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Thermodynamics

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Types of Fringes

(i) Circular fringes: Circular fringes are produced with monochromatic light in a Michelson interferometer. Here, the mirror M₁ and the virtual mirror M₂’ which is the image of M₂ must be parallel.

The source is an extended one and S₁ and S₂ are the virtual images of the source due to M₁ and M₂’. If the distance M₁M₂’ is d, the distance between S₁ and S₂ = 2d. The path difference between the two beams will be 2d cos θ. Therefore, the rays for which 2d cos θ = nλ will reinforce to produce maxima. These circular fringes which are due to interference with a phase difference determined by the inclination θ are known as fringes of equal inclination or Haidinger’s fringes. When M₁ and M₂’ coincide, the path difference is zero and the field of view is perfectly dark.

When M₂’ is nearer the eye than M₁ the fringes are as shown in fig. b. When M₁’ is farther from eye than M₁ the fringes are as shown in fig. c

(ii) Localized fringes: When the mirror M₁ and the virtual mirror M₂’ (image of M₂) are inclined, the air film enclosed is wedge-shaped and straight line fringes are observed. The shape of the fringes observed for various values of the path difference are shown in fig. The fringes are perfectly straight when M₁ actually intersects M₂’ in the middle. (ii) In the other positions, the shape of the fringes is as shown in (i) and (ii). They are curved and are always convex towards the thin edge of the wedge. This type of fringes are not observed for large path differences.

(iii) White light fringes: With white light, the fringes are observed only when the path difference is small. The different colours overlap on each other and only the first few coloured fringes are visible. The central fringe is dark and the other fringes are coloured. After about 10 fringes are useful for the determination of zero path difference, especially in the standardization of the meter.