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

  • Thread starter limonysal
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  • #1
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Homework Statement



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.




Homework 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.


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?
 

Answers and Replies

  • #2
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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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