Final answer:
The question deals with optical resolution, specifically using the Rayleigh criterion to calculate the maximum distance at which the human eye can resolve two separate points of light, like car headlights, relative to the size of the pupil and the wavelength of light.
Step-by-step explanation:
The question focuses on the optical resolution limit of the human eye, which determines how close two points of light, such as headlights on a car, can be to one another while still being distinguishable as separate sources of light. The typical scenario described is based on the Rayleigh criterion, which relates the angular resolution limit of an optical system to the wavelength of light and the aperture size (in this case, the pupil of the eye).
According to the Rayleigh criterion, the angle Θ in radians between two just-resolvable points is given by Θ = 1.22 λ/D, where λ is the wavelength of light (here assumed to be around 550 nm for average circumstances), and D is the diameter of the pupil (in this case, 0.40 cm or 4 mm if more commonly used units are needed). This formula can be used to calculate the maximum distance at which a car's headlights, spaced 1.3 meters apart, can be resolved by the human eye.
To answer question (b) related to the practical limit for the distance to resolve car headlights, you would rearrange the Rayleigh criterion formula to solve for the maximum distance, using the calculated angle for just-resolvable points. Question (c) regarding the resolvable distance between two points at arm's length follows the same principle, here focusing on the human eye's resolution at a typical viewing distance. Questions such as these are crucial for considering the visibility distance for safety and design in fields like engineering and traffic safety.