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