An interferometer is an instrument that uses interference phenomenon in the measurement of the wavelength of light in terms of standard of length or the measurement of distance in terms of the known wavelength of the light.

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## Michelson Interferometer Construction and Working

**Michelson Interferometer Principle**

In this instrument, light from an extended source is divided into two parts by partial reflection and transmission. These two beams are sent at right angles to each other in the two directions. They get reflected from the mirror and form interference fringes which are observed and investigated.

**Construction of Michelson Interferometer**

It consists of a semi silver plate P placed at an angle of 45 degrees to the horizontal. M1 and M2 are two highly polished silver mirrors. These Mirrors are provided with a labeling screw at the back.

Mirror M1 can be moved towards or away from plate P with the help of micrometer screws. P1 is another glass plate whose thickness is exactly equal to the thickness of plate P.

It is transparent and parallel to P. S is a monochromatic source of light, say sodium lamp. Lens L is a Converging lens whose function is made to the source of light as an extended one.

**Michelson Interferometer Working**

Light from an extended monochromatic source S rendered parallel by the lens L is made to fall on semi-silvered plate P. Here, the light is divided into a reflected and transmitted beam of equal intensity.

The reflected beam which falls on mirror M1 and the transmitted beam that falls on mirror M2 is incident normally. When the Apparatus is in normal adjustment.

After reflection from mirror M1 and M2, a part of the amplitude of the wave from M1 is transmitted along with AE. While a part of the amplitude of the wave from M2 is reflected along with AE.

As these two waves entering the telescope are derived from the same source S, hence these waves are coherent waves.

Coherent waves interfere with each other and interference fringes formed and seen through the telescope. The ray which gets reflected from M1 crosses the plate P twice while the ray which from M2 Travels only in the air.

This means that the ray which travels along the mirror M1 covers an additional part 2 (n-1) t. Where t is the thickness of the plate P and n is its refractive index.

Which does not get any difficulty if we are using monochromatic light but if white light is used. Then it does create a problem because of the variation of n with wavelength.

To overcome this difficulty another plate P1 is introduced between P and mirror M2. This plate P1 is called a compensating plate.

The plate P and P1 are of equal thickness being cut from a single optical plane parallel plate to ensure the equality of thickness and the nature of the material.

The function of the compensating plate is that the Ray of light traveling towards M1 and M2 must travel equally** pass through the glass plate. **

The phase changes on reflection at mirror M1 and M2 are smaller, the phase changes due to reflection in air and class are also similar, is equal to **π. **The two rays reaching the telescope interfere constructively or destructively depending upon the path difference.

The path difference between the two rays reaching the telescope is m**λ. Where M is the integer and λ is the wavelength of light used.** Then constructive interference takes place.

On the other hand, if the path difference is (2m+1) **λ/2, **Then destructive interference occurs. The path difference between the two beams AM1A and AM2A can be altered by moving mirror M1.

**Formation of Fringes**

**When we see through the telescope, the mirror M1 is seen directly and a virtual image of M2 is also seen in M1. **If the distance of M1 and M2 from plate P are not exactly equal, the image of M2 is formed slightly ahead or at the back of M1.

Thus the system reduces to the equivalent of an air film and enclosed between the mirror M1 and the virtual image of M2.

Now to see whether both the mirrors are at right angles to each other or not, a pin is placed between the source as and the plate P. Looking along EA, two images of the pin are seen.

The Adjustment of mirror M2 is made with the help of three screws such that both the images of the pin coincide. Which means both the mirrors are at right angles to each other.

The pin is now removed. Now if the distance AM1A and AM2A are exactly equal the field of view shall be totally dark. A slight movement of mirror M1 forward or backward shall produce concentric circular fringes in the field of view.

**Types of fringes in Michelson Interferometer.**

The shape of the fringes formed in the michelson interferometer depends on the inclination between mirror M1 and M2. Let M2 be the virtual image of mirror M1 as S’ be the image of source S.

Let D be the separation between mirror M1 and the virtual image M2’ of the mirror M2. Therefore, the interference pattern formed will be due to air film enclosed between M1 and M2’. Let S1’ and S2’ be the images of the Saras M1 and M2 respectively.

It means, we have two coherent sources S1’ and S2’ to obtain due to the process of the division of amplitude.

**Circular Fringes**

If the mirror M1 and M2 are exactly at right angles, then the mirror ember and the image M2’ two of the mirror M2 are parallel to each other.

Then circular fringes are formed. Let D be the distance of mirror M1 and mirror M2 from the plate P then the distance between M1 and M2’ who is also d. It means, the thickness of air film enclosed between M1 and M2’ is d as shown in the figure.

However, the distance between two coherent sources S1’ and S2’ is 2d. The path difference between the rays coming from S1’ and S2’=2d cos**θ. **Where **θ** is the angle of inclination of the ray Falling On The Mirror.

**Localised Fringes**

When mirrors M1 and M2’ are not exactly parallel or not equally distant, a wedge-shaped film is formed between them. The path of two reflected rays, originating from the same incident ray why reflection from M1 and M2’ you are no longer parallel.

They intersect near M1 and hence the fringes are formed near M1. The fringes are called localized fringes and to see them the eye must be focused on the vicinity of M1.

These fringes are curved with their convex side toward the thin edge of the wedge as shown in the figure. The thin edge of the wedge is to the left and therefore the observer fringes are convex toward the left.

As we go on decreasing the separation between M1 and M2’, the fringes move across the field of view away from the thin as of the wedge and at the same time gradually become straight. When M1 and M2’ intersect, the lines are perfectly straight as shown in the figure.

We have to wedges opposing each other so the line should appear curved on both sides of the intersection but for a small field of view, they appear straight. When M1 is still moved such that the mirror M1 and the virtual image M2’ of mirror M2 get a position as shown in the figure.

The fringes are again curved but with their convex side towards the right. Localized fringes become invisible for large path differences of the order of several millimeters.

**White Light Fringes**

If monochromatic light is replaced by white light, its constituent wavelength gives rise to its own set of fringes two different widths. The zero-order fringes corresponding to each wavelength will coincide and hence we get a dark central fringe.

But if the path difference between the interfering rays is considerable. The central fringe will be surrounded by a few colored fringes. And then there will be so much overlapping that the pattern appears to be white.

The importance of these white light fringes is that the position of zero-order fringe which is dark can be located very easily in the Michelson interferometer.

**Applications of Michelson Interferometer**

**Michelson Interferometer is used to determine:**

- Wavelength of monochromatic light.
- The refractive index of a thin film.
- Resolution of spectral lines.
- The evolution of meters in terms of the wavelength of light.
- The angular diameter of stars.
- Presence of ether.
- The accuracy of the surface of the prism and lens.

**FAQ on Michelson Interferometer** construction and working.

### Types of fringes in Michelson Interferometer.

1. Circular Fringes.

2. Localised Friges.

### How does interferometer work?

In this instrument, light from an extended source is divided into two parts by partial reflection and transmission. These two beams are sent at right angles to each other in the two directions. They get reflected from the mirror and form interference fringes which are observed and investigated.

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