Question

What is the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting 250 km above the Earth? Assume λ = 506 nm and a pupil diameter is 4.90 mm. (In this problem, you may use the Rayleigh criterion for the limiting angle of resolution of an eye.)

Answer 1

Answer:

the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting 250 km above the Earth is y = 31.495 m

Explanation:

Using Rayleigh criterion for the limiting angle of resolution of an eye

$\theta = \frac{1.22\lambda }{D } \\ \\ \theta = \frac{1.22*506 *10^{-9} }{4.90*10^{-3}m}$

$\theta = 1.2598*10^{-4}$ rad

$\theta = 125.98*10^{-6} \ rad$

Thus; the separation  between the two sources is expressed as:

$\theta = \frac{y}{L} \\ \\ y = L \theta \\ \\ y = (250*10^3 )(125.98*10^{-6} \ rad) \\ \\ y = 31.495 \ m$

Thus; the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting 250 km above the Earth is y = 31.495 m