The width of a telescope aperture is important because it determines what you will be able to resolve.
(a) You are out stargazing with your 14.2-cm telescope. You point your telescope at an interesting formation in the sky, which you think is a binary star system. A binary star system consists of two stars in orbit around each other. You guess that the average wavelength coming from the stars is 582 nm. What is the minimum angular separation between the two stars required for your telescope to resolve the two stars of the binary system?
(b) Having graduated with a degree in astronomy, you seek a job at the Arecibo radio telescope. You use a large radio telescope (300-m diameter) to observe the same binary system that you observed in part (a). You estimate that the average radio emissions from the system have a wavelength of 5.10 cm. What is the minimum angular separation required for the Arecibo telescope to resolve the two stars of the binary system?