Respuesta :
Answer:
The distance that you marginally able to discern that there are two headlights rather than a single light source is 6.084 km
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:
[tex]sin\theta =\frac{\lambda }{d_{p} } =\frac{537x10^{-9} }{0.00481} =1.116x10^{-4}[/tex]
In this case, the two small sources of the headlights have the same angle as the images that form inside the eye
[tex]d_{x} =\frac{d}{sin\theta } =\frac{0.679}{1.116x10^{-4} } =6.084x10^{3} m=6.084km[/tex]
