Final answer:
Headlights must be used when visibility is less than 500 feet to ensure visibility of vehicles for safety reasons. The regulation is standardized for safety and does not rely on the complex optical calculations of the human eye resolution.
Step-by-step explanation:
Headlights are required, day or night, when visibility is less than 500 feet. This is to ensure that vehicles are visible to each other and to pedestrians, which is critical for road safety. Poor visibility conditions can be caused by various factors such as fog, heavy rain, snow, or dust.
In a scenario where one is testing the limit of visibility for the human eye, like observing car headlights, factors to consider would include the resolution of the human eye, the pupil diameter, the distance between the headlights, and the intensity of light emitted by the headlights. The human eye can resolve two points as separate if the angle between them is sufficiently large according to the Rayleigh criterion. However, for practical purposes of driving and using headlights, regulations typically standardize the distance at which vehicles' headlights must be visible, irrespective of these complex calculations.