Michelson interferometer works on the principle of interference, it is a common method for optical interferometry invented by an American physicist Albert Abraham Michelson. The light must be coherent and monochromatic; its frequency and waveform must be same and a single color of light. The beam light is traveled in such a way as to produce interference fringes which is an important aspect in the field of science and engineering. The word interferometer means to measure and analyze interference; interfer-o-meter corresponds to interference meter. Let us see how it works and learn more about it.
Principle: A beam of light splits into two parts and later recombined producing interference patterns.
In the given arrangement below, it is clear that a beam of monochromatic light originates from the source ‘S’ as shown in the figure. This beam of light is then allowed to fall on a glass plate which divides this ray into two parts. One of these rays is directed towards the mirror ‘M1’ and the other to ‘M2’. These rays are reflected from the mirrors and travels back towards the glass plate ‘G1’. Both the rays travels through ‘G1’ and finally enters the eye through the telescope. Both the waves superimpose each other resulting in the phenomenon of interference.
Now if the paths ‘L1’ and ‘L2’ are the same, then we will observe construction interference producing bright fringes which can be easily seen with the help of a telescope as shown in the figure. We can also change the length of the path ‘L1’ by moving the mirror ‘M1’ and as a result, we will observe both constructive and destructive interference.
Alternate Bright and Dark Fringes
If the mirror ‘M1’ is moved through a distance of ‘λ/4’ backward, then the path difference between the two light beams will be equal to ‘λ/4’ resulting in destructive interference producing dark fringes.
If the mirror ‘M1’ is further moved through a distance of ‘λ/4’, then the path difference between the two light beams will be equal to ‘λ’ resulting in constructive interference producing bright fringes.
In this way, if we move the mirror ‘M1’ slowly through a distance of ‘λ/4’ each time, bright and dark fringes will appear alternatively.
Determination of Wavelength
The wavelength of a given beam of light can be determined by the following procedure.
Let ‘m’ be the total number of observed fringes. Now if the mirror ‘M1’ is moved backwards through a distance of ‘λ/4’ each time. The total distance ‘P’ is given by,
P = m(λ/4 + λ/4)
P = mλ/2
λ = 2P/m —> (1)
Using equation (1), we can easily calculate the wavelength of any beam of light for the given values of ‘P’ and ‘m’.
Uses of Michelson Interferometer
• It is used to observe and study interference of light.
• It is used to calculate the wavelength of a light beam.
Michelson interferometer consists of the following parts and devices:
• Source of monochromatic light ‘S’
• Two plane mirrors ‘M1’ and ‘M2’
• Half slivered glass plate ‘G1’
• Glass plate (Compensator plate) ‘G2’
There are two parallel mirrors ‘M1’ and ‘M2’ respectively. The light beam from the source hits on the two parallel mirrors, some rays penetrates into the mirrors and some reflects back from the mirrors. Let the distance between the two parallel mirrors be ‘d’ and between the virtual images formed due to the two mirros be ‘2d’. θ is the angle of the incident ray. The path difference between the light beams will be different according to the angle of θ in the relation 2dcosθ. Maximum bright fringes are obtained when 2dcosθ = λn produces circular rings in front of the mirrors. The centre of the circle; the axis line along the circles, virtual images, and mirrors is directed towards the observer eye’s. This axis line is perpendicular to the centre of the circle, virtual images, and mirrors. Each circle’s ring corresponds quite to a particular angle θ. These fringes are also known as fringes of equal inclination.
The fringes formed in Michelson Interferometer may be straight, curved, or circular depending upon the nature of the film used.
Circular fringes are also called fringes of equal inclination and or Haidinger fringes. These fringes is beyond the scope of normal studies; it is studied in university levels.
Q1) What is the use of compensator plate in the Michelson Interferometer?
Ans: The light which is traveled through ‘G2’ two times each in outward journey and after reflection. Due to the double movement of the light beam through ‘G2’ which covers equal distance from both sides. That’s why ‘G2’ is also known as compensator plate.
Q2) Why are circular fringes produced in Michelson Interferometer?
Ans: Different types of fringes are produced in Michelson interferometer. Circular fringes or fringes of equal inclination is one of them which is usually produced due to the difference of nature in air film.