Final answer:
The two most important properties of telescopes are their light collecting area, determining how much faint light they can gather, and angular resolution, indicating the detail level they provide in images.
Step-by-step explanation:
The two most important properties of telescopes are light collecting area and angular resolution. The light collecting area is essential because it determines the telescope's ability to collect faint light from astronomical sources, which enables the study of very distant or dim objects. The larger the aperture, the more light the telescope can gather.
The angular resolution defines the telescopes' ability to distinguish fine details in the images it captures, which is particularly important for studying the surface of planets and distant stars. Turbulence in Earth's atmosphere can degrade angular resolution, but adaptive optics can be employed to correct for this turbulence in real-time and vastly improve image quality.