Answer:
Minimum diameter of the camera lens is 22.4 cm
The focal length of the camera's lens is 300cm
Explanation:
y = Resolve distance = 0.3 m
h = Height of satellite = 100 km
λ = Wavelength = 550 nm
Angular resolution
[tex]tan\theta\approx \theta =\frac{y}{h}\\\Rightarrow \theta=\frac{0.3}{100\times 10^3}=3\times 10^{-6}[/tex]
From Rayleigh criteria
[tex]sin\theta=1.22\frac{\lambda}{D}\\\Rightarrow D=1.22\frac{\lambda}{sin\theta}\\\Rightarrow D=1.22\frac{550\times 10^{-9}}{sin3\times 10^{-6}}=0.2236\ m=22.4\ cm[/tex]
Minimum diameter of the camera lens is 22.4 cm
Relation between resolvable feature, focal length and angular resolution
[tex]d=f\Delta \theta\\\Rightarrow f=\frac{d}{\Delta \theta}\\\Rightarrow f=\frac{9\times 10^{-6}}{3\times 10^{-6}}=3\ m=300\ cm[/tex]
The focal length of the camera's lens is 300cm
