Lecture 26-27 Ch 36 - H 222 A Spring 2007 PH 222 3A Spring...

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Unformatted text preview: H 222- A Spring 2007 PH 222 3A Spring 2007 Diffraction Lectures 26-27 Chapter 36 (Halliday/Resnick/Walker, Fundamentals of Physics 8 th edition) 1 Chapter 36 Diffraction 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 ares— iffracts— Young's experiment. Diffraction through a single slit or 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. 2 Diffraction and the Wave Theory of Light Diffraction pattern from a single narrow slit. Side or secondary maxima i ht Light Central maximum hese patterns cannot be Fresnel Bright Spot. These patterns cannot be explained using geometrical optics (Ch. 34)! Bright Light spot 3 Diffraction by a Single Slit: Locating the Minima 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 nd ( ) sin r 1 and r 2 is ( a /2) sin θ . Fig. 36-4 4 Repeat previous analysis for pairs of rays, each separated by a Diffraction by a Single Slit: Locating the Minima, cont'd 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: (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....
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Lecture 26-27 Ch 36 - H 222 A Spring 2007 PH 222 3A Spring...

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