Michelson Interferometer
These fringes are concentric rings or straight line depending upon the mutual inclination of mirrors M1 and M2(M2' ). If mirrors M1 and M2 are parallel to each other the case similar to the air film between two parallel plate and fringes formed are concentric rings.
Michelson interferometer is used to determine the wavelength of monochromatic source, the difference between two wavelengths, determination of thickness/refractive index of thin transparent sheet. The experimental procedure is described below.
Determination of wavelength(
) (A) If the mirror M2 is not exactly perpendicular to mirror M1 (in this case mirror M1 and image M'2 of mirror M2 will not be exactly parallel), a wedge shaped air film is formed between M1 and M'2. The two reflected waves from M1 and M2 are no longer parallel but appear to diverge from some point near M1 (see fig) and are localised fringes.
Fig.D
These localized fringes are equidistant straight lines, parallel to the edge of wedge provided ‘d' is small so that variation in path difference is practically due to variation in film thickness only. If d is increased, the fringes will not be exactly straight due to some variation of path difference with the angle between M1 and M'2. In this case fringes
become convex towards the edge of wedge. If the separation between M1 and M'2 is decreased the fringes move across the field towards the thick part of wedge. As d is changed by 
, a new fringe crosses the center. At this time, fringes gradually become straighten.
Now if we change the position of movable mirror M2, then the path difference is changed. When the distance between the mirror is changed by 
, the next order bright ring appears at the center. Thus by recording the position of movable mirror and the number N of central bright rings moved, can determine 
using following relation.
where x is the difference between the position of movable mirror during which ‘n' new bright ring appear at the center.
Determination of difference in wavelength :When the light coming from the source consists of two closely spaced wavelength (such as D1 and D2 lines of sodium vapour lamp 
) each wavelength produces its own fringe pattern. When the separation between M1 and M'2 is small. The rings due to 
and 
almost coincide.
When separation ‘d' between the mirrors M1 and M'2 is increased the two rings patterns have different spacing (fringe width due to two are different) and rings of 
is gradually separated by those due to . At certain spacing ‘ d ' between mirrors, the dark ring of coincides with bright rings of 
and the rings have maximum indistinctness.
As the mirror M1 is moved further away ( d increases) the rings due to and become most distinct and indistinct periodically. Let x is the distinct by which the mirror M1 is moved for two consecutive situations when ring due to and are maximum indistinct. During the movement, n fringes of and fringes of have appeared at the center (only then dark ring of will again coincide with bright ring of ). Since each time mirror M1 is moved by , a new ring appear at the center hence,
or, 
and 
Since and are close together, 
product can be replaced by 
. Thus we have
knowing and x , we can determine the difference in wavelength of two very close wavelengths using michelson inferometer.