Final answer:
The maximum distance at which the eye can resolve two headlights on a car is approximately 25.43 meters.
Step-by-step explanation:
To determine the maximum distance at which the eye can resolve two headlights on a car, we can use the concept of angular resolution. The angular resolution of the eye is defined as the smallest angle that can be distinguished by the eye. In the case of resolving two headlights, we can consider the distance between the headlights as the size of the object being resolved.
We can use the formula for angular resolution:
Angular resolution = 1.22 * (wavelength/diameter)
where wavelength is the wavelength of light and diameter is the diameter of the pupil.
Given that the headlights are 1.3 m apart and the pupil diameter is 0.40 cm (0.004 m), we can calculate the maximum distance at which the eye can resolve the headlights using the formula:
Maximum distance = (1.22 * wavelength * distance between headlights) / (diameter * 0.004)
The maximum distance will depend on the wavelength of light being used. For visible light, the average wavelength is 550 nm (5.5 times 10^{-7} m).
Plugging in the values, we get:
Maximum distance = (1.22 * 5.5 times 10^{-7} * 1.3) / (0.004)
Simplifying the equation, the maximum distance at which the eye can resolve the two headlights is approximately 25.43 meters.