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