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

[limonysal]

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

\thetamin=1.22\lambda/D
where \lambda 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 \theta2. found that the distance from the eye to the car would be 60tan\theta2=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?

 

[Mr.Amin]

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.)