Final answer:
The maximum distance at which the human eye can resolve two headlights 1.3 meters apart, with a 3.00-mm pupil diameter and 550 nm light wavelength, is approximately 5.8 kilometers.
Step-by-step explanation:
The question posed is related to optical resolution and diffraction limits of the human eye when considering headlight separation on a car. To determine the greatest possible distance at which a person can resolve two headlights that are 1.3 meters apart, with a pupil diameter of 3.00 mm and assuming the average wavelength of light to be 550 nm, we can use the formula for the resolving power of the eye.
We start by calculating the minimum resolvable angle using the formula θ = 1.22 λ / D, where λ is the wavelength of light (550 nm, or 550 x 10^-9 meters), and D is the diameter of the pupil (3.00 mm, or 3 x 10^-3 meters).
θ = 1.22 × (550 x 10^-9 m) / (3 x 10^-3 m)
θ ≈ 2.24 x 10^-4 radians
We can then use this angle in conjunction with the separation of the headlights (1.3 m) to find the maximum distance (d) at which they can be resolved:
d = separation / θ
d ≈ 1.3 m / 2.24 x 10^-4 radians
d ≈ 5804 meters, or approximately 5.8 kilometers