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 ? = 578 nm and a pupil diameter is 5.30 mm. (In this problem, you may use the Rayleigh criterion for the limiting angle of resolution of an eye.)

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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 ? = 578 nm and a pupil diameter is 5.30 mm. (In this problem, you may use the Rayleigh criterion for the limiting angle of resolution of an eye.)

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Introduction:

We are given wavelength of light. We are also given pupil diameter and distance of astronaut orbiting. We first find the angle subtended to eye. We then find the size of smallest object resolved by eye.

The limit of resolution is given as

θ=1.22λD

Here λ,D are wavelength and diameter of pupil for case of eye respectively.

 

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