Final answer:
A driver should dim their headlights at a distance often stipulated by traffic laws, usually around 500 feet, to avoid blinding oncoming traffic. The ability to resolve two headlights as separate is influenced by the practical limit of the eye, pupil diameter, and distance between headlights.
Step-by-step explanation:
At night, when driving, it is important to dim your headlights when you see an oncoming vehicle to prevent blinding the other driver. The question of at what distance you should dim your headlights can be understood through the practical limit of the human eye's resolution, which depends on factors such as the pupil diameter and the distance between the headlights.
If the headlights are 1.3 meters apart and the pupil diameter is 0.40 cm, we can calculate this limit using the Rayleigh criterion or similar optical principles. However, exact distances at which to dim headlights for safety on the road are often determined by local traffic regulations, which commonly stipulate reducing high beams to low beams within 500 feet of an oncoming vehicle.
From a physics perspective, the ability to resolve two headlights as separate sources of light decreases as the distance from the observer increases. Reflecting on the inverse square law of illumination, which tells us that the area over which light is spread is proportional to the square of the distance from the light source, helps us understand why lights appear dimmer the further away we are from them.
This principle is also relevant in astronomy, where stars like Alpha Centauri A, despite having a similar energy output to the Sun, appear much fainter due to the vast distances involved.