If the numbers on the plate are 6.0 cm apart, and the spy satellite is at an altitude of 160 km, what must be the diameter of the camera's aperture? (Assume light with a wavelength of 560 nm.)

The diameter of the camera aperture must be greater than or equal to 1.49m

Explanation:

Let the distance separating two objects, x = 6.0 cm = 0.06 m

The distance between the observer and the two objects, d = 160 km = 160000 m

Let ∅ = minimum angular separation between the two objects that the satellite can resolve

tan (∅) = x/d

Since there is minimum angular separation, tan (∅) ≈∅

∅ = x/d

∅ = 0.06/160000

∅ = 3.75 * 10⁻⁷rad

For the satellite to be able to resolve the objects,

D ≥ 1.22λ/∅

λ = 560 nm = 560 * 10⁻⁹

D ≥ 1.22 * (560 * 10⁻⁹) / (3.75 * 10⁻⁷)

D ≥ 149.33 * 10⁻² m

D ≥ 1.49 m