You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.673 m 0.673 m apart. At what distance, in kilometers, are you marginally able to discern that there are two headlights rather than a single light source? Take the wavelength of the light to be 543 nm 543 nm and your pupil diameter to be 5.37 mm.

To solve this problem we will apply trigonometric and optical concepts that allow us to obtain the minimum distance required. The resolution of the eye is given under the following condition,

Here,

With the values we have that the diameter will be,

The relation between the distance of the lights and the distance from the eye to the lamp is given under the function,

For small angles , then

Here,

d = Distance between lights

L = Distance from eye to lamp

Therefore the distance will be 5.5km

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