Chapter 8,Wave Optics (1)(May 11, 2005),A brief summary to the last lecture,The structure of the eye,2. Vision of the human eye,vision of the human eye,from 0.1 1.5, is the viewing angle and in unit of minute.,3. Corrective eyeglasses for visual defects(1) Myopia (nearsighted); (2) Hyperopic eye (farsighted); (3) Astigmatic eye (散光眼),4. Optical instruments used in medicine(1) Magnifying glass(2) Compound microscope(3) Fibrescope,Wave optics (part 1) The corpuscular (微粒) theory of light (Until the middle of 17th century , Newton (1642-1727) supported). Ray optics can explain many of the properties of light, but there exist many other interesting and beautiful effects that cannot be explained by the geometric optics. For example, Experiments show that light bends around corners. The wave theory of light (Huygens (1629-95) Interference effects of light were first observed by Thomas Yong in 1800.,8.1 Interference (干涉) of light,Interference of wave motion, What is the phenomenon? Two coherent waves should be satisfied with the three conditions: what are they?,(1) the same frequency (2) the same vibrational direction(3) the same initial phase or constant phase change.,A chart of electromagnetic spectrum,Visible light (very approximately): 400450 nm Violet 450500 nm Blue 500550 nm Green 550600 nm Yellow 600650 nm Orange 650700 nm Red,8.1.1 Optical length (optical length, distance, path),In Chapter 4, we learned that the phase difference of two waves are expressed as,Light is also a part of electromagnetic waves. The light interference follows the rule of wave interference as you know in Yongs double-slit experiment.,It is known that light travels at a different speed in different medium. The speed of light in a medium depends on the refractive index of the medium. From the definition of the refractive index, we obtain,From the definition of wavelength, which is the period of the wave multiplying the speed of the wave, we have,Where 0 is wavelength of light in free space. So the wavelength of light becomes shorter in medium. Light path length is not the geometrical length of the light travel and it is defined as the product of refractive index and the geometrical distance the light travels.,Lets have a look at the light path length at the same period t when it travels in two different medium. We choose medium one is free space and medium two with refractive index n.in free space: opitacl length = n0 S = n0 c t = ct,In medium: optical length =,So it is found that though the lights traveling in different medium have different geometrical path (S and L) at the same period, they have the same light path length. So when we calculate the phase in medium n, we can use the formula directly,Again 0 is wavelength of light in free space, L is the geometrical length in the medium. Also we can use the similar formula to calculate the phase difference,8.1.2 Youngs double-slit experiments,20100cm,15m,Slits are 0.10.2 mm wide, separation of two slits 1mm,1. Coherent conditions of light: The wave has fixed wavelength. The incident beam should be monochromatic (单色的). The secondary wavelets that originate from the two small openings are in phase at their point of origin in the openings. The openings are small in comparison with the wavelength of the incident light. The distance between the two openings is not too big compared with the wavelength of the incident light.,2. Yongs formulas for bright and dark fringes,In the above figure, S1P = BP, the light path difference is S2B = . Therefore,what is the constructive conditions for two waves?by phase differenceby path difference,what is the initial phase change in double-slit interference experiment ?,how about total phase change? What does it depend on? Total phase change is therefore caused by the light path changes.,Constructive interference According to the interference theory of wave motion, whenever the path difference is an integer multiple of the wavelength, = m, the constructive interference or reinforcement interference should occurs as long as light is wave. Therefore,For bright fringes:,Destructive interference On the other hand, the opposite phenomenon occurs that the two light waves are cancelled each other. This condition is called destructive interference or cancellation and in this case, what is the light path difference should be equal to? 陈文灯,(m = 0, 1, 2, ),So for dark fringes:,The spacing of two bright or dark fringes:,Yongs experiments show that all the above formulas can describe the phenomena observed in his experiments very well, so the wave property of light is proved.,The analysis of the results,The spacing between two dark or bright fringes is independent from m, so they are equally spaced. As is small, so d cannot be too big, otherwise, they cannot be distinguished. What will you get if you use the sun (white) light as a light source? 陈善源,Example 1: In an interference pattern from two slits, the seventh-order bright fringe is 32.1mm from the zeroth-order bright fringe. The double slit is 5 meters away from the screen, and the two slits are 0.691mm apart. Calculate the wavelength of the light. Solution: the data we know arex7 = 3.2110-2 m, d = 6.9110-4 m, m = 7, L = 5 m, So we have:,