Final answer:
The angular resolution ranking from best to worst for the telescopes provided would be: 10m infrared on Mauna Kea, 2m infrared in space, 2m x-ray at the Pole, and 300m radio telescope. Large apertures and shorter wavelengths generally offer better resolution.
Step-by-step explanation:
The angular resolution of a telescope determines its ability to distinguish between two closely spaced objects. Theoretically, this resolution improves with larger apertures and shorter wavelengths of light. Given the types of telescopes listed, here is how they would rank from best to worst in terms of angular resolution:
- C) 10 meter infrared telescope on Mauna Kea - Infrared telescopes already have better resolution due to shorter wavelengths compared to radio, and a larger aperture contributes to placing this option as the best.
- B) 2 meter infrared telescope in space - While it has a much smaller aperture than option C, being in space reduces atmospheric distortion, which is why it's the second-best option.
- A) 2 meter x-ray telescope at the Pole - X-rays have even shorter wavelengths, which is good for resolution, but the small aperture size and potential atmospheric interference make this the third option.
- D) 300 meter radio telescope - Despite its large size, the long wavelengths of radio signals make its angular resolution the poorest among the options provided.
Noteworthy is that multiple factors affect resolution, such as atmospheric conditions and the wavelength of observed light. Larger apertures tend to collect more light, providing better resolution, but the clarity of images can also be limited by other factors, such as atmospheric distortion. For radio telescopes, which deal with much longer wavelengths, techniques like radio interferometry are employed to enhance resolution.