Final answer:
The maximum distance at which headlights must be dimmed is determined by the eye's ability to resolve two points of light, limited by diffraction by the pupil. This can be calculated by determining the angle between two just-resolvable points of light. Using these calculations, the maximum distance a car can be from you and still be able to resolve its two headlights can be determined.
Step-by-step explanation:
The maximum distance at which headlights must be dimmed at night when approaching another vehicle from behind is determined by the eye's ability to resolve two points of light. This is limited by the phenomenon of diffraction by the pupil. The practical limit for the eye can be calculated by determining the angle between two just-resolvable points of light for a given pupil diameter and average wavelength. Using the given pupil diameter of 0.40 cm and a wavelength of 550 nm, the angle between two just-resolvable points can be calculated.
The angle between two just-resolvable points of light for a 3.00-mm-diameter pupil, assuming an average wavelength of 550 nm, is approximately 1.22 x 10^-4 radians. This indicates the practical limit for the eye's resolution. The maximum distance a car can be from you and still be able to resolve its two headlights, given they are 1.3 m apart, can be calculated using trigonometry and the calculated angle. The answer will depend on the height of the observer's eyes above the ground. Lastly, the distance between two just-resolvable points held at an arm's length (0.800 m) from the eye can also be calculated using trigonometry and the calculated angle.