Answer:
a) θ = 1.67 10⁻⁵ m, b) Consequently we must affirm that the vehicle headlights cannot resolve.
Explanation:
a) To find the resolution of the camera we use the Rayleigh criterion for diffraction
a sin θ = m λ
where m = 1 for the first zero of the slit
we must remember that the angles in the experiments are measured in radians and are very small
sin θ = θ
we substitute
θ = [tex]\frac{\lambda}{a}[/tex]
this expression is for a slit, in the case of circular openings the expression must be solved in polar coordinates giving
θ = [tex]1.22 \ \frac{\lambda}{D}[/tex]
where D diameters of the opening
let's calculate
θ = [tex]1.22 \ \frac{550 \ 10^{-9}}{ 40\ 10^{-3}}[/tex]
θ = 1.67 10⁻⁵ m
b) let's use trigonometry to find the separation distance on earth
tan θ = y / x
y = x tan θ
let's calculate
remember that the angles must be in radians
y = 250 10³ tan 1.67 10⁻0-5
y = 4.18 m
as they indicate that the separation of the headlights is y = 1.6m,
we see that this separation is greater than the separation distance separation.
Consequently we must affirm that the vehicle headlights cannot resolve.
