Radio telescopes are typically constructed in remote areas to reduce the impact of radio frequency interference (RFI) from human-made sources. RFI, which includes signals from mobile phones, radios, and other electronic devices, can severely disrupt the sensitive measurements made by radio telescopes. These telescopes are designed to detect extremely faint radio waves emitted by distant celestial objects. Even a small amount of interference from terrestrial sources can mask or distort these signals, leading to inaccurate observations or data loss. Remote locations, preferably in valleys or other naturally shielded areas, provide a 'radio-quiet' environment, crucial for high-precision astronomical research. Furthermore, the remoteness also helps in mitigating the effects of ionospheric disturbances and ensures a clearer and more stable atmosphere for radio wave reception.

The resolving power, which determines the telescope's ability to distinguish between two close objects, varies significantly between radio and optical telescopes due to the difference in the wavelengths they observe. Optical telescopes, working with much shorter wavelengths of visible light, generally have higher resolving power than radio telescopes. However, the resolving power of radio telescopes can be enhanced by increasing the diameter of the dish or using techniques like Very Long Baseline Interferometry (VLBI), which combines the observations of multiple dishes spread across large distances.

In terms of collecting power, which is the ability to gather electromagnetic radiation, radio telescopes often have an advantage. The larger the dish or array, the more radio waves it can collect, thus improving sensitivity. This is especially important in radio astronomy since radio waves from celestial sources are typically very weak. Therefore, a large collecting area is crucial to detect and analyse these faint signals.

Designing and constructing X-ray telescopes presents several unique challenges, primarily due to the nature of X-rays themselves. Unlike visible light, which can be reflected by mirrors at relatively steep angles, X-rays have much shorter wavelengths and higher energies. They tend to penetrate most materials, including traditional mirrors. To overcome this, X-ray telescopes use a technique called grazing incidence, where X-rays are reflected at very shallow angles off the surfaces of specially shaped mirrors. This requires the mirrors to be extremely smooth and precisely shaped, often requiring innovative materials and construction techniques. Additionally, because Earth's atmosphere absorbs X-rays, these telescopes must be positioned in space, adding to the complexity and cost of their design and deployment. The harsh conditions of space also demand robust and durable components that can withstand temperature extremes and radiation.

Placing telescopes in space offers several significant advantages over ground-based observatories. One of the primary reasons is to avoid the distortion and absorption of electromagnetic radiation by Earth's atmosphere. For certain wavelengths, such as ultraviolet, X-ray, and parts of the infrared spectrum, the atmosphere acts as an opaque barrier. Space-based telescopes can observe these wavelengths without interference, providing clearer and more detailed images.

Another advantage is the ability to observe continuously without the interruption of the day-night cycle or weather conditions. This enables more prolonged and consistent monitoring of celestial events. Moreover, the lack of atmospheric distortion results in much sharper images. This is particularly crucial for high-resolution imaging and precise spectroscopic measurements. Space telescopes like the Hubble Space Telescope have revolutionised our understanding of the universe by providing unobstructed views of distant galaxies, nebulae, and other astronomical phenomena.

Infrared telescopes play a crucial role in the study of star formation, primarily because they can observe the cold, dusty regions of space where stars are born. These regions are often obscured from optical telescopes by clouds of dust and gas. However, infrared radiation can penetrate these clouds, allowing astronomers to observe the processes occurring within.

Infrared telescopes detect the heat emitted by objects in these dense molecular clouds, revealing the presence of protostars – stars in their earliest stages of formation. They also help in studying the circumstellar disks, where planetary systems may be forming. Additionally, infrared observations contribute to understanding the chemical composition and physical conditions within these star-forming regions. By examining the infrared spectra, astronomers can identify various molecules and dust grains, providing insights into the conditions and materials that contribute to star formation. This information is vital for developing comprehensive models of how stars and planetary systems evolve from interstellar clouds.