Describe what is meant by the Rayleigh criterion for the resolution of two point-like sources.
A space-based observatory is designed to detect extreme ultraviolet (EUV) radiation in the spectral range of 12 nm12\text{ nm}12 nm to 48 nm48\text{ nm}48 nm.
Explain why EUV observations cannot be conducted using ground-based instruments, and discuss one major advantage of this telescope's resolving capabilities compared to an optical space telescope of the same primary aperture diameter.
Table 1 provides specifications for two proposed ground-based radio dishes designed to study interstellar gas clouds.
TelescopeDiameter / mDish ShapeTelescope Gamma150sphericalTelescope Delta30parabolic \begin{array}{c|c|c} \textbf{Telescope} & \textbf{Diameter / m} & \textbf{Dish Shape} \\ \hline \text{Telescope Gamma} & 150 & \text{spherical} \\ \text{Telescope Delta} & 30 & \text{parabolic} \end{array} TelescopeTelescope GammaTelescope DeltaDiameter / m15030Dish ShapesphericalparabolicBoth instruments are tuned to detect a spectral emission line at a wavelength of λ=8.0 cm\lambda = 8.0\text{ cm}λ=8.0 cm.
Compare the performance of Telescope Gamma and Telescope Delta when observing the same faint, distant emission source. Your comparison must include a quantitative calculation of their relative collecting powers.
