Question

Spy planes fly at extremely high altitudes (20 km) to avoid interception. Their cameras are reportedly able to discern features as small as 5 cm. What must be the minimum aperture of the camera lens to afford this resolution? (Use λ = 550 nm.)

Answer 1

To calculate the minimum lens aperture for a spy plane to discern features of 5 cm at an altitude of 20 km, the Rayleigh criterion formula D = 1.22 λ L / d is used, where D is the lens diameter, λ is the wavelength of light, L is the altitude, and d is the detail size.

Step-by-step explanation:

To determine the minimum aperture of the camera lens required for a spy plane flying at extremely high altitudes, such as 20 km, to discern features as small as 5 cm, we can make use of the formula that relates the resolving power of a lens to its diameter:

D = 1.22 λ L / d,

Given that the wavelength λ is 550 nm (nanometers), the altitude L is 20,000 meters (20 km), and the smallest detail d is 0.05 meters (5 cm), rearranging and solving for D gives us the minimum diameter of the aperture that the camera lens must have.

It is important to note that this formula is derived from the Rayleigh criterion, which considers the diffraction limit of optical systems such as telescopes and cameras.