Microscopes are used to look at small objects that are close to you, and telescopes are used to look at small objects that are far away from you.

$1)$ The bacterium E$.$ Coli measures $1$ micron across. What minimum numerical aperture is required to resolve a single bacterium? $($hint: to resolve an object, the blur circle diameter is at most $0\mathrm{.}5$ x the size of the object$)$

$2)$ It is thought that a space$-$based surveillance telescope $(200$ km altitude$)$ can resolve grapefruit$-$sized objects on the Earth's surface. What is the required diameter of the telescope?