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

## 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

$$\theta$$min=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 $$\theta$$2. found that the distance from the eye to the car would be 60tan$$\theta$$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?

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.)