Resolution and Multiwavelength Astronomy

An aperture diffracts light from a point into a diffraction pattern. Two nearby stars become distinguishable when their patterns are sufficiently separated. For the AQA approximation the minimum angular separation is wavelength divided by aperture diameter, in radians. A smaller limiting angle means better resolution.

Collecting power instead measures how much radiation enters the telescope. At the same wavelength and exposure time it scales with aperture area. Doubling diameter collects four times the power but halves the diffraction angle. These are different benefits and should be calculated separately.

A radio dish uses a conducting concave surface and receiver near a focus. Radio wavelengths are much longer than visible wavelengths, so very large dishes are needed for similar angular resolution. Mesh can reflect radio waves if the gaps are sufficiently smaller than the wavelength. Radio observations can often continue through clouds.

Much ultraviolet and essentially astronomical X-ray radiation is absorbed by the atmosphere, so those telescopes operate above it. X-rays need grazing-incidence optics rather than ordinary normal-incidence mirrors. Infrared instruments are often placed at dry high sites or in space and cooled: water vapour absorbs infrared and a warm telescope emits its own unwanted infrared signal.

A CCD converts a relatively large fraction of incident visible photons into recorded charge: high quantum efficiency. It integrates faint signals over a long exposure, gives digital data for analysis and can record a wide brightness range. The eye is useful for immediate viewing but has lower quantum efficiency and cannot store long exposures.

A large ground-based optical telescope may be limited by atmospheric seeing rather than its theoretical diffraction limit. Compare detectors through efficiency, pixel sampling and convenience, and state whether the calculation assumes diffraction-limited optics.

Try each problem before opening the worked solution. State the physical model, show substitutions with consistent units, and explain what your answer means.