Which telescope optical or X-ray would have higher resolving power for the same aperture Calculate the magnitude of the faintest object that a 20 m optical telescope can detect?

X-ray telescopes generally have higher resolving power than optical telescopes for the same aperture due to the shorter wavelengths of X-rays, which allows for finer detail in imaging. The resolving power is proportional to the wavelength, so shorter wavelengths (like X-rays) yield better resolution. To calculate the magnitude of the faintest object a 20 m optical telescope can detect, we can use the formula ( m = m_0 - 2.5 \log_{10}(A \cdot t) ), where (m_0) is the magnitude limit for a given area and time, (A) is the aperture area, and (t) is the exposure time. Assuming good conditions, a 20 m telescope can detect objects around magnitude 30, depending on the exposure time and sky brightness.