Answer:
The farthest distance is [tex]L_{max}=11.48 km[/tex]
Explanation:
The angular resolution is mathematically represented as
[tex]\theta = \frac{Z}{L} = \frac{1.22 \lambda}{d}[/tex]
Where Z is the distance between the car head lamp with a value Z = 1.4 m
L is the distance between the eye and the car
[tex]\lambda[/tex] is the wavelength with a value 500 nm = [tex]= 500 *10^{-9}m[/tex]
d is the diameter of the eye with a value d = 0.50 cm = [tex]= \frac{0.50}{100} = 0.005m[/tex]
The maximum distance [tex]L_{max}[/tex] is given as
[tex]L_{max} = \frac{(1.4) *0.005}{1.22 * (500 *10^{-9})}[/tex]
[tex]= 11.48*10^{3}m[/tex]
[tex]=11.48 km[/tex]
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