The pattern will be more spread out in the vertical direction, as the slit is narrower there. A pattern that is wider than it is high is desired, so the speaker should be high and narrow. (a) Would you expect the diffraction pattern to be more spread out in the vertical direction or in the horizontal direction? (b) Should a rectangular loudspeaker horn at a stadium be high and narrow, or wide and flat? Solution: a. A pattern that is wider than it is high is desired, so the speaker should be high and narrow.ġ6 Conceptual Example 35-2: Diffraction spreads. Light shines through a rectangular hole that is narrower in the vertical direction than the horizontal. The width is 46 cm.ġ5 Conceptual Example 35-2: Diffraction spreads. The first minimum occurs at sin θ = λ/D = 0.75, or θ = 49°. How wide is the central maximum (a) in degrees, and (b) in meters, to an ear 10 m away? Solution: a. Sound of wavelength 30 cm passes through a slit 1.0 m wide. The width is 46 cm.ġ4 Example 35-1: Single-slit diffraction maximum How wide is the central maximum (a) in degrees, and (b) in centimeters, on a screen 20 cm away? Solution: a. Light of wavelength 750 nm passes through a slit 1.0 x 10-3 mm wide. The width is 46 cm.įigure (a) Diffraction factor, (b) interference factor, and (c) the resultant intensity plotted as a function of θ for d = 6D = 60λ.ġ3 Example 35-1: Single-slit diffraction maximum Single-slit diffraction Slit Diameter = D (or ‘s’) D is small! D sinq = ml for minima since sinq D typically d sinq = ml for maxima sinq = ml/d bright fringes at small q Solution: a. The width is 46 cm.ġ0 Single-slit diffraction vs. Note that the central maximum is not only much higher than the maxima to each side, but it is also twice as wide (2λ/D wide) as any of the others (only λ/D wide each).Ĩ What? Wait a minute! The minima of the single-slit diffraction pattern occur when The maxima of the double-slit interference pattern occured when dĩ Single-slit diffraction vs. The minima of the single-slit diffraction pattern occur when Figure Intensity in the diffraction pattern of a single slit as a function of sin θ. Figure Analysis of diffraction pattern formed by light passing through a narrow slit of width D. Pattern arises because different points along slit create wavelets that interfere with each other just as a double slit would. Figure Diffraction pattern of (a) a circular disk (a coin), (b) razor, (c) a single slit, each illuminated by a coherent point source of monochromatic light, such as a laser. The resulting pattern of light and dark stripes is called a diffraction pattern. Figure If light is a wave, a bright spot will appear at the center of the shadow of a solid disk illuminated by a point source of monochromatic light. If light is a wave, it will diffract around a single slit or obstacle. Peak Widths and Resolving Power for a Diffraction Grating X-Rays and X-Ray Diffraction Polarization Liquid Crystal Displays (LCD) Scattering of Light by the Atmosphere Intensity in Single-Slit Diffraction Pattern Diffraction in the Double-Slit Experiment Limits of Resolution Circular Apertures Resolution of Telescopes and Microscopes the λ Limit Resolution of the Human Eye and Useful Magnification Diffraction Gratingģ Units of Chapter 35 The Spectrometer and Spectroscopy Finally we study the polarization of light.Ģ Units of Chapter 35 Diffraction by a Single Slit or Disk We will see how diffraction affects the resolution of optical instruments, and that the ultimate resolution can never be greater than the wavelength of the radiation used. We also discuss diffraction gratings and diffraction of X-rays by crystals. We will examine diffraction by a single slit, and how it affects the double-slit pattern. Diffraction patterns are washed out when typical extended sources of light are used, and hence are not seen, although a careful examination of shadows will reveal fuzziness. Instead of a clean shadow, there is a dramatic diffraction pattern, which is a strong confirmation of the wave theory of light. Parallel coherent light from a laser, which acts as nearly a point source, illuminates these shears. 1 Chapter 35 Diffraction and PolarizationĬhapter 35 opener.
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