Final answer:
The resolving power of telescopes depends on both the wavelength of light and the diameter of the aperture, not only on wavelength. The resolving power is inversely proportional to the wavelength and the aperture size. For radio telescopes, interferometry can greatly enhance resolution.
Step-by-step explanation:
The question is asking about the resolving power of telescopes and its dependency on wavelength. Specifically, the question involves the comparison of the resolving power of different types of telescopes as influenced by factors like wavelength, aperture size, and the use of interference techniques in radio astronomy.
For optical telescopes, the resolving power is indeed dependent on the wavelength of light being used and the diameter of the aperture. However, the assertion that resolving power depends only on wavelength is false, as it also depends on the aperture size. Similarly, the reason provided, stating that resolving power is proportional to the square of the wavelength, is incorrect. The resolving power is actually inversally proportional to both the diameter of the aperture and the wavelength. Thus, the correct option in this case is (d): A and R are false.
For radio telescopes, resolutions are often improved by linking telescopes together in an arrangement called an interferometer since radio wavelengths are much longer and require a larger aperture for good resolution when used individually. The ALMA (Atacama Large Millimeter/submillimeter Array) achieves high resolution by operating as an interferometer with its longest baseline, considerably enhancing its resolving power over single-dish telescopes like the Arecibo Observatory.