Final answer:
The distance at which a person can resolve two points, like headlights, is influenced by the resolving power of the human eye using the Rayleigh criterion. While exact optical calculations are not provided here, bicycle lights must be visible from a distance at night, with specifics varying depending on local laws. Light intensity from sources such as bike lights diminishes according to the inverse square law.
Step-by-step explanation:
The distance at which a person can resolve the headlights of a car that are 1.3 meters apart depends on the resolving power of the human eye. Given the pupil diameter is 0.40 cm, one can use the Rayleigh criterion in optics to determine this distance. However, the specifics of the optical calculation are not provided in the question. In terms of bicycle safety at night, bicycles must be equipped with a light on the front that is visible from a significant distance to ensure that they are visible to other road users, with such requirements often being specified in local traffic regulations.
Light intensity diminishes according to the inverse square law, which states that the intensity is inversely proportional to the square of the distance from the light source. As such, the amount of light that reaches the eye from a source like a bicycle light or car headlights weakens quickly as one moves away from the source. This principle also explains why stars, like Alpha Centauri A, appear as faint points of light despite their powerful energy emissions.
To deduce the maximum visibility range of a bicycle light, one would need to think about the light intensity required for the human eye to detect it and any legal requirements stipulated for safety purposes. Ultimately, the distance stated in local traffic laws for bicycle light visibility at night would be the authoritative specification to follow.