物理光学重点

1、What is interference? What is the most important to have interference? What is the intensity of light, and what is the unit?,Youngs double slits experiment,The electric field at P:,Difference of optical path,Youngs double slit experiment,x,Conclusions,1、Overlapping intensity：,2、Path difference：,3、St

2、ripes means (physically)：,4、Distance between stripes：,Same path difference,Amplitude Separate 振幅分割 Interference between two point sources (S1 and S2) 两个干涉的点源：由两个反射面对S点的象S1和S2,2.3 Interference at surfaces of transparent block medium,Equal inclination interference平行平板干涉（等倾干涉）,n,n,1.Calculation of the

3、optical path difference,Equal inclination interference平行平板干涉（等倾干涉）,2. Setup of Equal inclination interference Note: if the light source are parallel light, the stripes extends to infinity. If use lens to focus, stripes are in focal plane. 注意：采用扩展光源，条纹域在无穷远。 条纹成象在透镜的焦平面上。,n,n,Equal inclination interf

4、erence,Concentric rings,Equal inclination interference,P,P,n,n,（3）Distances between stripes,中央条纹宽，边缘条纹窄。,Equal inclination interference,Largest stripes in the center,Dh,Equal thickness interference楔形平板干涉（等厚干涉）,a,Equal thickness interference楔形平板干涉（等厚干涉）,HuygensFresnel principle: a method of analysis

5、applied to problems of wave propagation both in the far-field limit and in near-field diffraction.,1、Generation and Propagation of wavefront,2、 HuygensFresnel principle,图2 点光源S对P点的作用,图1 光波通过圆孔的惠更斯作图法,Consider the case of a point source located at a point P0, vibrating at a frequency f. The disturban

6、ce may be described by a complex variable U0 known as the complex amplitude. It produces a spherical wave with wavelength , wavenumber k = 2/. The complex amplitude of the primary wave at the point Q located at a distance r0 from P0 is given by,子波向P点的球面波公式,子波法线方向的振幅,子波振幅随q角的变化,图3,3.2 Fresnel Diffrac

7、tion,In optics, the Fresnel diffraction equation for near-field diffraction, is an approximation of Kirchhoff-Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around

8、an object, when viewed from relatively close to the object,Complex amplitude of j (j is the number of order),j define j as the radius of j (order) see the figure,when,从中心C向外第 j 波带在P0产生的复振幅为,Different half-wave-bands have equal areas 各波带的面积近似相等,The complex amplitude at P0:,since,Thus：,Ei单调下降，且变化缓慢，所以

9、近似有：,Discussion： 1、 P0的振幅与强度与衍射屏所包含的波带数有关，当波带数为奇数时，强度较大，反之强度较小。 2、对于一定大小的衍射孔和光波波长，波带数取决于距离z1，因此沿光轴移动接收屏，可见P0忽明忽暗交替变化。 3、当圆孔非常大时， P0点的复振幅等于第1波带产生复振幅的一半，强度为第1波带强度的1/4。（符合直线传播定律）,n为奇数时取正， n为偶数时取负。,Ei decreases monotonously and slowly changes，thus (approximately)：,E 0 when n odd; E0 when n even.,Discuss

10、ion： 1、Electric field amplitude E smaller when n even. 2、With a fixed size of hole for diffraction, the number of half-wave band is decided by distance z1. Thus once the screen moves according to the light source. P0 changes from bight to black alternatively. 3、When the hole is quite large, the comp

11、osed electric amplitude of P is half of the amplitude for the electric amplitude of the first half-wave band. First half-wave-band: j=1,Discussion： 1、 P0的振幅与强度与衍射屏所包含的波带数有关，当波带数为奇数时，强度较大，反之强度较小。 2、对于一定大小的衍射孔和光波波长，波带数取决于距离z1，因此沿光轴移动接收屏，可见P0忽明忽暗交替变化。 3、当圆孔非常大时， P0点的复振幅等于第1波带产生复振幅的一半，强度为第1波带强度的1/4。（符合直

12、线传播定律）,Fresnel Diffraction of Round hole,E,K,y,1,x,1,y,z1 +,P,0,x,z1+/2,z1 +3/2,P,Thus once the screen moves according to the light source. P0 changes from bight to black alternatively. The pattern are concentric rings.随P点离开P0点逐渐向外，其光强将时大时小变化，由于系统的对称性，距离P0相同的点P有相同的光强。故衍射图样为同心圆。,Pattern for round scr

13、een (block) in contrast to round hole (Fresnel Diffraction),2、As distance varies from P to P0, intensity changes (bright/dark alternatively). Since it is symmetry over 360o, the Pattern is concentric rings.点离开P0点逐渐向外，其光强将时大时小变化，由于系统的对称性，距离P0相同的点P有相同的光强。故衍射图样为同心圆。,Discussion： 1、Round screen small eno

14、ugh, P0 always bright. (圆屏较小时，轴上点P0总是亮点),3、If the screen (block) is large enough, the intensity at P0 is 0.圆屏较大时，P0点的光强度接近于0。,Fresnel lens is iris which blocks the odd or even half-wave-band. It acts like a lens. (将奇数波带或偶数波带挡住的特殊光阑称为菲涅尔波带。由于它的聚光作用类似于一个普通透镜，故称为菲涅尔透镜。),Fresnel lens half-wave-band菲涅尔波带

15、,Fresnel lens 菲涅尔透镜,Known the complex amplitude of Fresnel diffraction at P0.(已知菲涅尔圆孔衍射P0点复振幅为)：,Resolution of imaging systems(常见光学系统分辨本领),(1) Angular resolution of human eye (人眼的分辨本领）,(2) Resolution of camera (照像物镜的分辨本领）,If l=550mm, then R=1490D/f,Resolution of imaging system成像系统的分辨率,angular resolu

