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Interferometry It deals with experimental study of the phenomenon of interference. Instruments used in this study are based on principle of interference and are called Interferometers. It deals with experimental study of the phenomenon of interference. Instruments used in this study are based on principle of interference and are called Interferometers. One of such interferometers was designed by Michelson and is known as Michelson Interferometer.

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Michelson Interferometer M1&M2 are highly polished mirrors placed perpendicular to each other. M1&M2 are highly polished mirrors placed perpendicular to each other. B&C are two glass plates placed parallel to each other at an angle of 45°.C is compensating plate. B&C are two glass plates placed parallel to each other at an angle of 45°.C is compensating plate. Plate B is half silvered Plate B is half silvered S is the source of light S is the source of light E is the eyepiece through which observer observes the fringes. E is the eyepiece through which observer observes the fringes.

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working 1) Path difference between interfering waves 1) Path difference between interfering waves Half of the light from source S falling on plate B is reflected towards M1 and other half is transmitted towards mirror M2. The two rays coming from M1& M2 interfere and fringes are formed. Half of the light from source S falling on plate B is reflected towards M1 and other half is transmitted towards mirror M2. The two rays coming from M1& M2 interfere and fringes are formed. The wave reflected from M1 crosses the plate B twice before entering the eyepiece twice while the other wave falling on mirror M2 travels totally in air. Hence an extra path 2(μ-1)t is introduced in first wave where t is the thickness of the plate and μ is the refractive index of the light wave. where t is the thickness of the plate and μ is the refractive index of the light wave.

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Role of compensating plate This extra path difference is compensated by another glass plate C.Thickness and material of this glass plate is same as that of plate B. So, this glass plate C is called Compensating plate. This extra path difference is compensated by another glass plate C.Thickness and material of this glass plate is same as that of plate B. So, this glass plate C is called Compensating plate. Now Light from M2 will also pass through the plate C twice and extra optical path 2(μ- 1)t produced in plate B is thus compensated by introduction of plate C. Now Light from M2 will also pass through the plate C twice and extra optical path 2(μ- 1)t produced in plate B is thus compensated by introduction of plate C.

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2) Phase change on reflection A phase change of π occurs on reflection at M1 and M2 both(Stoke’s Law).Further, the phase changes due to reflection from silver coating on plate B, in air and in glass are also equal to π each. Hence, the two emergant waves will interfere constructively or destructively according as the path difference(∆) between them is even or odd multiple of λ/2 i.e. A phase change of π occurs on reflection at M1 and M2 both(Stoke’s Law).Further, the phase changes due to reflection from silver coating on plate B, in air and in glass are also equal to π each. Hence, the two emergant waves will interfere constructively or destructively according as the path difference(∆) between them is even or odd multiple of λ/2 i.e. ∆ = (2n)λ/2 = nλ ; maxima ∆ = (2n)λ/2 = nλ ; maxima ∆ = (2n+1)λ/2 ; minima ∆ = (2n+1)λ/2 ; minima If plate B is unsilvered, then conditions of maxima & minima are:- If plate B is unsilvered, then conditions of maxima & minima are:- ∆ = (2n)λ/2 = nλ ; minima ∆ = (2n)λ/2 = nλ ; minima ∆ = (2n+1)λ/2 ; maxima ∆ = (2n+1)λ/2 ; maxima The observer sees a virtual image M2’ of M2.Therefore, one of the interfering beams comes by reflection from M1 & other from M2 as if it had come from M2’. The observer sees a virtual image M2’ of M2.Therefore, one of the interfering beams comes by reflection from M1 & other from M2 as if it had come from M2’.

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Adjustment of Michelson Interferometer Michelson Interferometer is said to be in normal adjustment when imageM2’ of M2 is exactly parallel to M1. In this case, the fringes would be concentric circles. To make this adjustment,the distances of mirror M1 and M2 from plate B is adjusted nearly the same. Michelson Interferometer is said to be in normal adjustment when imageM2’ of M2 is exactly parallel to M1. In this case, the fringes would be concentric circles. To make this adjustment,the distances of mirror M1 and M2 from plate B is adjusted nearly the same.

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When M1 &M2 are not exactly perpendicular to each other,two pairs of images (1,2),(3,4) are formed. When M1 &M2 are not exactly perpendicular to each other,two pairs of images (1,2),(3,4) are formed.

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M1&M2 are turned in proper direction until the pair of images coincide as shown in figure. M1&M2 are turned in proper direction until the pair of images coincide as shown in figure. The adjustment is said to be perfect if circular fringes do not expand or contract. The adjustment is said to be perfect if circular fringes do not expand or contract.

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Forms of fringes The fringes may be straight lines, parabolas, circles,ellipse depending on distance between M1 and M2’ and angle α between them. The fringes may be straight lines, parabolas, circles,ellipse depending on distance between M1 and M2’ and angle α between them.

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Circular fringes These fringes are produced when α=0 These fringes are produced when α=0 as shown in fig (a) & (c) as shown in fig (a) & (c) When M1and M2’ coincide the path difference becomes zero and field of view is perfectly dark as shown in fig (b) When M1and M2’ coincide the path difference becomes zero and field of view is perfectly dark as shown in fig (b)

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Localized fringes When M1& M2’ are inclined the air film is wedge shaped When M1& M2’ are inclined the air film is wedge shaped When M1 intersects M2’ in middle straight line fringes are observed. When M1 intersects M2’ in middle straight line fringes are observed. In other positions, the shape of fringes is curved-- convex towards thin edge of wedge as shown in figure. In other positions, the shape of fringes is curved-- convex towards thin edge of wedge as shown in figure.

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Determination of wavelength of monochromatic light by Michelson Interferometer: The mirrors M1 andM2 are adjusted so as to get a pattern of circular fringes. Telescope is focused on center of bright fringe.Then,mirrorM1 is displaced parallel to itself either in forward or in backward direction. In doing so, fringe pattern also gets shifted to one side in the field of view. The mirrors M1 andM2 are adjusted so as to get a pattern of circular fringes. Telescope is focused on center of bright fringe.Then,mirrorM1 is displaced parallel to itself either in forward or in backward direction. In doing so, fringe pattern also gets shifted to one side in the field of view. Corresponding to displacement d=λ/4 of the mirror,the path difference in interfering beams changes by 2d= λ /2 so that center of dark fringe will coincide with crosswire. Corresponding to displacement d=λ/4 of the mirror,the path difference in interfering beams changes by 2d= λ /2 so that center of dark fringe will coincide with crosswire.

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Let l be known distance through which mirror M1 is displaced and m the number of fringes which shift across the crosswire. Then change in path difference is 2l and Let l be known distance through which mirror M1 is displaced and m the number of fringes which shift across the crosswire. Then change in path difference is 2l and 2l=mλ 2l=mλ λ=2l/m λ=2l/m Thus the value of wavelength λ of monochromatic light can be determined by measuring l and counting m in the experiment. Thus the value of wavelength λ of monochromatic light can be determined by measuring l and counting m in the experiment.

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