Q. Describe the construction and working of Michelson Interferometer. Explain how you will determine the wavelength difference of two components of a line by Michelson Interferometer.
Explain the working of Michelson's interferometer. How circular fringes he produced with it.
Ans. Working of Michelson's Interferometer : Michelson designed an instrument for the measurement of wavelength of sodium light, thickness of thin film and for many applications. The instrument is based on principle of interference of light known as Michelson's Interferometer.
It is based on principle of interference of light by the way of division of amplitude. According to this the incident beam is divided into two parts and sent into two perpendicular directions and brought back together by using plane mirror to interfere each other.
A schematic diagram of Michelson's Interferometer is given in Fig.
Construction: It consists of two highly polished plane mirror M1 and M2, with two optically plane glass plate G1 and G2 which are of same material and same thickness. The mirror M1 and M2 are adjusted in such a way that they are mutually perpendicular to each other. The plate G1 and G2 are exactly parallel to each other and placed at 45° to mirror M1 and M2. Plate G1 is half silvered from its back while G2 is plane and act as compensating plate. Plate G1 is known as beam-splitter plate.
The mirror M2 with screw on its back can slightly titled about vertical and horizontal direction to make it exactly perpendicular to mirror M1. The mirror M1 can be moved forward or backward with the help of micrometer screw and this movement can be measured very accurately.
Working: Light from a broad source is made paralied by using a convex lens L. Light from lens L is made to fall on glass plate G1 which is half silver polished from its back. This plate divides the incident beam into two light rays by the partial reflection and partial transmission, known as Beam splitter plate. The reflected ray travels towards mirror M1 and transmitted ray towards mirror M2. These rays after reflection from their respective mirrors meet again at 'O' and superpose to each other to produce interference fringes. This firings pattern is observed by using telescope.
Functioning of Compensating Plate: In absence of plate G2 the reflected ray passes the plate G1 twice, whereas the transmitted ray does not passes even once. Therefore, the optical paths of the two rays are not equal. To equalize this path the plate G2 which is exactly same as the plate G1 is introduced in path of the ray proceeding towards mirror M2 that is why this plate is called compensating plate because it compensate the additional path difference.
Measurement of Wavelength of Monochromatic Light: Monochromatic Light is allowed to fall on plate G1. The M.I. is adjusted for circular fringes. For this mirror M1 is made exactly perpendicular to mirror M2 with the help of leveling screw and movable mirror M1 is moved in such a way so that G1M2 = G1M1.
Consequently circular fringes are observed when viewed through telescope.
Suppose the separation between real mirror M1 and image of mirror M2, M2' is such that a nth order dark ring is formed at the centre in the field of view. Thus the conditions for dark fringe at centre.
Formation of Circular Fringes: The shape of fringes in M.I. depends on inclination of mirror M1 and M2.
Circular fringes are produced with monochromatic light, if the mirror M1 and M2 are perfectly perpendicular to each other. In this position an image of mirror M2, M2' is formed due to half silvered polished plate G1, just below the mirror M1. The virtual image of mirror M2 and the mirror M1 must be parallel. Therefore it is assumed that an imaginary air film is formed in between mirror M1 and virtual image mirror M'2.
The interference pattern can be considered as the rays of light reflected, from the surface of mirror M1 (real) and mirror M2 (virtual). Therefore, the interference pattern will ve obtained due to imaginary air film enclosed between M1 andM'2.
From Fig. if the distance M1 and M2 and M'2 is'd', the distance between S'1 and S'2 will be 2D.
These circular fringes which are due to interference with a phase difference with a phase difference determined by the inclination '∂' are known as fringes of equal inclination.
Circular fringes can be seen by telescope because they are formed at infinity because they are formed due to two parallel interfering rays. When d becomes zero, the whole pattern becomes dark. Since a circular fringe is formed at the same inclination so they are called fringe of equal inclination and also called Haidinger's fringes.
Measurement of Difference in Wavelength of Sodium D1 and D2 Lines: For the measurement of difference in wavelength of two closely spaced sodium lines firstly the M1 is adjusted for circular fringes.
For this mirror M1 and M2 should be perpendicular to each other and optical path G1M1 and G2M2' should be equal.
Let the source have two wavelength ¥ and ¥2 (¥1>¥2), which are much closed to each other. Both the wavelength will form their separate fringe pattern but due to very small difference in wavelength both the pattern overlaps.
As the mirror M1 is moved slightly the two patterns separated out and when the path difference is such that the dark fringe ¥1 falls on the bright rings of ¥2 the result is maximum indistinctness. Now if mirror M1 is further move, a condition comes when dark fringe of ¥2, and the dark rings of ¥2j, (bright of ¥1 and ¥2) will overlap to each other. The result is maximum distinctness.
Let the mirror M1 is to be moved by a distance x between two successive positions of distinctness. In this position nth order fringe at ¥1 will overlap with the (n+1)th order of ¥2.