Answer
220 m.
Work Step by Step
The diameter D of the telescope determines the resolution.
The resolving power is $ \theta_{r}=1.22\frac{\lambda}{D}$.
We are told that the resolving powers are to be identical.
$$\frac{\lambda_1}{D_1}=\frac{\lambda_2}{D_2}$$
$$D_2=D_1 \frac{\lambda_2}{\lambda_1}=(8000000m)\frac{550\times10^{-9}m 2}{2.0\times10^{-2}m }=220m$$
