Yes. The ESO's VLT used the wobble method to detect Proxima Centauri b, a planet with a radius estimated at 0.8–1.5 R⊕ and a semi-major axis estimated at 0.0485 (+0.0041,−0.0051) AU, at a distance of 4.224 ly.
The Hubble Telescope can see the Proxima Centauri system's Sun.
The ground based VLT consists of four individual telescopes, each with a primary mirror 8.2 m across, they can achieve an angular resolution of about 0.001 arc-second. In single telescope mode of operation the angular resolution is about 0.05 arc-second.
Best case ground based conditions give a seeing disk diameter of ~0.4 arcseconds and are found at high-altitude observatories on small islands such as Mauna Kea or La Palma.
At the best high-altitude mountaintop observatories, the wind brings in stable air which has not previously been in contact with the ground, sometimes providing seeing as good as 0.4".
Under bad conditions a ground based telescope over 10 meters with poor seeing can limit the resolution to be about the same as given by a space-based 10–20 cm telescope.
Ground based telescopes must look through the atmosphere, which is opaque in many infrared bands (see figure of atmospheric transmission). Even where the atmosphere is transparent, many of the target chemical compounds, such as water, carbon dioxide, and methane, also exist in the Earth's atmosphere, vastly complicating analysis.
Existing space telescopes such as Hubble cannot study these bands since their mirrors are not cool enough (the Hubble mirror is maintained at about 15 degrees C) and hence the telescope itself radiates strongly in the IR bands.
The JWST telescope has an expected mass about half of Hubble Space Telescope's, but its primary mirror (a 6.5 meter diameter gold-coated beryllium reflector) will have a collecting area about five times as large (25 m^2 or 270 sq ft vs. 4.5 m^2 or 48 sq ft).
The JWST is oriented toward near-infrared astronomy, but can also see orange and red visible light, as well as the mid-infrared region, depending on the instrument.
JWST's primary mirror is a 6.5-meter-diameter gold-coated beryllium reflector with a collecting area of 25 m^2.
From the JWST FAQ:
At which wavelengths will Webb observe?
Webb will work from 0.6 to 28 micrometers, ranging from visible gold-colored light through the invisible mid-infrared. The short wavelength end is set by the gold coating on the primary mirror. The long wavelength cut-off is set by the sensitivity of the detectors in the Mid-Infrared Instrument.
How faint can Webb see?
Webb is designed to discover and study the first stars and galaxies that formed in the early Universe. To see these faint objects, it must be able to detect things that are ten billion times as faint as the faintest stars visible without a telescope. This is 10 to 100 times fainter than Hubble can see.
What are the main science goals of Webb?
Webb has four mission science goals:
- Search for the first galaxies or luminous objects that formed after the Big Bang.
- Determine how galaxies evolved from their formation until the present.
- Observe the formation of stars from the first stages to the formation of planetary systems.
- Measure the physical and chemical properties of planetary systems and investigate the potential for life in those systems.
How far will Webb look?
One of the main goals of Webb is to detect some of the very first star formation in the Universe. This is thought to happen somewhere between redshift 15 and 30 (redshift explained in question 45). At those redshifts, the Universe was only one or two percent of its current age. The Universe is now 13.7 billion years old, and these redshifts correspond to 100 to 250 million years after the Big Bang. The light from the first galaxies has traveled for about 13.5 billion years, over a distance of 13.5 billion light-years.
Will Webb see planets around other stars?
The Webb will be able to detect the presence of planetary systems around nearby stars from their infrared light (heat). It will be able to see directly the reflected light of large planets - the size of Jupiter - orbiting around nearby stars. It will also be possible to see very young planets in formation, while they are still hot. Webb will have coronagraphic capability, which blocks out the light of the parent star of the planets.
This is needed, as the parent star will be millions of times brighter than the planets orbiting it. Webb will not have the resolution to see any details on the planets; it will only be able to detect a faint light speckle next to the bright parent star.
Webb will also study planets that transit across their parent star. When the planet goes between the star and Webb, the total brightness will drop slightly. The amount that the brightness drops tells us the size of the planet. Webb can even see starlight that passes through the planet's atmosphere, measure its constituent gasses and determine whether the planet has liquid water on its surface. When the planet passes behind the star, the total brightness drops, and we can again determine more of the planet's characteristics.
Super short version: They're launching a slightly larger telescope than you have asked for that will reach ("detect", not provide close-up photos) virtually to the known edge of the universe.