physics!

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Late one night on a highway, a car speeds by you and fades into the distance. Under these conditions the pupils of your eyes have diameters of about 7.0 mm. The taillights of this car are separated by a distance of 1.2 m and emit red light (wavelength = 669 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?

  • physics! -

    angular spot size of each tail light =
    (lambda)/d = 669*10^-9/7*10^-3 = 9.6*10^-5 radians

    This equals the tail light spot angular separation at distance X, if
    (1.2 m)/X = 9.6*10^-5
    X = 13000 m = 13 km

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