$($a$)$

A radio telescope has an angular resolution of $0\mathrm{.}137$ for incident radio waves of wavelength

$=3\mathrm{.}23$ mm$.$

What is the minimum diameter $($in m$)$ required for the telescope's parabolic receiving dish?

m

What If$?$ The $21\mathrm{.}1$ cm line, corresponding to emissions from hyperfine transitions in hydrogen, plays an important role in radio astronomy.

$($b$)$

What minimum diameter $($in m$)$ is required for a radio telescope's receiving dish if the telescope is to have an angular resolution of $0\mathrm{.}137$ for this wavelength?

m

$($c$)$

What would be the angular resolution $($in degrees$)$ of the telescope receiving dish from part $($a$)$ for the $21\mathrm{.}1$ cm line?