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Young ’ s Experiment. 2 Coherence 35- Two sources to produce an interference that is stable over time, if their light has a phase relationship that does.

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Presentation on theme: "Young ’ s Experiment. 2 Coherence 35- Two sources to produce an interference that is stable over time, if their light has a phase relationship that does."— Presentation transcript:

1 Young ’ s Experiment

2 2 Coherence 35- Two sources to produce an interference that is stable over time, if their light has a phase relationship that does not change with time: E(t)=E 0 cos(  t+  ) Coherent sources : Phase  must be well defined and constant. When waves from coherent sources meet, stable interference can occur - laser light (produced by cooperative behavior of atoms) Incoherent sources :  jitters randomly in time, no stable interference occurs - sunlight

3 3 Fig Intensity and phase 35- Eq Eq

4 E1E1 E2E2 4 Intensity in Double-Slit Interference 35-

5 5 Intensity in Double-Slit Interference 35- Fig

6 Ex wavelength 600 nm n 2 =1.5 and m = 1 → m = 0

7 Interference form Thin Films

8 8 Reflection Phase Shifts 35- Fig n1n1 n2n2 n 1 > n 2 n1n1 n2n2 n 1 < n 2 Reflection Reflection Phase Shift Off lower index 0 Off higher index 0.5 wavelength

9 9 Phase Difference in Thin-Film Interference 35- Fig Three effects can contribute to the phase difference between r 1 and r 2. 1.Differences in reflection conditions 2.Difference in path length traveled. 3.Differences in the media in which the waves travel. One must use the wavelength in each medium (  / n ), to calculate the phase.

10 10 Equations for Thin-Film Interference 35- ½ wavelength phase difference to difference in reflection of r 1 and r 2

11 11 Color Shifting by Paper Currencies,paints and Morpho Butterflies 35- weak mirror looking directly down : red or red-yellow tilting : green better mirror soap film

12 大藍魔爾蝴蝶大藍魔爾蝴蝶

13 雙狹縫干涉之強度

14 Ex Brighted reflected light from a water film thickness 320 nm n 2 =1.33 m = 0, 1700 nm, infrared m = 1, 567 nm, yellow-green m = 2, 340 nm, ultraviolet

15 Ex anti-reflection coating

16 Ex thin air wedge

17 17 Fig Michelson Interferometer 35-

18 18 Determining Material thickness L 35-

19 19 Problem In Fig , an airtight chamber of length d = 5.0 cm is placed in one of the arms of a Michelson interferometer. (The glass window on each end of the chamber has negligible thickness.) Light of wavelength λ = 500 nm is used. Evacuating the air from the chamber causes a shift of 60 bright fringes. From these data and to six significant figures, find the index of refraction of air at atmospheric pressure.

20 20 Solution to Problem φ 1 the phase difference with air ; 2 : vacuum N fringes

21 21 Diffraction Pattern from a single narrow slit Diffraction and the Wave Theory of Light 36- Central maximum Side or secondary maxima Light Fresnel Bright Spot. Bright spot Light These patterns cannot be explained using geometrical optics (Ch. 34)!

22 The Fresnel Bright Spot (1819) Newton corpuscle Poisson Fresnel wave

23 Diffraction by a single slit

24 單狹縫繞射之強度單狹縫繞射之強度

25 Double-slit diffraction (with interference) Double-slit diffraction (with interference) Single-slit diffraction Single-slit diffraction 雙狹縫與單狹縫

26 Diffraction by a Single Slit: Locating the first minimum (first minimum)

27 Diffraction by a Single Slit: Locating the Minima (second minimum) (minima-dark fringes)

28 Ex Slit width

29 29 Fig Intensity in Single-Slit Diffraction, Qualitatively 36- N=18  = 0  small 1st min. 1st side max.

30 30 Intensity and path length difference 36- Fig. 36-9

31 31 Here we will show that the intensity at the screen due to a single slit is: 36- Fig Intensity in Single-Slit Diffraction, Quantitatively In Eq. 36-5, minima occur when: If we put this into Eq we find:

32 Ex

33 33 Diffraction by a Circular Aperture 36- Distant point source, e,g., star lens Image is not a point, as expected from geometrical optics! Diffraction is responsible for this image pattern d  Light  a  a

34 34 Rayleigh’s Criterion: two point sources are barely resolvable if their angular separation θ R results in the central maximum of the diffraction pattern of one source’s image is centered on the first minimum of the diffraction pattern of the other source’s image. Resolvability 36- Fig

35 Diffraction – ( 繞射 )

36 Ex pointillism D = 2.0 mm d = 1.5 mm

37 Ex d = 32 mm f = 24 cm λ = 550 nm

38 38 The telescopes on some commercial and military surveillance satellites 36- = 550  10 – 9 m. (a) L = 400  10 3 m , D = 0.85 m → d = 0.32 m. (b) D = 0.10 m → d = 2.7 m. Resolution of 85 cm and 10 cm respectively

39 39 Diffraction by a Double Slit 36- Two vanishingly narrow slits a<< Single slit a ~ Two Single slits a~

40 Ex d = 32 μ m a = μ m λ = 405 nm

41 41 Diffraction Gratings 36- Fig Fig Fig

42 42 Width of Lines 36- Fig Fig

43 43 Separates different wavelengths (colors) of light into distinct diffraction lines Grating Spectroscope 36- Fig Fig

44 Compact Disc

45 45 Optically Variable Graphics 36- Fig

46 全像術

47 Viewing a holograph

48 A Holograph

49 49 Gratings: Dispersion 36- Differential of first equation (what change in angle does a change in wavelength produce?) Angular position of maxima For small angles

50 50 Gratings: Resolving Power 36- Substituting for  in calculation on previous slide Rayleigh's criterion for half- width to resolve two lines

51 51 Dispersion and Resolving Power Compared 36-

52 52 X-rays are electromagnetic radiation with wavelength ~1 Å = m (visible light ~5.5x10 -7 m) X-Ray Diffraction 36- Fig X-ray generation X-ray wavelengths to short to be resolved by a standard optical grating

53 53 d ~ 0.1 nm → three-dimensional diffraction grating Diffraction of x-rays by crystal 36- Fig

54 Fig X-Ray Diffraction, cont’d

55 Structural Coloring by Diffraction

56


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