Michelson's Interferometer

August 07, 2024

Michelson's Interferometer

The Michelson interferometer was invented by an American physicist A.A.Michelson (1852-1931). The Michelson interferometer played an interesting role in the history of science during the latter part of the nineteenth century. It has a great scientific importance and had an equally important role in establishing high precision standards of the unit of length. In contrast to the Young's double slit experiment for producing interference fringes which make use of light from two narrow sources, the Michelson interferometer uses light from broad, spread source (extended source).

The essential features of a Michelson interferometer are shown schematically in figure given below:

Fig Schematic diagram of Michelson Interferometer

Michelson interferometer consists of two highly polished plane mirrors M1 and M2. The mirror M1 is fixed where as the mirror M2 is moveable as shown in the above figure. In addition to this, it has glass plate C which has a thin coating of silver on its right side. This partially silvered plate is called beam splitter and is inclined at 45° relative to the incident light beam. It has also another plate D which is identical to the plate C except it is not silvered. Its purpose is to ensure that the beam I and II pass through the same thickness of glass. Therefore it is known as compensating plate. This is particularly important when white light fringes (colored fringes) are desired.
A monochromatic beam of light from an extended source of light falls on the half silvered plate C. Part of the light is reflected from the silver surface of the beam splitter C (at the point P) to the moveable mirror M2. After reflection at M2 it returns to the observer eye through the plate C. The remaining part of the light passes through silvered surface of the plate C, continues its journey passes through the compensating plate D and finally falls on the fixed mirror M1. The light is reflected back from the fixed mirror M1. It passes through the compensating plate D on its return journey and finally it is incident on the silvered surface of the plate C from where it is reflected to the observer's eye as shown in the figure. After reflection from mirror M1 and M2, the two beam eventually recombine to produce an interference pattern which can be viewed.

The interference pattern for the two beams is determined by the difference in their path lengths L1 and L2. When the two beams are viewed , the virtual image (say M1') of mirror M1 is formed by reflection at the silvered surface of plate C coincides with the mirror M2 provided L1 is exactly equal to L2 and the mirror M1 and M2 are kept exactly at right angles. If L1 and L2 are not exactly equal the image of the mirror M1 is displaced slightly from M2 (still parallel to one another) and if the angle between the mirrors is not exactly 90° the virtual image M1' of the mirror M1 makes a slight angle with M2. Under this situation the mirror M2 and the virtual image M1' of the mirror M1 behave in the same manner as the two surfaces of a thin film and the same sort of interference fringes result from the light reflected from these surfaces. The effective thickness of the air film is varied by moving mirror M2 parallel to itself. Under these conditions, the interference pattern is a series of bright and dark rings, if the extended source is monochromatic. If a dark ring appears at the centre of the interference pattern, the two beams interfere constructively.

Suppose then extended source is monochromatic of wavelength λ and the mirror M2 is then moved a distance λ/4, the path difference changes by λ/2 (twice the separation between M2 and M1) a dark ring will appear again at the center of the interference pattern. Thus successive dark and bright rings are formed each time M2 is moved a distance λ/4. The wavelength of light used is then measured by counting the number of fringes shift for a given displacement of the mirror M2. If the displacement is represented by d then,

$d=m\; \frac{\lambda }{2}\; \; \; or\; \; \; \lambda =\frac{2d}{m}$

If m is several thousand, the displacement d is large enough so that it can be measured with good precision, and hence a precise value of the wavelength λ can be determined.

Interference fringes in Michelson Interferometer .

Michelson measured the length of standard metre in terms of the wavelength of red cadmium light and showed that the standard metre was equivalent to 1,553,163.5 wavelengths of this light.

The Michelson Interferometer