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At what distance can your eye no longer resolve two headlights?

  1. Feb 4, 2009 #1
    1. The problem statement, all variables and given/known data

    Once dark adapted, the pupil of your eye is approximately 7 mm in diameter. The headlights of an oncoming car are 120 cm apart. If the lens of your eye is diffraction limited, at what distance are the two headlights marginally resolved? Assume a wavelength of 600 nm and that the index of refraction inside the eye is 1.33.




    2. Relevant equations

    [tex]\theta[/tex]min=1.22[tex]\lambda[/tex]/D
    where [tex]\lambda[/tex] is the wavelength, D is the diameter of the lens, and theta min is the angular resolution of a lens.


    3. The attempt at a solution

    So I've tried finding the distance according to the angle...but I'm confused. Why is the index of refraction included?

    I got 1.0457*10^-4 as the angle. Then divided that by half, 5.229*10^-5, call it [tex]\theta[/tex]2. found that the distance from the eye to the car would be 60tan[tex]\theta[/tex]2=6.574*10^7 cm. The question also said that the answer you would get would be more than what the eye can resolve, but I still think this might be off. Maybe it has to do with the lens being diffraction limited?
     
  2. jcsd
  3. Feb 4, 2009 #2
    Your eye not diffraction limited of course.
    Usually problems do not hand you extra information in first/second year physics.
    What happens to light when it enters a lens?
    (Hint: The equation you are using works well for mirrors telescopes.)
     
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