Answer
(a) $1.3\times 10^{-3}rad$
(b) $115m$
Work Step by Step
(a) We can find the required angular resolution as follows:
$\theta_{min}=1.22\frac{\lambda}{D}$
We plug in the known values to obtain:
$\theta_{min}=\frac{(1.22)(520\times 10^{-9}m)}{0.50\times 10^{-3}m}$
$\theta_{min}=1.3\times 10^{-3}rad$
(b) We know that
$y=L tan\theta$
This can be rearranged as:
$L=\frac{y}{tan\theta_{min}}$
We plug in the known values to obtain:
$L=\frac{0.15m}{tan(0.0013)}$
We know that if $\theta$ is small then $tan\theta\approx \theta$
$\implies L=\frac{0.15m}{0.0013}$
$L=115m$
