A good starting point is to provide a good description of what an exoplanet is, an exoplanet can be defined as any planet that is outside our solar system that orbits another star. Prior to the 1990’s it would be rare to find physicists delegating on planets outside our own solar system, although their existence was theorised. As such the first ever detected exoplanet was in October of 1995, where the discovery of 51 Pegasi by Michel Mayor and Didier Queloz changed the course of astrophysics forever. Since then we have detected over 4,000 confirmed exoplanets have been discovered using various techniques of measurement. Now is the time for a new era in astrophysics where better telescopes and equipment are needed detect these exoplanets more reliably with greater detail. The James Webb Space Telescope (JWST) provides an answer to this, the leading frontier in infrared photometry, the JWST will be the successor to the Hubble telescope. The current diameter of the Hubble telescope is 2.4m, compared to the JWST which is 6.5m, which will roughly improve the light gathering power by 6.25 times that of the Hubble [1].

A picture of the JWST.
The JWST will improve on current exoplanet detection methods which are summarised in the following video:
Two and a half decades after the discovery of 51 Pegasi b and we have now found over 4200 exoplanets, with many more awaiting confirmation [2].

Total confirmed number of exoplanet detections per year.
The numbers of detected exoplanets are only going to increase with the introduction of the JWST as it will be a far greater improvement in infra-red telescope optics. This improvement will allow us to see regions previously obscured by dust and gas in the visible spectra enhancing the telescoped practicality and increasing the amount of data available.
This improvement in space-based infra-red photometry by upgrading from the Hubble Telescope to the JWST does not come at a small cost. The initial outline in 2003 suggested that the JWST would cost around $900 million USD, then later updated in 2006 the budget was set to be $4.5 billion USD, then finally in 2018 the final cost of the project is set to be around $9.66 billion USD [3]. A very costly project to say the least, but is it worth it? Well, some of the long-term goals for exoplanet detection for the JWST include: developing of theories on planetary formation so that we can understand key fundamentals of the Universe and our own planetary system, search for extra-terrestrial life, and most importantly will develop the backbone for information regarding the human races first trips outside the solar system, including various space probes and landers. This alone will save billions of dollars in the future, a more than worth wile investment.
If you find exoplanets and their detection interesting to you, be sure to head over to “About Me”, where you will be able to find more information about myself and my research, as well as my LinkedIn profile with my email address, where you can get in touch with me if you have an interest in exoplanets and want to learn more.
References - Are located after information from sources are used, I have hyperlinked them to [1], [2], and [3] found in the paragraphs above. The text under the images are also hyperlinks to the sources of the image.