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 0.641 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 549 nm and your pupil diameter to be 4.89 mm.

Answer 1

Answer:

$d_e=4.679km$

Explanation:

x' = 2 * 1.22 * lambda * ( f / D )

lambda = wavelength of light in mm

f = focal length in mm

D = aperture diameter in mm

$sin(\beta)=1.22*\frac{L}{d}$

$sin(\beta)=1.22*\frac{549x10^{-9}m}{4.98x10^{-3}m}$

$sin(\beta)=1.36x10^{-4}m$

sinβ=light separation/ distance eye

distance eye=light /sinβ

$d_e=\frac{0.641m}{1.369x10^{-4}m}=4679.87m$

$d_e=4.679km$