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1. the Doppler effect 2. the nature of light, wave-particle duality 3. Light as electromagnetic waves 4. Coherent light, Interferences of light 1 Geometric Optics ray model, path reversible Optics Wave Optics: Wave model electromagnetic waves, Huygens’ principle Quantum Theory: particle-wave duality, etc reflection refraction imaging prism interference diffraction polarization Photoelectric effect Compton effect Blackbody radiation 2 Interference of Light (光的干涉) Conditions for Interference (干涉条件) ① identical wavelengths ② constant phase difference ③ vibrating in parallel direction Yes coherent Conditions for interference fulfilled? No incoherent Again, to observe obvious interference effects, the intensity difference between the individual waves can’t be too large . 3 Optical Path Length (光程) f light Path length: r ni ri i 0 2 r 0 is the wavelength of light in vacuum. 4 Young’s Double-Slit Experiment (杨氏双缝试验) 5 Optical Path Difference in Double-Slit Experiment r2 r1 y d sin d L 6 d 2 d 2 2 r2 r1 L ( y ) L ( y ) 2 2 d d d y y y L 2 )2 ( 2 )2 ] [( 2 for 2 L L L yd L 2 yd L d y 2 for L 1 1 7 Case 1: m , m 0, 1, 2, (or y m L d ) interfere constructively bright fringes (亮纹) Case 2: 1 (m ) , m 0, 1, 2, 2 1 L (or y (m ) ) 2 d interfere destructively dark fringes (暗纹) 8 Order Number of Bright Fringes (亮纹的级数) m , m 0, 1, 2, m is called order number. ( m 称为级数) m = 0: y = 0, central bright fringe (中央亮纹) zeroth-order maximum (零级极大) m 1 y = λL/d, first-order maximum (一级极大) 9 Spatial Distribution of the Fringes (干涉条纹的空间分布) Bright Fringes xm m xm xm 1 Dark Fringes L d d L d 1 L ym ( m ) 2 d ym ym 1 sin m m L angular positions 1 sin m (m ) 2 d d 10 Intensity Distribution of the Double-Slit Interference Pattern (双缝干涉图样的强度分布) A A A 2 A1 A2 cos ; 2 1 2 2 I I1 I 2 2 I1I 2 cos 2 2 11 About the Light Source The position of the bright fringes: ym m L d Monochromatic light(单色光) As discussed above. White light(白光) All bright fringes except the central one are chromatic. (除了中央亮纹,其他亮纹都是彩色的) 12 Question If there exists medium in space, the refraction index of which is n, what are the positions of the bright and dark fringes? nyd ( n(r2 r1 ) ) L 13 Lloyd’s Mirror (劳埃德镜) n(r2 r1 ) 2 Dark fringe is found at p’ due toπ-phase shift. 14 Fresnel’s Double-Mirror (菲涅尔双镜) M1 M2 Interference pattern can only be observed in dark zone. (只有阴影区域可以观察到干涉图样) 15 Interference in Thin Films (薄膜干涉) air n1 (air) n2 (film) film 16 a a 2n2t 2t tan i ' n1 sin i 2n2t cos i ' cos i ' 2 2 2t n n sin i 2 2 2 1 2 a 2 Lenses do not influence the optical path difference (透镜不引起附加的光程差) 17 m 1 or 2n2t cos i ' (m ) 2 1 ( m ) 2 or 2n2t cos i ' m interfere constructively bright fringes interfere destructively dark fringes i i ' interferences of equal inclination (等倾干涉) 18 Pattern Bright/dark fringes P Viewing screen lens L Planar light source mirror Thin film 19 The Interferences of Equal Inclination (等倾干涉) 1 m or 2n2t cos i ' (m ) 2 cos i 'm1 cos i 'm 2n2t 1. The fringes are rings with a common center (干涉条纹是同心圆环) 2. The distance between the adjacent fringes is not uniform (相邻条纹的间距不相等) 3. The order number reaches its maximum at the center. (中央条纹的级数是最大的) 20 Interferences of Transmission (透射光的干涉) 1 i 2t n n sin i 2 2 i 2 1 2 3 2 For a given incident angle, if the reflected light interfere to produce bright fringes, then the transmitted light produce dark fringes. 21 Interference in a Wedge-shaped Film 22 lens Light source microscope S mirror h l Wedge with very small θ 23 n1 n2 1 n2 n1 , 2nh 2 1 n2 n1 , 2nh 2 m bright fringes 1 ( m ) 2 dark fringes 24 Discussions on Wedge-Shaped Film Case1: h = 0 1 2 dark fringes 1 Case 2: m h ( m ) 2 2n2 bright fringes height difference between adjacent bright fringes: h 2n2 So, the distance between two adjacent bright fringes is h x tan 2n2 tan 2n2 25 The total number of bright fringes which can be observed thus can be obtained as (在劈尖上能够观测到的亮条纹的条数可以计算如下) l N x And it is easily to find the fringes are spaced uniformly. (易得,条纹是均匀分布的) The interference in a wedge-shaped film is called interference of equal thickness for the obvious reason. (劈尖上的干涉被称为等厚干涉) 26 Quick Quiz What if? (1) What happens to the fringes if the upper (lower) surface of the wedge-shaped film moves upward a little? (2) What happens if the angle of the wedge-shaped film increases? 27