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The **Michelson interferometer** is a precision instrument that generates interference fringes by dividing a coherent light beam into two separate paths and then recombining them after they have traveled different optical paths. It is also a beam division interferometer, splits light beam into two or more segments. The setup consists of two mirrors, a beam splitter and a compensating plate. It was Albert A. Michelson, an American physicist, who invented this amplitude-splitting device in 1890. It remains an important tool in modern laboratories and is commonly employed to measure the wavelength of unknown light sources, detects extremely small distances, and investigate the properties of optical media.

**Construction of Michelson Interferometer**

Michelson interferometer consists of three mirrors: two reflectors (highly polished mirrors) M_{1} (fixed) & M_{2} (movable), a beam splitter (semi-transparent mirror) and a compensatory glass plate as given in Figure 1. M_{1} and M_{2 }are placed at different distances from the beam splitter. The mirrors are aligned in such a way that the beam reflects directly back along the path from which it came. The beam splitter and the compensatory glass plate are placed parallel to each other between the mirrors at an angle of 45°. The opposite side of the beam splitter is semi-silvered such that the light from the source is equally reflected and transmitted by it, which paves the way for the division of amplitude.

**Working of Michelson Interferometer**

When light from a monochromatic source, passes through the beam splitter, it generates two beams that are perpendicular to each other with equal intensity. Half of the light falling on the beam splitter is reflected towards the mirror M_{1}, where it is reflected back through the beam splitter to the observer. As depicted in Figure 2, the transmitted half of the original beam is reflected back by the mirror, M_{2}, and then traverses towards the observer by the beam splitter. As the beams reunite at the beam splitter, the coherent beams interfere with each other either constructively or destructively and fringes can be observed.

Let’s consider, the beam reflected by the beam splitter and M_{1} as beam A and the beam transmitted through the beam splitter and reflected by M_{2} as beam B.

Beam B traverses the thickness of the beam splitter thrice whereas beam A traverses the beam splitter only once. This introduces an extra optical path for beam B even when M_{1} and M_{2} are at the same radiation distance from the beam splitter.

To compensate this extra optical path, a compensating plate is introduced between the beam splitter and M_{1}. The compensating plate is a transparent glass block identical to the beam splitter (without the silver coating). Any phase difference between the two beams is due solely to the difference in the distances they travel when the compensating plate is in place.

**Interference**

The type of interference depends on the relative phase of each of the combining light beams. This is determined by the path length difference, 2d_{1} - 2d_{2}, where d_{1} is the distance between the beam splitter and M_{1}, and d_{2} is the distance between the beam splitter and M_{2}.

The phase difference in the Michelson interferometer arises from the path difference between the two arms of the interferometer. Also, there is an additional phase difference of π because beam B undergoes internal reflection at the beam splitter whereas beam A undergoes external reflection.

Thus the phase difference is given by:

Where m is the order of the fringe = 0,1,2,…

θ_{m} is the angle of the m^{th} order fringe and λ is the wavelength of the incoming light.

**Constructive Interference**

With constructive interference, the wave amplitudes get added to produce a maximum intensity beam and a bright image is observed. The condition for maximum constructive interference as shown in Figure 4 is

When the path length difference is an integer multiple of the wavelength, the recombining light beams will be in phase as they both come from the same source. The amplitude of the combined beam will be the sum of the amplitudes of the individual beams.

**Destructive Interference**

Conversely, with destructive interference, if the phases of the two beams are such that they destructively interfere, the recombined beams will cancel each other out.

The condition for maximum destructive interference as shown in Figure 5 is

When the path length is an odd half integer multiple of the wavelength, the recombining light beams will be exactly out of phase. The amplitude of the combined beam will be the difference between the amplitudes of the individual beams. Additionally, if the beams have equal amplitudes when split, the combined beam will have zero amplitude.

**Applications of Michelson Interferometer**

The Michelson interferometer is one of the most widely used types of interferometers. Some of the applications of Michelson interferometers include:

- Measuring the speed of light
- Measuring small displacements, such as the distance between two mirrors or the thickness of a thin film
- Measuring the refractive index of a material
- Detecting gravitational waves
- Studying the properties of surfaces, such as roughness and flatness
- Analyzing the spectra of light sources, including stars and gases
- Measuring the Doppler shift of light from moving objects
- Testing the validity of the theory of relativity
- Developing and testing optical components and systems, such as mirrors and lenses
- Studying the properties of atoms and molecules using laser light.