InterferometryInterferometry

It deals with experimental study of It deals with experimental study of the phenomenon of interference. the phenomenon of interference. Instruments used in this study are Instruments used in this study are based on principle of interference based on principle of interference and are calledand are called Interferometers Interferometers..

One of such interferometers was One of such interferometers was designed by Michelson and is designed by Michelson and is known as Michelson known as Michelson Interferometer.Interferometer.

Michelson Michelson InterferometerInterferometer

M1&M2 are highly M1&M2 are highly polished mirrors placed polished mirrors placed perpendicular to each perpendicular to each other.other.

B&C are two glass B&C are two glass plates placed parallel plates placed parallel to each other at an to each other at an angle of 45angle of 45°.C is °.C is compensating plate.compensating plate.

Plate B is half silveredPlate B is half silvered S is the source of lightS is the source of light E is the eyepiece E is the eyepiece

through which through which observer observes the observer observes the fringes.fringes.

workingworking 11) ) Path difference between Path difference between interfering wavesinterfering waves Half of the light from source S Half of the light from source S falling on plate B is reflected falling on plate B is reflected towards M1 and other half is towards M1 and other half is transmitted towards mirror M2. transmitted towards mirror M2. The two rays coming from M1& The two rays coming from M1& M2 interfere and fringes are M2 interfere and fringes are formed. formed. The wave reflected from M1 The wave reflected from M1 crosses the plate B twice before crosses the plate B twice before entering the eyepiece twice entering the eyepiece twice while the other wave falling on while the other wave falling on mirror M2 travels totally in air . mirror M2 travels totally in air . Hence an extra path 2(Hence an extra path 2(μμ-1)t is -1)t is introduced in first waveintroduced in first wave where t is the thickness of the where t is the thickness of the plate and plate and μμ is the refractive is the refractive index of the light wave.index of the light wave.

Role of compensating plateRole of compensating plate

This extra path difference is This extra path difference is compensated by another glass plate compensated by another glass plate C .Thickness and material of this glass C .Thickness and material of this glass plate is same as that of plate B. So, this plate is same as that of plate B. So, this glass plate C is called glass plate C is called Compensating Compensating plateplate . .

Now Light from M2 will also pass Now Light from M2 will also pass through the plate C twice and extra through the plate C twice and extra optical path 2(optical path 2(μμ-1)t produced in plate B -1)t produced in plate B is thus compensated by introduction of is thus compensated by introduction of plate C.plate C.

2) Phase change on 2) Phase change on reflectionreflection

A phase change of A phase change of ππ occurs on reflection at M1 and occurs on reflection at M1 and M2 both(Stoke’s Law).Further, the phase changes M2 both(Stoke’s Law).Further, the phase changes due to reflection from silver coating on plate B, in air due to reflection from silver coating on plate B, in air and in glass are also equal to and in glass are also equal to ππ each. Hence, the two each. Hence, the two emergant waves will interfere constructively or emergant waves will interfere constructively or destructively according as the path difference(destructively according as the path difference(∆)∆) between them is even or odd multiple of between them is even or odd multiple of λλ/2 i.e./2 i.e.

∆ ∆ = (2n)= (2n)λλ/2 = n/2 = nλλ ; maxima ; maxima ∆ ∆ = (2n+1)= (2n+1)λλ/2 ; minima/2 ; minima If plate B is unsilvered, then conditions of maxima & If plate B is unsilvered, then conditions of maxima &

minima are:-minima are:- ∆ ∆ = (2n)= (2n)λλ/2 = n/2 = nλλ ; minima ; minima ∆ ∆ = (2n+1)= (2n+1)λλ/2 ; maxima/2 ; maxima The observer sees a virtual image M2’ of The observer sees a virtual image M2’ of

M2.Therefore, one of the interfering beams comes by M2.Therefore, one of the interfering beams comes by reflection from M1 & other from M2 as if it had come reflection from M1 & other from M2 as if it had come from M2’.from M2’.

Adjustment of Michelson Adjustment of Michelson InterferometerInterferometer

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

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

M1&M2 are M1&M2 are turned in proper turned in proper direction until direction until the pair of images the pair of images coincide as shown coincide as shown in figure.in figure.

The adjustment is The adjustment is said to be perfect said to be perfect if circular fringes if circular fringes do not expand or do not expand or contract.contract.

Forms of fringesForms of fringes

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

Circular fringesCircular fringes These fringes are These fringes are

produced when produced when αα=0=0

as shown in fig (a) as shown in fig (a) & (c)& (c)

When M1and M2’ When M1and M2’ coincide the path coincide the path difference becomes difference becomes zero and field of zero and field of view is perfectly view is perfectly dark as shown in fig dark as shown in fig (b)(b)

Localized fringesLocalized fringes When M1& M2’ are When M1& M2’ are

inclined the air film inclined the air film is wedge shapedis wedge shaped

When M1 intersects When M1 intersects M2’ in middle M2’ in middle straight line fringes straight line fringes are observed.are observed.

In other positions, In other positions, the shape of fringes the shape of fringes is curved-- convex is curved-- convex towards thin edge of towards thin edge of wedge as shown in wedge as shown in figure.figure.

Determination of Determination of

wavelength ofwavelength of monochromatic light by monochromatic light by Michelson Interferometer:Michelson Interferometer: The mirrors M1 andM2 are adjusted so as to The mirrors M1 andM2 are adjusted so as to

get a pattern of circular fringes. Telescope is get a pattern of circular fringes. Telescope is focused on center of bright focused on center of bright fringe.Then,mirrorM1 is displaced parallel to fringe.Then,mirrorM1 is displaced parallel to itself either in forward or in backward direction itself either in forward or in backward direction . In doing so, fringe pattern also gets shifted to . In doing so, fringe pattern also gets shifted to one side in the field of view.one side in the field of view.

Corresponding to displacement d=Corresponding to displacement d=λλ/4 of the /4 of the mirror ,the path difference in interfering mirror ,the path difference in interfering beams changes by 2d= beams changes by 2d= λλ /2 so that center of /2 so that center of dark fringe will coincide with crosswiredark fringe will coincide with crosswire . .

Let l be known distance through Let l be known distance through which mirror M1 is displaced and m which mirror M1 is displaced and m the number of fringes which shift the number of fringes which shift across the crosswire. Then change in across the crosswire. Then change in path difference is 2l and path difference is 2l and

2l=m2l=mλλ

λλ=2l/m=2l/m Thus the value of wavelength Thus the value of wavelength λλ of of

monochromatic light can be monochromatic light can be determined by measuring l and determined by measuring l and counting m in the experiment.counting m in the experiment.