The headlights of a car are 1.6 m apart and produce light of wavelength 575 nm in vacuum. the pupil of the eye of the observer has a diameter of 4.0 mm and a refractive index of 1.4. what is the maximum distance from the observer that the two headlights can be distinguished?

To solve this problem it is necessary to apply the concepts related to angular resolution, for which it is necessary that the angle is

Where

d = Diameter of the eye

n = Index of refraction

D = Distance between head lights

= Wavelength

Replacing with our values we have that

Using the proportion of the arc length we have to

Where L is the maximum distance, therefore

Therefore the maximum distance from the observer that the two headlights can be distinguished is 12.77km

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