The radio window is a range of frequencies of electromagnetic radiation that penetrate the Earth's atmosphere. It plays an important role in astronomy; up until World War II, astronomers could only use the visible and near infrared portions of the optical window for their measurements. With the development of radio telescopes however, the radio window became more and more utilizable, leading to the development of radio astronomy that provided astrophysicists with valuable observational data. Range Typically, the lower limit of the radio window's range has a value of about 15 MHz (λ ≈ 20 m); the best upper limit achievable from optimal terrestrial observation sites is equal to approximately 1 THz (λ ≈ 0.3 mm). Factors affecting lower and upper limits The lower and upper limits of the radio window's range of frequencies are not fixed; they depend on a variety of factors. Absorption of mid-IR The upper limit is affected by the vibrational transitions of atmospheric molecules such as oxygen (O2), carbon dioxide (CO2), and water (H2O), whose energies are comparable to the energies of mid-infrared photons: these molecules largely absorb the mid-infrared radiation that heads towards Earth. Ionosphere The radio window's lower frequency limit is greatly affected by the ionospheric refraction of the radio waves whose frequencies are approximately below 30 MHz (λ > 10 m); radio waves with frequencies below the limit of 10 MHz (λ > 30 m) are reflected back into space by the ionosphere. The lower limit is proportional to the density of the ionosphere's free electrons and coincides with the plasma frequency: where is the plasma frequency in Hz and the electron density in electrons per cubic meter. Since it is highly dependent on sunlight, the value of changes significantly from daytime to nighttime usually being lower during the day, leading to a decrease of the radio window's lower limit and higher during the night, causing an increase of the radio window's lower frequency end. However, this also depends on the solar activity and the geographic position. Troposphere When performing observations, radio astronomers try to extend the upper limit of the radio window towards the 1 THz optimum, since the astronomical objects give spectral lines of greater intensity in the higher frequency range. Tropospheric water vapour greatly affects the upper limit since its resonant absorption frequency bands are 22.3 GHz (λ ≈ 1.32 cm), 183.3 GHz (λ ≈ 1.64 mm) and 323.8 GHz