Question

You stand on a straight desert road at night and observe a vehicle approaching. This vehicle is equipped with two small headlights that are 0.683 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 557 nm and your pupil diameter to be 5.39 mm.

Answer 1

5.42 Km

Step-by-step explanation:

Given

separation between source = 0.683 m

wavelength of light = 557 nm

diameter of human pupil = 5.39 nm

The picture attached below shows the full explanation

Answer 2

Step-by-step explanation:

The problem is based on the resolving power of the eye . For it the formula is as follows :

Resolving power = 1.22 λ / D , λ is wavelength of light and D is diameter of the eye.

Putting the given values

R.P = 1.22 x 557 x 10⁻⁹ / 5.39 x 10⁻³

= 126.074 x 10⁻⁶ radian

This is the minimum angular separation that can be resolved .

minimum linear separation that can be resolved = distance x angular separation that can be resolved

.683 = distance x 126.074 x 10⁻⁶

distance = .683 / 126.074 x 10⁻⁶

= 5417.5 m

= 5.417 km