Monday, July 17, 2006

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Chapter 28:  Physical Optics: Interference and Diffraction

28-1:  Superposition and Interference
    The adding of waves (superposition) can result in an increased amplitude (constructive interference) or reduced amplitude (destructive interference).
    Light waves interfere much like sound waves, but since light waves have much shorter wavelengths, the effects appear quite different.
    Monochromatic light has only one frequency, and hence a single color.
    Coherent light waves have a constant phase relationship, which is a necessary condition for the creation of interference patterns.

28-2:  Young's Two-Slit Experiment
    When light passes through two narrow slits separated by a distance d, an interference pattern will be produced with bright fringes at angles theta:  d*sin(theta) = m*lambda, m = 0, +/-1, +/-2,...  and dark fringes at d*sin(theta) = (m-0.5)*lambda, m = 0, +/-1, +/-2,...

28-3:  Interference in Reflected Waves
    Light waves reflected from different surfaces can interfere if they are observed simultaneously.
    When light is reflected from a surface with a higher index of refraction (like a solid surface), a 180-degree phase change (half-wavelength) occurs, but no phase change results when light reflects from a surface with a lower index of refraction (as in total internal reflection, i.e. fiber optics).
    These effects result in color variations seen in thin films and air wedges.
    CQ11 - A film of oil on water appears dark near the edges where it is thinnest.  Estimate the index of refraction of this oil.

28-4:  Diffraction - Light changes direction when it encounters an edge.
    A single slit produces a diffraction pattern with dark fringes located at:  Wsin(theta) = m*lambda, m = +/-1, +/-2,...
Demo:  http://www.phys.hawaii.edu/~teb/optics/java/slitdiffr/

28-5:  Resolution - The ability of a visual system (like an eye or camera) to distinguish between closely spaced objects.
    A circular aperture produces a diffraction pattern where the first dark fringe is at angle theta:  sin(theta) = 1.22lambda/D.
    Rayleigh's criterion:  If the angular separation between two objects is less than 1.22lambda/D, then they will appear as a single object.  This is when the first maximum and minimum of the adjacent diffraction patterns overlap.

28-6:  Diffraction Gratings
    A diffraction grating produces maxima where:  d*sin(theta) = m*lambda, m = 0, +/-1, +/-2,...

Concept Tests