Interferometers are a physical phenomenon studied unto themselves and have an additional purpose of being sensitive detectors, specifically used for the Laser Interferometer Gravitational Wave Observatory (LIGO) to detect gravitational waves from supernovae. An interferometer was first used in the classical optics Michelson-Morley experiment in which researchers sought to detect 'aether' flow, the movement of the aether within they thought light travelled. The experimental setup consisted of a single incoming beam of light incident on a beam splitter. The beam splitter passed half of the incident beam through itself (the transmitted beam) toward a mirror and the other half was reflected (the reflected beam) toward another mirror. The beam paths were orthogonal and referred to as the "arms" of the interferometer. At each mirror, the beam was reflected back toward the beam splitter, and at the beam splitter the beams were reunited, or "superimposed" upon each other to create one output beam. The output beam tells us about the relative properties of the transmitted and reflected beams. Because of light's wave nature, there are three possibilities for the output beam. If the output beam is twice as bright as either the transmitted or reflected beams, total constructive interference has occurred by the crests and troughs of each wave aligning as they overlap to create the output beam. If the output beam is nonexistent, total deconstructive interference has occurred by crest-trough and trough-crest alignment when the two beams overlapped. Crest-crest interactions and trough-trough interactions yield brighter beams at the interaction locations. Crest-trough and trough-crest interactions cancel each other out at the interaction locations. The most likely option to occur is both constructive and deconstructive interference, in which crest-crest, trough-trough, and crest-trough interactions all partially occur. This is observed as an alternating pattern of areas of light and dark at the output beam, referred to generally as wave interference fringes.
In application, LIGO exploits the wave nature of light in interferometers by making arm lengths 4km long and in making mirrors as reflective as possible in order to confirm through detection the presence of gravitational waves. Gravitational waves are literal ripples in the fabric of spacetime caused by massive energy events, such as a supernovae, which occur when a star explodes and radiates all of its energy into its environment, spacetime. LIGO operates on the assumption that if such waves exist, they will propagate to Earth and cause minor disruptions in the spacetime surrounding us. Interferometers are used to detect these disruptions by having freely mounted mirrors at the end of the interferometer arms. Mirrors are suspended from mounts in a setup similar to a pendulum. If a gravitational wave disrupts the spacetime near the mirror, this will be detectable through an infinitesimal change in position of the mirror and thus a correspondingly small change in the arm length of the mirror. Changing the arm length of the mirror changes how the light interacts when recombined at the output beam, and this is observable through a change in the fringes.