Final answer:
The maximum visibility distance for resolving car headlights is calculated based on the angular resolution limit of the human eye using the Rayleigh criterion, which involves the average wavelength of light and the diameter of the pupil.
Step-by-step explanation:
The question relates to the optical resolution of the human eye and involves calculating the maximum visibility distance at which car headlights can be resolved as separate points of light.
Using the Rayleigh criterion and the given diameter of the pupil, we estimate this distance by applying the formula for the angular resolution limit Ø = 1.22 × (λ / D), where λ is the wavelength of light (average taken as 550 nm for visible light), and D is the diameter of the pupil.
Assuming that the eye can resolve points at the limit given by this formula, we can then use the geometry of similar triangles to find the maximum distance.
For example, if two headlights are 1.3 m apart, and using a pupil diameter of 0.40 cm, we would first calculate the angular resolution limit, then use the formula d = L × tan(Ø), where d is the distance between the headlights, L is the maximum separation distance, and Ø is the angular resolution limit, to find the maximum distance L at which the headlights are resolvable.