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Homework Help: Resolving Power and diffraction

  1. Apr 11, 2007 #1
    1. The problem statement, all variables and given/known dataLate one night on a highway, a car speeds by you and fades into the distance. Under these conditions the pupils of your eyes (average refractive index = 1.36) have diameters of about 7.0 mm. The taillights of this car are separated by a distance of 1.3 m and emit red light (wavelength = 660 nm in vacuum). How far away from you is this car when its taillights appear to merge into a single spot of light because of the effects of diffraction?
    [URL=http://img58.imageshack.us/my.php?image=resolvingpoweruz3.jpg][PLAIN]http://img58.imageshack.us/img58/1871/resolvingpoweruz3.th.jpg[/URL][/PLAIN]



    2. Relevant equations
    s=r(theta)
    Rayleigh criterion for resolution: theta min = 1.22 (lambda/D)



    3. The attempt at a solution

    lambda eye = lambda vacuum/ n eye
    (660x10^-9m) / 1.32 = 5x10^-7m

    1.22(lambda eye/D)=s/r
    1.22(5x10^-7m)/0.007m = 1.3m/r
    r = 15385 meters
    What am i doing wrong here??
     
    Last edited: Apr 11, 2007
  2. jcsd
  3. Apr 11, 2007 #2

    malawi_glenn

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    the answer should be?
     
  4. Apr 11, 2007 #3
    the only thing i can think of is:
    a^2 + b^2 = c^2

    (15385m^2) - (.65m^2 ) = answer .....i got 15384.99 which i know isn't right
     
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