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**Young’s Experiment ․Young’s Double-Slit interference Exp.**

Constructive interference/maxima/bright fringes Destructive interference/minima/dark fringes

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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 35-

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Intensity and phase Fig Eq Eq 35-

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**Intensity in Double-Slit Interference**

35-

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**Intensity in Double-Slit Interference**

Fig 35-

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Ex wavelength 600 nm n2=1.5 and m = 1 → m = 0

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**Interference form Thin Films**

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

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**Reflection Phase Shifts**

n1 > n2 Fig Reflection Reflection Phase Shift Off lower index Off higher index wavelength n1 n2 n1 < n2 35-

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**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 35-

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**Equations for Thin-Film Interference**

½ wavelength phase difference to difference in reflection of r1 and r2 35-

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**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 35-

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大藍魔爾蝴蝶 Iridescence 彩虹色, 真珠光 terrace 階梯 cuticle角質層

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雙狹縫干涉之強度

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**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

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

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Ex thin air wedge

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**Michelson Interferometer**

Fig 35-

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**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 35-

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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. 35-

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**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. 35-

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**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 36-

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**The Fresnel Bright Spot (1819)**

Newton corpuscle Poisson Fresnel wave

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**Diffraction by a single slit**

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單狹縫繞射之強度

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

Single-slit diffraction

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**Diffraction by a Single Slit: Locating the first minimum**

36-

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**Diffraction by a Single Slit:**

Locating the Minima (second minimum) (minima-dark fringes) 36-

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Ex Slit width Human hair 100μm

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**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 36-

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**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. 36-

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**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: 36-

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Ex

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**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 36-

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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 36-

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Diffraction – (繞射)

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**Ex.11-8 36-3 pointillism D = 2.0 mm d = 1.5 mm**

Red dots become indistinguishable first

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Ex d = 32 mm f = 24 cm λ= 550 nm

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**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. 36-

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**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 36-

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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?

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**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. 36-

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Fig Width of Lines Fig 36-

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

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Compact Disc 2t is ½ of a wavelength, Grating used in tracking, pit 0.1 μm

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**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. 36-

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全像術

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Viewing a holograph

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A Holograph

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**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 36-

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**Gratings: Resolving Power**

Rayleigh's criterion for half-width to resolve two lines Substituting for Dq in calculation on previous slide 36-

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**Dispersion and Resolving Power Compared**

36-

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**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 36-

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**Diffraction of x-rays by crystal**

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

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**X-Ray Diffraction, cont’d**

Fig 36-

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**Structural Coloring by Diffraction**

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