Question

The objective lens of a certain refracting telescope has a diameter of $58.0cm$. The telescope is mounted in satellite that orbits the Earth at an altitude of $270km$ to view objects on the Earth's surface. Assuming an average wavelength of $500nm$, find the minimum distance between two objects on the ground if their images are to be resolved by this lens.

Answer 1

Using Rayleigh's criterion, ${\theta }_{min}=1.22\frac{\lambda }{D}=\frac{y}{L}.$ Therefore,
$\begin{array}{cc}y& =1.22\left(\frac{\lambda }{D}\right)L=1.22\left(\frac{500\times {10}^{-9}m}{58.0\times {10}^{-2}m}\right)(270\times {10}^{3}m)\\ & =0.284m\end{array}$