Question

A low orbit satellite at 100 km altitude had a camera that resolved a car location to within 0.3 meter. Find the minimum diameter of the camera lens when operating at 550nm sunlight. Find the focal length of the camera's lens when the photographic film had a resolution of 9-micro-meter due to grain size. CAS TI-7nspire cx

Answer 1

Minimum diameter of the camera lens is 22.4 cm

The focal length of the camera's lens is 300cm

Step-by-step explanation:

y = Resolve distance = 0.3 m

h = Height of satellite = 100 km

λ = Wavelength = 550 nm

Angular resolution

`tan\theta\approx \theta =(y)/(h)\\\Rightarrow \theta=(0.3)/(100* 10^3)=3* 10^(-6)`

From Rayleigh criteria

`sin\theta=1.22(\lambda)/(D)\\\Rightarrow D=1.22(\lambda)/(sin\theta)\\\Rightarrow D=1.22(550* 10^(-9))/(sin3* 10^(-6))=0.2236\ m=22.4\ cm`

Minimum diameter of the camera lens is 22.4 cm

Relation between resolvable feature, focal length and angular resolution

`d=f\Delta \theta\\\Rightarrow f=(d)/(\Delta \theta)\\\Rightarrow f=(9* 10^(-6))/(3* 10^(-6))=3\ m=300\ cm`

The focal length of the camera's lens is 300cm