A spy satellite is in orbit at a distance of 1.0 × 10⁶ m above the ground. It carries a telescope that can resolve the two rails of a railroad track that are 1.4 m apart using light of wavelength 600 nm. Which one of the following statements best describes the diameter of the lens in the telescope? A)It is less than 0.14 m. B)It is greater than 0.14 m and less than 0.23 m. C)It is greater than 0.23 m and less than 0.35 m. D)It is greater than 0.35 m and less than 0.52 m. E)It is greater than 0.52 m.

Question

Quizplus · Accepted Answer

The resolving power of a telescope is determined by the Rayleigh criterion, which states that the minimum resolvable angle θ is approximately 1.22(λ/D), where λ is the wavelength and D is the diameter of the lens. Given the distance and separation, the diameter must be large enough to resolve the 1.4 m separation at 1.0 × 10^6 m distance, which requires a diameter greater than 0.52 m.

A Spy Satellite Is in Orbit at a Distance of 1.0