16、tion:,Focal length:,D is diameter of imaging system (human eye/camera),24,2 偏振光的产生（Production of polarized (partially polarized) light）,(主要方法：反射和折射、二向色性、散射、双折射),(1) Polarization by reflection (2) Polarization by transmission (3) Polarization by dichroism (4) Polarization by scattering (5) Polarizati

17、on by double refraction,Five ways to generate polarized (partially polarized) light from randomly polarized light:,25,Reflected light is linearly polarized, with the polarization perpendicular to the incident plane. Transmitted light is partially polarized. 反射光为线偏振光。振动方向垂直于入射面。透射光为部分线偏振光。,布儒斯特定律( Br

18、ewsters Law ),自然光投射到两种不同介质的分界面上时，若入射角满足关系式 ，则反射光中没有振动平行于入射面的分量。,Incident angle is Brewsters angle:,1、Generate polarized light through reflection and refraction由反射和折射产生偏振光,26,2、Polarization by Dichroism (由二向色性产生偏振光),二向色性：各向异性的晶体对光的吸收本领随波长改变外，还随光矢量相对晶体的方位而改变。,Dichroism: when light propagates inside a

19、dichroic crystal, polarization components perpendicular or parallel to the incident plane of crystal have different transmission rate.,27,一束非偏振光入射到气体上，那麽在与入射光束垂直的方向上被散射的光是线偏振光。散射光的振动方向 在光线传播方向的垂直平面内。,3、 Polarization by scattering (由散射产生偏振光),An randomly polarized light incident on gases, the light sc

20、attered perpendicular to the light propagation direction is linearly polarized. The electrical field (polarization direction) is within the plane which is perpendicular to the light propagation direction.,28,2、 Principal plane(主平面) and Principal section (主截面)：,Principal plane：light (incident) and op

21、tical axis.,Principal plane of o light: o light and optical axis,Principal plane of e light: e light and optical axis,Principal section (主截面)： Optical axis and normal of crystal,光线在一般情况下入射晶体， o光和e光是不同面的。当入射光线在主截面内时，两面重合。,Principal planes of o light and e light are normal different. However, in case

22、incident light are within the principal section, principal planes of o light and e light overlap.,29,2、主平面(Principal plane)和主截面(Principal section)：,主平面：光线和光轴所组成的平面。,o光主平面：o光和晶体光轴组成的面为o主平面。,e光主平面：e光和晶体光轴组成的面为e主平面。,主截面(Principal section)： 光轴和晶体表面法线 (Normal line)组成。,光线在一般情况下入射晶体， o光和e光是不同面的。当入射光线在主截面内时

23、，两面重合。,30,3晶体的分类（Types of crystal）：,Isotropic crystal（各向同性晶体）：no birefringence (double refractive), e.g. NaCl crystal,Anisotropic crystal（双折射晶体）：,Uniaxial crystal （单轴晶体）：crystal with only one axis. e.g. Calcite, Quartz.只有一个光轴方向的晶体。如：方解石(Calcite)、石英(Quartz)。,Biaxial crystal（双轴晶体）： crystal with two ax

24、es . e.g. Mica. 有两个光轴方向的晶体 如：云母(Mica)等。,31,(1) Birefringence (Double Refraction),Birefringence is the optical property of a material having a refractive index that depends on the polarization and propagation direction of light.1 These optically anisotropic materials are said to be birefringent (or b

25、irefractive). The birefringence is often quantified as the maximum difference between refractive indices exhibited by the material. Crystals with asymmetric crystal structures are often birefringent, as are plastics under mechanical stress. 光束在某些晶体中传播时，由于晶体对两个相互垂直振动矢量的光的折射率不同而产生两束折射光，这种现象称为双折射 (Doub

26、le Refraction)。,1. Birefringence (Double Refraction) in Crystal,4.2 Light propagates in birefringent medium,32,2. Ordinary light, o光 and Extraordinary light, e光 寻常光和非寻常光,In the two refracted lights, one follows refraction law, we call it ordinary light. 两束折射光中，有一束光遵守折射定律，称为寻常光（o光）； The other not fol

27、lows refraction law, we call it extraordinary light另外一束一般不遵守折射定律，称为非寻常光（e光）。,Note：1 Ordinary & Extraordinary lights are connected with crystal, after propagates through crystal, no ordinary & extraordinary light. 2 Ordinary & Extraordinary lights have different refractive index no , ne. Different sp

28、eed in crystal vo , ve respectively.,33,3晶体的分类（Types of crystal）：,Isotropic crystal（各向同性晶体）：no birefringence (double refractive), e.g. NaCl crystal,Anisotropic crystal（双折射晶体）：,Uniaxial crystal （单轴晶体）：crystal with only one axis. e.g. Calcite, Quartz.只有一个光轴方向的晶体。如：方解石(Calcite)、石英(Quartz)。,Biaxial crys

29、tal（双轴晶体）： crystal with two axes . e.g. Mica. 有两个光轴方向的晶体 如：云母(Mica)等。,34,4Positive & Negative crystal Vo Ve: Positive crystal (正晶体) Vo Ve: Negative crystal (负晶体),Positive Crystal：no ne,Negative crystal ：no ne,35,Double refraction for normal incident. Optical axis is perpendicular to surface of crystal 光线垂直入射时的双折射现象(晶体表面垂直于光轴),e,e,A,o,A,A,o,A,O,Wo,E,Incident ray (入射光),optical axis (光轴),Here the light propagates in Negative crystal (负晶体) Vo Ve, no ne,We,Wo s