s Double-Slits Experiment 杨氏双缝实验
S1
r1 P r2 O D x ·
x

S
x x0
d

S2
x I
Wave path difference：
How to obtain Coherent Light?
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4. Obtain of Coherent Light Way 1: Two beams interference by division of wavefront（从光波发出的同一波列的波面上取出 两个次波源，即分波阵面法）
——Young’s Interference(杨氏干涉)
(2) The essence(本质) of electromagnetic wave:
electromagnetic waves is vector wave(矢量波) of electric field intensity (电场强度)and magnetic field intensity(磁场强度).
I I1 I 2
I I1 I 2 2 I1I 2 cos coherent superposition
I1 I 2
I max
4 I1 cos 2
2
(相干叠加)
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Three conditions that coherent lights must be met are
Way 2: Two beams interference by division of amplitude（或把同一波列的波分为两束，即分振 幅法）
——Film Interference(薄膜干涉)
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1 Young’s Double-Slits Experiment 杨氏双缝实验
Experimental device
x r2 r1 d sin dtg d D
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Discussions:
bright fringe
(1)When δ=kλ,I=Imax
光强达最大，形成明条纹。
D x k d
k=0:
k 0,1,2
-3 -2 -1 0 1 2 3
central bright fringe；
For simplicity, we assume that two light vectors vibrating in the same directions, and have the same angular frequency, so the superposition is:
r1 E1 E01cos [(t ) 01 ] u r2 E2 E02 cos [(t ) 02 ] u
度。
H、u三者满足右螺旋法则。
③对空间任一点，有
②电磁波是横波: E 和 H 互相垂直，且与传播方向垂直， 、 E
E H
④电磁波的传播速度取决于介质的介电常数ε和磁导率μ，且 满足： 1 1 1 1 u r 0 r 0 0 0 r r
Introduction
§12-6 Single-Slit Fraunhofer Diffraction §12-7 Diffraction Grating §12-8 Polarized Light
§12-9 Polarization by Reflection or Refraction
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§12-1 Optics Source and the Coherence of Light
D x d
(2) Since λ is very small, only if D is large enough and d is small enough, can the fringes be easily distinguishable. 由于λ极小，故只有D足够大，d足够小，干涉条纹△x 才可能大到可以分辨。
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(3) Properties：
①光源中原子的激发和辐射是独立的、随机的，间歇性的， 因此，同一时刻不同原子发的光其频率、振动方向相位差各 不相同。 ②每个原子每次发射的电磁波为 一段有限波长、振动方向和频率均 一定的正弦波列。
Question:多盏日光灯发 出的光不会发生干扰.
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§12-1 Optics Source and the Coherence of Light