1. Young’s Experiment ․Young’s Double-Slit interference Exp.
 Constructive interference/maxima/bright fringes
 Destructive interference/minima/dark fringes

2. Coherence
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)=E0cos(wt+f)
Coherent sources: Phase f 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: f jitters randomly in time, no stable interference occurs － sunlight
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3. Intensity and phase
Fig Eq Eq
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4. Intensity in Double-Slit Interference
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5. Intensity in Double-Slit Interference
Fig
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6. Ex
wavelength 600 nm
n2=1.5 and
m = 1 → m = 0

7. Interference form Thin Films
․Interference from Thin Films - soap bubbles, morpho’s wing, peacock’s tail

8. Reflection Phase Shifts
n1 > n2
Fig
Reflection Reflection Phase Shift
Off lower index
Off higher index wavelength n1 n2
n1 < n2
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9. Phase Difference in Thin-Film Interference
Three effects can contribute to the phase difference between r1 and r2.
Differences in reflection conditions
Difference in path length traveled.
Differences in the media in which the waves travel. One must use the wavelength in each medium (l / n), to calculate the phase.
Fig
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10. Equations for Thin-Film Interference
½ wavelength phase difference to difference in reflection of r1 and r2
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11. Color Shifting by Paper Currencies,paints and Morpho Butterflies
weak mirror
soap film
better mirror
For the same path difference, different wavelengths (colors) of light will interfere differently. For example,
2L could be an integer number of wavelengths for red light but a half integer wavelengths for blue.
Furthermore, the path difference 2L will change when light strikes the surface at different angles, again changing the interference condition for the different wavelengths of light.
looking directly down ： red or red-yellow
tilting ：green
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12. 大藍魔爾蝴蝶
Iridescence 彩虹色, 真珠光 terrace 階梯 cuticle角質層

13. 雙狹縫干涉之強度

14. Ex.11-3 35-3 Brighted reflected light from a water film
thickness 320 nm
n2=1.33
m = 0, 1700 nm, infrared
m = 1, nm, yellow-green
m = 2, nm, ultraviolet

15. Ex.11-4 35-4 anti-reflection coating

16. Ex thin air wedge

17. Michelson Interferometer
Fig
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18. Determining Material thickness L
For each change in path by 1l, the interference pattern shifts by one fringe at T. By counting the fringe change, one determines Nm- Na and can then solve for L in terms of l and n
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19. Problem 35-81
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.
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20. Solution to Problem 35-81 φ1 the phase difference with air ； 2 ：vacuum
N fringes
Let f1 be the phase difference of the waves in the two arms when the tube has air in it, and let f2 be the phase difference when the tube is evacuated. These are different because the wavelength in air is different from the wavelength in vacuum. If l is the wavelength in vacuum, then the wavelength in air is l/n, where n is the index of refraction of air.
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21. 11-3 Diffraction and the Wave Theory of Light
Diffraction Pattern from a single narrow slit.
Side or secondary
maxima
Light
Central
maximum
Fresnel Bright Spot.
These patterns cannot be explained using geometrical optics (Ch. 34)!
Light
Bright
spot
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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

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

26. Diffraction by a Single Slit: Locating the first minimum
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27. Diffraction by a Single Slit:
Locating the Minima
(second minimum)
(minima-dark fringes)
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28. Ex Slit width
Human hair 100μm

29. Intensity in Single-Slit Diffraction, Qualitatively
To obtain the locations of the minima, the slit was equally divided into N zones, each with width Δx. Each zone acts as a source of Huygens wavelets. Now these zones can be superimposed at the screen to obtain the intensity as function of θ, the angle to the central axis.
1st side
max.
N=18
q = 0
q small
1st min.
Fig. 36-7
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30. Intensity and path length difference
Fig. 36-9
If we divide slit into infinitesimally wide zones Dx, the arc of the phasors approaches the arc of a circle. The length of the arc is Em. f is the difference in phase between the infinitesimal vectors at the left and right ends of the arc. f is also the angle between the 2 radii marked R.
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31. Intensity in Single-Slit Diffraction, Quantitatively
Fig. 36-8
Here we will show that the intensity at the screen due to a single slit is:
In Eq. 36-5, minima occur when:
If we put this into Eq we find:
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32. Ex

33. Diffraction by a Circular Aperture
Distant point
source, e,g., star d
Image is not a point, as expected from geometrical optics! Diffraction is responsible for this image pattern q
lens
Light q a
Commercial satellite 85cm -> 32cm aperture
Military satellite 10cm -> 2.7m aperture
Light q a
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34. Resolvability
Rayleigh’s Criterion: two point sources are barely resolvable if their angular separation θR 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.
Fig
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35. Diffraction – (繞射)

36. Ex.11-8 36-3 pointillism D = 2.0 mm d = 1.5 mm
Red dots become indistinguishable first

37. Ex
d = 32 mm
f = 24 cm
λ= 550 nm

38. The telescopes on some commercial and military surveillance satellites
Resolution of 85 cm and 10 cm respectively
Commercial satellite 85cm -> 32cm aperture
Military satellite 10cm -> 2.7m aperture
l = 550 × 10–9 m.
(a) L = 400 × 103 m ， D = 0.85 m → d = 0.32 m.
(b) D = 0.10 m → d = 2.7 m.
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39. Diffraction by a Double Slit
Single slit a~l
Two vanishingly narrow slits a<<l
Double slit experiment described in Ch. 35 where assumed that the slit width a<<λ.
For such narrow slits, the central maximum of the diffraction pattern of either slit covers the entire viewing screen.
Two Single slits a~l
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40. Ex
d = 32 μm
a = μm
λ= 405 nm
How many bright interference fringes are w ithin the central peak of the diffraction envelope?
(b) How many bright fringes are within either of the first side peaks of the diffraction envelope?

41. Diffraction Gratings Fig. 36-20 Fig. 36-19 Fig. 36-18 36-
Device with N slits (rulings) can be used to manipulate light, such as separate different wavelengths of light that are contained in a single beam. Double-slit interference can not be used because its fringes overlap too much.
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42. Fig
Width of Lines
Fig
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43. Grating Spectroscope
Separates different wavelengths (colors) of light into distinct diffraction lines
Fig
Fig
Separates different wavelengths (colors) of light into distinct diffraction lines
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44. Compact Disc
2t is ½ of a wavelength, Grating used in tracking, pit 0.1 μm

45. Optically Variable Graphics
Fig
Gratings embedded in device send out hundreds or even thousands of diffraction orders to produce virtual images that vary with viewing angle. Complicated to design and extremely difficult to counterfeit, so makes an excellent security graphic.
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46. 全像術

47. Viewing a holograph

48. A Holograph

49. Gratings: Dispersion Angular position of maxima
Differential of first equation (what change in angle does a change in wavelength produce?)
For small angles
Dispersion: the angular spreading of different wavelengths by a grating
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50. Gratings: Resolving Power
Rayleigh's criterion for half-width to resolve two lines
Substituting for Dq in calculation on previous slide
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51. Dispersion and Resolving Power Compared
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52. X-Ray Diffraction X-ray generation
X-rays are electromagnetic radiation with wavelength ~1 Å = m (visible light ~5.5x10-7 m)
X-ray generation
Fig
X-ray wavelengths to short to be resolved by a standard optical grating
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53. Diffraction of x-rays by crystal
Fig
Diffraction of x-rays by crystal
d ~ 0.1 nm
→ three-dimensional diffraction grating
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54. X-Ray Diffraction, cont’d
Fig
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55. Structural Coloring by Diffraction