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 0.679 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 537 nm and your pupil diameter to be 4.81 mm.

Answer 1

The distance that you marginally able to discern that there are two headlights rather than a single light source is 6.084 km

Step-by-step explanation:

Given:

d = distance = 0.679 m

λ = wavelength of the light = 537 nm = 537x10⁻⁹m

dp = pupil diameter = 4.81 mm = 0.00481 m

Question: What distance, in kilometers, are you marginally able to discern that there are two headlights rather than a single light source, dx = ?

For the separation of the peak from the central maximum it is:

`sin\theta =(\lambda )/(d_(p) ) =(537x10^(-9) )/(0.00481) =1.116x10^(-4)`

In this case, the two small sources of the headlights have the same angle as the images that form inside the eye

`d_(x) =(d)/(sin\theta ) =(0.679)/(1.116x10^(-4) ) =6.084x10^(3) m=6.084km`