Answer
(a) $D = 3.8~cm$
(b) The light from Jupiter would be very hard to detect in comparison with the light from the sun.
Work Step by Step
(a) We can find the required angular resolution:
$\theta = \frac{d}{L}$
$\theta = \frac{7.8\times 10^{11}~m}{(4.3)(9.46\times 10^{15}~m)}$
$\theta = 1.9175\times 10^{-5}~rad$
We can find the minimum diameter:
$\theta = \frac{1.22~\lambda}{D}$
$D = \frac{1.22~\lambda}{\theta}$
$D = \frac{(1.22)~(600\times 10^{-9}~m)}{1.9175\times 10^{-5}~rad}$
$D = 0.0382~m$
$D = 3.8~cm$
(b) The light from Jupiter would be very hard to detect in comparison with the light from the sun. It would be like trying to detect a firefly on the circumference of a car headlight.
