Question

You're driving with your high beam headlights on and a car is approaching. You must dim them when the approaching car is within:

a) 200 feet.
b) 300 feet.
c) 500 feet.
d) 100 feet.

Answer 1

The distance at which the eye can resolve two headlights of a car and the distance between just-resolvable points at an arm's length are calculated using trigonometry and assumptions about the diameter of the pupil and average wavelength of light. The maximum distance a car can be from you to resolve its headlights is found to be approximately 43.36 meters.

Step-by-step explanation:

The maximum distance at which the eye can resolve two headlights of a car is determined by the angle between the headlights. This angle can be calculated using the diameter of the pupil and the average wavelength of light. Assuming a pupil diameter of 0.40 cm and an average wavelength of 550 nm, the angle between two just-resolvable points of light is determined to be 3.03 degrees.

To find the greatest possible distance a car can be from you, given that the headlights are 1.30 m apart, you can use trigonometry. By using the tangent function, the distance is found to be approximately 43.36 meters.

The distance between two just-resolvable points held at an arm's length (0.800 m) from your eye can also be calculated using trigonometry. Again, using the tangent function, the distance is found to be approximately 0.48 meters.

In everyday circumstances, details observed are usually much smaller than the distance between two just-resolvable points held at an arm's length.