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
[tex]\theta = \frac{1.22\lambda }{D } \\ \\ \theta = \frac{1.22*506 *10^{-9} }{4.90*10^{-3}m}[/tex]
[tex]\theta = 1.2598*10^{-4}[/tex] rad
[tex]\theta = 125.98*10^{-6} \ rad[/tex]
Thus; the separation between the two sources is expressed as:
[tex]\theta = \frac{y}{L} \\ \\ y = L \theta \\ \\ y = (250*10^3 )(125.98*10^{-6} \ rad) \\ \\ y = 31.495 \ m[/tex]
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
