Final answer:
The maximum distance at which the eye can resolve two headlights is approximately 465.67 meters.
Step-by-step explanation:
The resolution of the eye can be calculated using the formula:
angular resolution = 1.22 x (wavelength / diameter of the pupil)
For headlights on a car that are 1.3 m apart, we assume the average visible wavelength is 550 nm and the diameter of the pupil is 0.40 cm. Plugging these values into the formula, we can calculate the angular resolution:
angular resolution = 1.22 x (550 x 10^-9 m) / (0.0040 m) = 0.167 degrees
To find the maximum distance at which the eye can resolve the two headlights, we can consider the angle formed by the two headlights and the observer. Assuming a right triangle where the distance between the headlights is the base and the distance to the observer is the height, we can use the tangent function:
tan(angle) = (1.3 m) / (distance)
Solving for the distance:
distance = (1.3 m) / tan(0.167 degrees) = 465.67 m
Therefore, the maximum distance at which the eye can resolve the two headlights is approximately 465.67 meters.