Interference- Michelson Interferometer. Interference lecture by Dr. T.Vishwam

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1 Interference- Michelson Interferometer Interference lecture by Dr. T.Vishwam

2 * Measurement of the coherence length of a spectral line * Measurement of thickness of thin transparent flakes * Measurement of refractive index of gases * Standardization meter Interference lecture by Dr. T.Vishwam

3 Principle: In Michelson interferometer, a beam of light from an extended source is divided into two parts of equal intensities by partial reflection and refraction. These beams travel in two mutually perpendicular directions and come together after reflections from plane mirrors. The beams overlap on each other and produce interference fringes Convex lens M2 M1 Adjustment screw source Observation screen Interference lecture by Dr. T.Vishwam

4 Experiment Principle M 2 Mirror d= d 2 d 1 M 1 ' Virtual image d 1 S d 2 M 1 Mirror G 1 Beam splitter G 2 Compensating plate Observation screen Interference lecture by Dr. T.Vishwam

5 Experiment Demonstration Path difference Δ = 2dcosѳ+λ/2 Δ= 2d+λ/2 Since d=(d 2 -d 1 ) Initially ѳ=0 If d=0 then Δ= λ/2 destructive interference If d=λ/4 then Δ= λ constructive interference If d=λ/2 then Δ= 3λ/2 destructive interference If d=3λ/4 then Δ= 2λ constructive interference Interference lecture by Dr. T.Vishwam

6 Experiment Demonstration Path difference Δ = 2dcosѳ+λ/2 Δ= 2d+λ/2 Since d=(d 2 -d 1 ) Initially ѳ=0 If d=0 then Δ= λ/2 destructive interference If d=λ/4 then Δ= λ constructive interference If d=λ/2 then Δ= 3λ/2 destructive interference If d=3λ/4 then Δ= 2λ constructive interference Interference lecture by Dr. T.Vishwam

7 Experimental set up

8 M 2 M 1 fix Image of M 1 x 1 x 2 Where d = x 1 ~ x 2 x 2 M 1 movable

9 Effective arrangement of the interferometer Circular fringes SPK

10 Source fix M 2 variable M 1 S S θ 2d S 2dcosθ observer d path difference in between two rays (travel) 2dcosθ= nλ n is maximum at the centre fix variable Circular fringes: Because of constant (equal) inclination Haidinger Fringes

11 Film coated plate Condition for dark 2dcosθ= (n + ½ ) λ Condition for bright 2dcosθ= nλ Where d = x 1 ~ x 2 Note: No additional phase change In OPTICS by Ghatak Plane glass plate Condition for bright 2dcosθ= (n + ½ ) λ Condition for dark 2dcosθ= nλ Note: Additional phase change of π

For d=0.3mm and λ=6 10-5 cm the bright fringes occur at θ = cos -1 (m/1000) = 0,2.56,3.62,4.44,5.13,5.73,6.28,.

15mm, the angles at which the bright rings occur will θ = cos -1 (m/500) = 0,3.62,5.13,6.28,7.25,.

12 For d=0.3mm and λ= cm the bright fringes occur at θ = cos -1 (m/1000) = 0,2.56,3.62,4.44,5.13,5.73,6.28,... m=1000,999,998,997,996,995,... For d=0.15mm, the angles at which the bright rings For d=0.15mm, the angles at which the bright rings occur will θ = cos -1 (m/500) = 0,3.62,5.13,6.28,7.25,... m=500,499,498,497,496,495,.. Thus as d reduces, the fringes will appear to collapse at the center and the fringes become less closely placed in figure(b).

Now, if d is slightly decreased, from 0.15 to 0.

disappear and the central fringe will become dark.

13 Now, if d is slightly decreased, from 0.15 to mm, then the bright central spot corresponding to m =500 would disappear and the central fringe will become dark. Thus, as d decreases, the fringe pattern tends to collapse toward the center. Conversely, if d is increased, the fringe pattern will expand.)

14 Compensating plate can be used to compensate additional optical path traveled by ray 1 inside beam splitter. Use of compensating plate is necessary for white light fringes. Compensator

15 WHITE-LIGHT FRINGES G R

16 To obtain circular fringes---the planes of mirrors M 1 and M 2 should be made perfectly perpendicular to each other.

17 Newton s Ring Michelson s Interferometer 2µt cos r=nλ variable fix fix 2dcosθ= nλ Variable (angle of incidence) Circular fringes because of locus of equal thickness of film Circular fringes because of equal inclination of light of incidence. Newton s ring have minimum order at the centre Michelson s interferometer have maximum order at the centre.

18 Applications 1: Determination of wavelength 2dcosθ= nλ For Normal incidence cosθ=1, Bright λ= 2 d / n If we shift the position of variable mirror by d (d 2 -d 1 = ), number of fringes n (n 2 -n 1 =1) will appear or disappear on the screen accordingly. Finally we can decide the wavelength of source.

$2. Determination of refractive index or thickness of a plate Inserting a plate in the optical path increases path difference by (µ-1)t.$

19 2. Determination of refractive index or thickness of a plate Inserting a plate in the optical path increases path difference by (µ-1)t. Hence, 2(µ-1)t= n λ Where n :number of fringes appeared or disappeared because of the insertionofthinglassplateinthepathofanyoneray. µ :refractive index of the plate

20 3: Difference between two neighboring spectral lines 2d = n λ = n λ If λ > λ and n = n, n = n Where, λ= wavelength d = separation between two position of distinctness 2d = n λ = (n + 1) λ (1) 1 2 nλ = nλ + λ n( λ λ ) = λ λ = ( λ λ ) 2 n (2) 1 2 Substituting in eq 1 2d λ λ 1 2 = λ 1 λ 2 λ λ 2d 1 2 λ1 λ 2 = = 2 λ 2d

22 15.9 In the Michelson interferometer arrangement, if one of the mirrors is moved by a distance 0.08 mm, 250 fringes cross the field of view. Calculate the wavelength. [Ans: 6400 Å] The Michelson interferometer experiment is performed with a source which consists of two wavelengths of 4882 and 4886 Å. Through what distance does the mirror have to be moved between two positions of the disappearance of the fringes? [Ans: mm]

23 15.11 In the Michelson interferometer experiment, calculate the various values of θ (correspondingtobrightrings)ford=5 10 3cm. Show that if d is decreased to cm, the fringe corresponding to m = 200 disappears. What will be the corresponding values of θ? Assume λ= cm.

24 measuring laser wavelength 2dcos d ϕ =k λ k=0,1,2, LL When k λ are invariable, with the decrease of d, ϕ decreases. Then radius of ring fringe of the same k order decreases, as appears that interference circles contract entad. Similarly with the increase of d, interference circles expand forth. If the fringes in the circle center contract entad or expand forth N times, the variation of optical path difference is 2 d=nλ, then we have λ = 2 d / N

Michelson Interferometer

Michelson Interferometer Objective Determination of the wave length of the light of the helium-neon laser by means of Michelson interferometer subsectionprinciple and Task Light is made to produce interference