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Chapter 7: Interference of light. 2.Sports. Obstruction of an opponent, resulting in penalty. in·ter·fer·ence constructivedestructive 3.Physics.Superposition.

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Presentation on theme: "Chapter 7: Interference of light. 2.Sports. Obstruction of an opponent, resulting in penalty. in·ter·fer·ence constructivedestructive 3.Physics.Superposition."— Presentation transcript:

1 Chapter 7: Interference of light

2 2.Sports. Obstruction of an opponent, resulting in penalty. in·ter·fer·ence constructivedestructive 3.Physics.Superposition of two or more waves, resulting in a new wave pattern. 1.Life. Hindrance or imposition in the concerns of others.

3 HeNe laser

4 Radio City Rockettes, New York, NY

5 J.R. Stroop "Studies of interference in serial verbal reactions" Journal of Experimental Psychology 18: (1935). rood blauw oranje paars oranje blauw groen rood blauw paars groen rood oranje blauw rood groen paars oranje rood blauw groen rood blauw paars oranje blauw rood groen paars oranje rood blauw

6 Peacock

7 Soap bubbles

8 2-beam interference propagation distance from source of disturbance initial phase (at t =0) from superposition principle:

9 - Electric fields are rapidly varying ( ~ Hz) - Quickly averages to 0 -Instead of measuring E directly, measure radiant power density = irradiance, E e (W/m 2 ) = time average of the square of the electric field amplitude -Note: to avoid confusion, Pedotti 3 now uses the symbol I instead of E e Measuring interference

10 Irradiance at point P I1I1 I2I2 I 12 I =++ - when E 1 and E 2 are parallel, maximum interference - when orthogonal, dot product = 0; no interference

11 The interference term I 12 dot product of electric fields: simplify by introducing constant phases: use trigonometry: 2cosAcosB = cos(A+B) + cos(B-A) and consider again the time average: kills it

12 The interference term I 12 simplify by introducing : to yield the interference term of the irradiance:

13 Irradiance formula if E 1 E 2, then -where is the phase difference -for parallel electric fields

14 Interference mutually incoherent beams (very short coherence time) mutually coherent beams (long coherence time) constructive interference destructive interference maximum when cos = 1 minimum when cos = -1 = ( 2m ) = ( 2m+1 )

15 Interference fringes maximum when I 1 = I 2 = I = 4 !?!

16 Interference in time and space Youngs experiment wavefront division Michelson interferometer amplitude division

17 The double slit experiment (first performed in 1803)

18 Double slit experiment with electrons

19 Criteria for light and dark bands conditions for interference: - approximate arc S 1 Q to be a straight line - optical path difference = a sin constructive destructive m = 0, 1, 2, 3, …

20 Interference from 1 source: reflection Fresnels mirrors Lloyds mirror part of the wavefront is reflected off each mirror part of the wavefront is reflected; part goes direct to the screen

21 Fresnels mirrors as solar collectors

22 part of the incident light is refracted downward and part upward Interference from 1 source: refraction Fresnels biprism

23 Interference via amplitude division - thin films - oil slicks - soap bubbles - dielectric coatings - feathers - insect wings - shells - fish - …

24 Interference intermezzo

25

26 The Dancing Couple-1663-Jan Steen

27

28 Anatomy of a soap bubble

29 Soap bubble interference

30 optical path difference: = n f ( AB + BC ) = n f (2 t ) Thin film interference: normal incidence

31 = m : constructive interference = (m + ½) : destructive interference where m = 0,1,2,… Thin film interference: non-normal incidence optical path difference: = n f ( AB + BC ) – n 0 ( AD ) = 2 n f t cos t

32 Keep in mind the phase Simple version: phase of reflected beam shifted by if n 2 > n 1 0 if n 1 > n 2 Correct version: use Fresnel equations! hard reflection soft reflection

33 Summary of phase shifts on reflection TE modeTM mode air glass external reflection n 1 < n 2 TE modeTM mode air glass internal reflection n 1 > n 2 n1n1 n2n2 n1n1 n2n2

34 Back to the bubbles

35 How thick here (red band)? t n>1 180 o phase change 0 o phase change Constructive interference for 2t ~ (m + ½) At first red bandm = 0 t ~ ¼ (700 nm) Colors indicate bubble thickness

36 Bright: Colored monochromatic stripes occur at (1/4) for visible colors White: Multiple, overlapping interferences (higher order) Dark:Super thin; destructive interference for all wavelengths (no reflected light) pop! Dark, white, and bright bands

37 Multiple beam interference r, t : external reflection r, t: internal reflection Note: thickness t ! geometric series where is the phase difference

38 Multiple beam interference Introduce Stokes relations: r=-r and tt=1-r 2 and simplify to get: Irradiance:

39 Working through the math, youll arrive at: Multiple beam interference where I i is the irradiance of the incident beam Likewise for transmission leads to:

40 Fabry-Perot interferometer (1897) d This simulation was performed for the two sodium lines described above, with reflectivity and the separation of the mirrors increasing from 100 microns to 400 microns. simulation of two sodium lines: 1 = m 2 = m mirror reflectivity r = 0.9 mirror separation: m

41 Fabry-Perot interferometer where F is the coefficient of finesse: see chapter 8

42 Fabry-Perot interferometer: fringe profiles Michelson - transmission maxima occur when = 2 m - as r approaches 1 (i.e. as F increases), the fringes become very narrow - see Chapter 8 for more on Fabry-Perot: fringe contrast, FWHM, finesse, free spectral range

43 Constructive reflection 2d = (m+1/2)λm=0, 1, 2, 3... Destructive reflection 2d = mλ m=0, 1, 2, 3... Fringes of equal thickness

44 Newtons rings pattern depends on contact point: goal is concentric rings white-light illumination

45 Constructive reflection 2d = mλ m=0, 1, 2, 3... Destructive reflection 2d = (m+1/2)λm=0, 1, 2, 3... Oil slick on pavement

46 Glass: n = 1.5 MgF 2 coating: n = 1.38 To make an AR coating for = 550 nm, how thick should the MgF 2 layer be? Thin film coatings: anti-reflective

47 Broadband anti-reflective films

48 thin layers with a high refractive index n 1,interleaved with thicker layers with a lower refractive index n 2 path lengths l A and l B differ by exactly one wavelength each film has optical path length /4: all reflected beams in phase ultra-high reflectivity: % or better over a narrow wavelength range Multilayer mirrors

49 Anodized titanium

50 Natural multi-layer reflectors

51 Exercises You are encouraged to solve all problems in the textbook (Pedrotti 3 ). The following may be covered in the werkcollege on 5 October 2011: Chapter 7: 1, 2, 7, 9, 15, 16, 24


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