Let’s Do Physics
Michelson Interferometer:
The Michelson interferometer is the best example of what is called an amplitude-splitting interferometer. It was invented in1893 by Albert Michelson, to measure a standard meter in units of the wavelength of the red line of the cadmium spectrum. With an optical interferometer, one can measure distances directly in terms of wavelength of light used, by counting the interference fringes that move when one or the other of two mirrors are moved. In the Michelson interferometer, coherent beams are obtained by splitting a beam of light that originates from a single source with a partially reflecting mirror called a beam splitter. The resulting reflected and transmitted waves are then re-directed by ordinary mirrors to a screen where they superimpose to create fringes. This is known as interference by division of amplitude. This interferometer, used in 1817 in the famous Michelson- Morley experiment, demonstrated the non-existence of an electromagnetic-wave-carrying ether, thus paving the way for the Special theory of Relativity.
Light from a monochromatic source S is divided by a beam splitter (BS), which is oriented at an angle 45° to the beam, producing two beams of equal intensity. The transmitted beam (T) travels to mirror M1 and it is reflected back to BS. 50% of the returning beam is then reflected by the beam splitter and strikes the screen, E. The reflected beam (R) travels to mirror M2, where it is reflected. 50% of this beam passes straight through beam splitter and reaches the screen.
Since the reflecting surface of the beam splitter BS is the surface on the lower right, the light ray starting from the source S and undergoing reflection at the mirror M2 passes through the beam splitter three times, while the ray reflected at M1 travels through BS only once. The optical path length through the glass plate depends on its index of refraction, which causes an optical path difference between the two beams. To compensate for this, a glass plate CP of the same thickness and index of refraction as that of BS is introduced between M1 and BS. The recombined beams interfere and produce fringes at the screen E. The relative phase of the two beams determines whether the interference will be constructive or destructive. By adjusting the inclination of M1 and M2, one can produce circular fringes, straight-line fringes, or curved fringes. This lab uses circular fringes.
measurement of wavelength:
Using the Michelson interferometer, the wavelength of light from a monochromatic source can be determined. If M1 is moved forward or backward, circular fringes appear or disappear at the centre. The mirror is moved through a known distance d and the number N of fringes appearing or disappearing at the centre is counted. For one fringe to appear or disappear, the mirror must be moved through a distance of λ/2. Knowing this, we can write,
so that the wavelength is,
Applications
1. The Michelson – Morley experiment is the best known application of Michelson Interferometer.
2. They are used for the detection of gravitational waves.
3. Michelson Interferometers are widely used in astronomical Interferometry.
From the screen, an observer sees M2 directly and the virtual image M1′ of the mirror M1, formed by reflection in the beam splitter, as shown in Fig. 3. This means that one of the interfering beams comes from M2 and the other beam appears to come from the virtual image M1′. If the two arms of the interferometer are equal in length, M1′ coincides with M2. If they do not coincide, let the distance between them be d, and consider a light ray from a point S. It will be reflected by both M1′ and M2, and the observer will see two virtual images, S1 due to reflection at M1′, and S2 due to reflection at M2. These virtual images will be separated by a distance 2d. If θ is the angle with which the observer looks into the system, the path difference between the two beams is 2dcosθ. When the light that comes from M1 undergoes reflection at BS, a phase change of π occurs, which corresponds to a path difference of λ/2.
Source
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