Final answer:
The maximum distance at which two headlights can be resolved depends on the diffraction limit, influenced by both the pupil diameter and the wavelength of light. This concept is rooted in physics, specifically the study of light and optics.
Step-by-step explanation:
The question pertains to the ability of the human eye to resolve two separate points of light, which in this case are the headlights on a car. The maximum distance at which the eye can resolve these two headlights is determined by the diffraction limit, which is a function of the wavelength of light and the diameter of the pupil. Assuming an average pupil diameter of 0.40 cm and using the average wavelength of visible light (550 nm), Rayleigh's criterion can give us an estimation for the maximum distance. However, to properly answer this question, one would need to employ the formula for resolving limit or perform an experiment to determine this value practically. It's important to note that illumination also diminishes with the square of the distance from the light source as per the inverse square law, which is another factor affecting the visibility of the headlights from a distance.