It is an instrument used for the measurement of various quantities like wavelength of monochromatic light, thickness & refractive index of thin sheets, diameter of thin wires, refractive index of gases etc.

Construction

Michelson interferometer consists of two optically plane & highly polished mirrors M₁ & M₂ which are silvered on front surfaces and are perpendicular to each other. G₁ & G₂ are two optically plane glasses of same material and thickness. They are kept inclined at 45^o with M₁ & M₂.

The back surface of G₁ is partially polished, so that the light falling on it is divided into two beams of equal intensity, one transmitted towards mirror M₂ and other reflected towards M₁.Planes of M₁ & M₂ can be tilted using three leveling screws at their back. M₁ can be forward and backward using a micrometer screw. T is the telescope to receive the light from the glass plate G₁.

Working

        Light from an extended monochromatic source of light S is rendered parallel using a convex lens. The beam of light fall on G₁ which is partially polished so that the light falling on it is divided into two beams of equal intensity, one transmitted towards mirror M₂ and the other reflected towards M₁. The two mirrors M₁ and M₂ return the light to G₁ which are coherent so they interfere and produce clear interference fringes. The fringes can be observed through the telescope. Since the reflection at G₁ occurs at the rear surface, the light reflected at M₁ will pass through G₁ three times while the light reflection at M₂ will pass through G₁ only once. For this reason a compensating plate G₂ identical to G₁ is introduced in the path of OM₂ so that OM₂ also travels twice through G₂. Hence G₂ is called the compensating plate.   

M₂’ is the position of the reflected image (virtual image) of the mirror M₂, from the glass plate G₁. Hence the two interfering beams appear to come from M₁ & M₂’. Therefore Michelson interferometer is equivalent to an air film enclosed between two mirrors M₁ & M₂’.

Before traveling towards the telescope T, ray OM₂ get reflected at the back of the plate G₂, in a denser medium. This introduces a phase change of П or a corresponding path difference of l/2 on the ray OM₂.

The interference fringes obtained ma be circular, straight, or curved depending on the thickness of the air film, the angle between the planes M₁ & M₂ and the ale of inclination of the rays of the light.

Types of Fringes

1)    Circular Fringes (Haidinger Fringes)

When mirrors M₁ & M₂ are perpendicular to each other then M1 & M₂’ are parallel. Therefore the system is equivalent to a thin film of air enclosed between the mirrors. The rays of light falling from an extended source fall at different angles, but the ray of light falling at the same inclination but at different parts travel parallel to one another after reflection and are brought to focus along a circle by the objective of the telescope. Hence a circular fringe is obtained whose centre is the principal focus of the objective of the telescope. These fringes are called fringes of equal inclination o haidinger fringes.

2)   Localized fringes

When one of the two mirrors M₁ or M₂ is slightly tilted then M₁ & virtual image M₂’ are slightly inclined. Now the air film enclosed is wedge shaped. Since an extended source is used the path difference change due to the difference in the thickness of the air film and also the angle of inclination of rays of light. This causes the fringes to appear concave towards the thicker part of the wedge. If the path difference is small the fringes appear as straight and parallel to the line of intersection of M₁ & M₂’.

        If M₁ & M₂’ intersect at the middle the fringes are straight and parallel. The zero order fringe corresponding to zero path difference lies along the line of intersection of M₁ & M₂’ and is exactly straight.

3)   White light fringes

When white light is used, the zero order fringes are white because the path difference is zero for all wavelengths. On ether side of the central white fringe colored fringes are observed. The fringes of shorter wavelength on inner side. In the outer part of the field of view colored fringes overlap and disappear to form uniform white light. The significance of central white fringe indicates the position of the mirror M1 for zero path difference and also shows that M₁ & M₂’ have actually intersected.

Visibility of fringes

        Michelson defined the visibility of friges by the relation

V= ( I_max-I_min ) / ( I_max+I_min )

Where I_max – intensity of bright fringe

            I_min – intensity of a dark fringe

        For a monochromatic source of light Imin i.e. in the dark fringe is perfectly dark. Therefore the visibility is unity for monochromatic light and is constant over the field of view. The fringes are clearly visible when monochromatic light is used.

        If the source light is not monochromatic, it contains two slightly different wavelengths l₁ & l₂ fringes for both wavelengths are observed. When mirror M₁ is slowly moved, for  certain distances (d) between M₁ & M₂’ the path difference is an integral multiple of both the wavelengths. Then bright fringes of l₁ coincide with bright fringes for l₂. Therefore the visibility of fringes is maximum.

        But for the intermediate vales of the path difference the visibility decreases i.e. at some position the bright fringes for one wavelength may fall on the dark fringe for the other wavelength. Then fringes disappear and uniform illumination is observed. If l₁=l₂, the visibility of fringes is equal to zero. If l₁¹l₂, the minimum visibility is zero.

        Hence if visibility of fringes varies when M₁ is move, we can conclude that the source of light is not monochromatic.

        If a₁ & a₂ are the amplitudes of the waves, the minimum visibility is  V = ( a₁²-a₂² ) / (a₁² + a₂²)