how do optical telescopes and radio telescopes gather information about stars?

Question

how do optical telescopes and radio telescopes gather information about stars?

Answer 1

Optical telescope based information about these bodies largely comes from the frequency spectrum of the light we receive. Peaks and dips at particular frequencies can identify relative abundance of some of the elements in the star which emit those frequencies, and substances in the light path that absorb specific frequencies. Frequency shifts of these features indicate velocities.

Other information comes from distortion of the image due to gravitational "lensing" (bending of the light by objects in the light path).

Answer 2

Basically all telescopes gather photons (remember that light and radio waves are really the same thing just at different frequencies). Some use lenses some use mirrors others metal reflecting surfaces. They all do the same thing by using a large objective to gather as much light as possible then concentrating it by bending the light path so that it converges to a point so that it can be read by the human eye or electronic detectors.