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PHY2049_07-18-11 - Chapter 36 Diffraction and the Wave...

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1 1 Chapter 36 In Chapter 35, we saw how light beams passing through different slits can interfere with each other and how a beam after passing through a single slit flares-diffracts- in Young's experiment. Diffraction through a single slit or past either a narrow obstacle or an edge produces rich interference patterns. The physics of diffraction plays an important role in many scientific and engineering fields. In this chapter we explain diffraction using the wave nature of light and discuss several applications of diffraction in science and technology. Diffraction 36- 2 Diffraction Pattern from a single narrow slit. Diffraction and the Wave Theory of Light 36- Central maximum Side or secondary maxima Light Fresnel Bright Spot. Bright spot Light These patterns cannot be explained using geometrical optics (Ch. 34)! 3 When the path length difference between rays r 1 and r 2 is λ /2, the two rays will be out of phase when they reach P 1 on the screen, resulting in destructive interference at P 1 . The path length difference is the distance from the starting point of r 2 at the center of the slit to point b . For D >> a , the path length difference between rays r 1 and r 2 is ( a /2) sin θ . 36- Fig. 36-4 Diffraction by a Single Slit: Locating the Minima 4 Repeat previous analysis for pairs of rays, each separated by a vertical distance of a /2 at the slit. Setting path length difference to λ /2 for each pair of rays, we obtain the first dark fringes at: 36- Fig. 36-5 Diffraction by a Single Slit: Locating the Minima, Cont'd (first minimum) sin sin 2 2 a a λ θ θ λ = = For second minimum, divide slit into 4 zones of equal widths a /4 (separation between pairs of rays). Destructive interference occurs when the path length difference for each pair is λ /2. (second minimum) sin sin 2 4 2 a a λ θ θ λ = = Dividing the slit into increasingly larger even numbers of zones, we can find higher order minima: (minima-dark fringes) sin , for 1,2,3 a m m θ λ = = K 5 Fig. 36-6 To obtain the locations of the minima, the slit was equally divided into N zones, each with width x . Each zone acts as a source of Huygens wavelets. Now these zones can be superimposed at the screen to obtain the intensity as function of θ , the angle to the central axis.
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