Final answer:
The maximum distance at which the eye can resolve two points such as car headlights depends on the eye's diffraction limit given the pupil size and the wavelength of light. To find this distance, calculations involving the Rayleigh criterion and simple trigonometry would be used.
Step-by-step explanation:
The question relates to the visual acuity of the human eye in terms of how the diffraction limit due to a pupil's size affects the distance at which two points of light (such as car headlights) can be resolved as separate.
Given that the headlights of a car are 1.3 meters apart and the pupil diameter is taken to be 0.40 cm (4.0 mm), one can use the Rayleigh criterion for resolution to determine this distance.
Though the question does not provide all the specifics needed for a complete calculation, typically, optical resolution can be determined using the formula θ = 1.22 λ / D, where θ is the angular resolution, λ is the wavelength of light, and D is the pupil diameter. The distance between the headlights and the eye, x, can then be found with x = l / θ, where l is the distance between the headlights.
This calculation would fall under wave optics, specifically dealing with the phenomenon of diffraction and its impact on the resolving power of optical systems like the human eye.