Final answer:
The ability to resolve car headlights at a distance is determined by the diffraction limit of the eye, and the visibility of stars is affected by the square of the distance rule and light pollution.
Step-by-step explanation:
The question relates to the ability of human eyes to resolve two points of light, such as car headlights, at a distance. The maximum distance at which a person can resolve headlights that are 1.3 meters apart is determined by the diffraction limit of the human eye - which involves the diameter of the pupil and the wavelength of light. Using a typical pupil diameter of 0.4 cm, calculations based on this optic phenomenon allow us to approximate the greatest distance at which car headlights can be resolved, thus connecting to the safety guideline that headlights should be used whenever you can't see vehicles up to 1000 feet away.
To understand why distant stars appear as faint pinpoints, we can note that the intensity of light diminishes with the square of the distance due to the increase in the area it covers. This is also why light pollution affects the visibility of stars and why astronomical observatories are situated far from city lights.