How does the angular resolution of the 305-m Arecibo telescope in Puerto Rico, which observes radio waves, compare with the angular resolution of the 10-m Keck telescope on Mauna Kea, Hawaii, which observes optical light? Assume each telescope observes the light they were designed to see.
A) It is not possible to compare their angular resolution because they work in different wavelength ranges.
B) The 305-m Arecibo telescope has much better angular resolution than the 10-m Keck telescope.
C) They have about the same angular resolution because angular resolution is limited by turbulence in Earth's atmosphere, not by mirror diameter.
D) The 305-m Arecibo telescope has much worse angular resolution than the 10-m Keck telescope.

Question

Quizplus · Accepted Answer

The angular resolution of a telescope is determined by its diameter and the wavelength of light it observes. The formula for angular resolution, $\theta \approx \frac{\lambda}{D}$, where $\lambda$ is the wavelength and $D$ is the diameter of the telescope, shows that larger diameters and shorter wavelengths yield better (smaller) angular resolutions. Since radio waves (observed by Arecibo) have much longer wavelengths than optical light (observed by Keck), and despite Arecibo's larger diameter, the Keck telescope has much better angular resolution due to its observation of much shorter wavelengths.

How Does the Angular Resolution of the 305-M Arecibo Telescope