The aperture diameter required in the detector if the two headlights are to be resolved at a distance of 20.0 km is 1.2 cm.
When a vehicle approaches with separated headlights S = 1.80 m and resolved at a distance of r = 20.0 km = 2 × 10⁴ m. The angle for the headlights is
S = θr
θ = S ÷ r
θ = 1.8 ÷ (2 × 10⁴)
θ = 9 × 10⁻⁵ radians
The Rayleigh criterion for the diffraction limit is the formula to calculate the aperture and limited angle with the radiation wavelength = λ = 885 nm = 885 × 10⁻⁹ m
θ = 1.22 × (λ ÷ D)
θD = 1.22 × λ
9 × 10⁻⁵ × D = 1.22 × 885 × 10⁻⁹
D = 1.0797 × 10⁻⁶ ÷ (9 × 10⁻⁵)
D = 0.012 m
D = 1.2 cm
Learn more about The Rayleigh criterion here: https://brainly.com/question/13063889
#SPJ4
