Question

What is the approximate size of the smallest object on the Earth that astronauts can resolve by eye when they are orbiting $250km$ above the Earth? Assume $\lambda =$ $500nm$ and a pupil diameter of $5.00mm$

Answer 1

When the pupil is open wide, it appears that the resolving power of human vision is limited by the coarseness of light sensors on the retina. But we use Rayleigh's criterion as a handy indicator of how good our vision might be. We are given

$L=250\times {10}^{3}m,\lambda =5.00\times {10}^{-7}m,\text{and}d=5.00\times {10}^{-3}m$

The smallest object the astronauts can resolve is given by Rayleigh's criterion,

${\theta }_{min}=1.22\frac{\lambda }{D}=\frac{y}{L}.$

Therefore,

$y=1.22\frac{\lambda }{D}L=1.22\left(\frac{5.00\times {10}^{-7}m}{5.00\times {10}^{-3}m}\right)(250\times {10}^{3}m)=30.5m$