Question

Visibility v. Speed: (Darkness) Your headlights will let you see about ___ feet ahead. You should drive at a speed that allows you to stop within this distance or about __ mph.

Answer 1

The maximum distance at which the eye can resolve the two headlights of a car can be calculated using the concept of angular resolution. We can use the formula angular resolution (in radians) = 1.22 * (wavelength of light) / (diameter of the pupil) to calculate the angle subtended by the headlights and then solve for the distance. For a given pupil diameter of 0.40 cm and a headlight separation of 1.3 m, the maximum distance is found to be approximately 734 m.

Step-by-step explanation:

In order to determine the distance at which the eye can resolve the two headlights of a car, we can use the concept of angular resolution. The angular resolution is the smallest angle that two objects can be separated by and still be distinguishable to the eye. It can be calculated using the formula:

angular resolution (in radians) = 1.22 * (wavelength of light) / (diameter of the pupil).

Using the given pupil diameter of 0.40 cm and assuming the headlight's separation to be the diameter of the objects, we can calculate the maximum distance at which the eye can resolve the two headlights.

angular resolution = 1.22 * (580 * 10^-9 m) / (0.40 * 10^-2 m) = 1.77 * 10^-3 radians.

Since the angle subtended by the headlights decreases as the distance from the eye increases, we can use the formula:

angle = (separation between headlights) / (distance between car and eye).

Substituting the values:

1.77 * 10^-3 radians = 1.30 m / distance.

Solving for the distance, we find:

distance = 1.30 m / (1.77 * 10^-3 radians) = 734 m.