Final answer:
The question deals with the optical resolution of the human eye and involves calculating the maximum distance at which the headlights of a car, which are 1.3 meters apart, can be resolved, using the diameter of the pupil. The Rayleigh criterion is used for this calculation, and then trigonometry is applied to find the greatest possible viewing distance.
Step-by-step explanation:
The question appears to focus on the optical resolution of the human eye and its ability to distinguish between two separate points of light, such as car headlights. To solve this problem, we would typically use the Rayleigh criterion, which states that the minimum angle (θ) at which two points of light can be resolved is given by θ = 1.22λ/D, where λ is the wavelength of light (typically assumed to be around 550 nm for visible light) and D is the diameter of the pupil through which light enters the eye.
In the context of the question, to find the maximum distance at which car headlights can be resolved, we would calculate the angle θ using the given pupil diameter and then use trigonometry to relate the angle to the distance between the headlights and the maximum viewing distance.
If the headlights are 1.3 meters apart and the pupil diameter is 0.4 cm (or 0.004 meters), we would set up the following equation: θ = 1.22λ/D. Then, using the small angle approximation, we can say that θ ≈ L/d, where L is the distance between the headlights (1.3 meters) and d is the maximum distance at which they can be resolved. From here, we could solve for d to find the greatest possible distance a car can be while still resolving its headlights.