1Monday, Jan. 28 Phy208 Lecture 21From last time… Waves InterferencePlease pick up pack of color sheetsMonday, Jan. 28 Phy208 Lecture 22Interference of 2 speakerscresttroughconstructiveinterference,loud tonedestructiveinterferencequit toneMonday, Jan. 28 Phy208 Lecture 23QuestionSuppose that the frequency of the soundwave increases by a factor of two.The adjacent maxima areA) Farther apartB) Closer togetherC) SameD) Need to know speaker spacingMonday, Jan. 28 Phy208 Lecture 24Light waves• Light is a wave just like sound.• But can propagate in vacuum– at speed c = 3x108 m/s• Has same wave properties, e.g.• Can also propagate in glass, water, but slower– Speed in medium = v = c/n– n = Index of refraction• Has same superposition / interference properties! "vac=cf! "med=cnf="vacnMonday, Jan. 28 Phy208 Lecture 25LRecordingplateInterference of light• Light wavelength much shorter than sound• Interference fringes much closer togetherLightbeamFoil with twonarrow slitsθy! y / L = tan"Monday, Jan. 28 Phy208 Lecture 26Interference pattern2Monday, Jan. 28 Phy208 Lecture 27θδ = Extra path length! "= d sin#Extra phase =! 2"#$= 2"yLd$y = position on screen =! L tan"! "~ dyLfor #$ 0Monday, Jan. 28 Phy208 Lecture 28• For bright fringes: extra phase = 2πm• For dark fringes: extra phase = 2π(m+1/2)Fringe separation & wavelengthFringe separation = ! "Ld ! ybright="Ldm m = 0, ± 1, ± 2 K ! ydark="Ldm +12# $ % & ' ( m = 0, ± 1, ± 2 KMonday, Jan. 28 Phy208 Lecture 29QuestionA two-slit interference pattern is observed in air(n=1). Then the entire system is immersed inwater (n=1.33). The interference fringes areA) 1.33 times closer togetherB) 1.33 times farther apartC) 2.66 times closer togetherD) 2.66 times farther apartE) Spacing unchangedMonday, Jan. 28 Phy208 Lecture 210Interference of multiple sources Evenly-spaced slits have maxima at samelocation as two-slits. Maxima become sharper, more intense Interference of multiple sources often calleddiffractionMonday, Jan. 28 Phy208 Lecture 211Diffraction gratings• Diffraction grating is pattern of multiple slits.• Very narrow, very closely spaced.• Expect very narrow interference peaks.(15,000 lines/inch)x(1 inch/2.54 cm)x(100 cm/m)=5.9x105/mSo a spacing of 1/(5.9x105/m) = 1.7x10-6 m = 1700 nm.1700 nmMonday, Jan. 28 Phy208 Lecture 212QuestionSuppose white light is shined through adiffraction grating. What would the patternon the screen look like?A)B)C)D)3Monday, Jan. 28 Phy208 Lecture 213Thin film interferenceBlackColorschangingwiththicknessMonday, Jan. 28 Phy208 Lecture 214Thin film interference• If film is much thinner than wavelength, ~ no phase shiftfrom extra path length• But top reflection has 180˚ phase shift, bottom not• Destructive interference for all wavelengths,film appears blackair: n=1n>1180˚ (π radians) phase shiftno phase shifttλλ/nMonday, Jan. 28 Phy208 Lecture 215Thicker parts• Phase differencecomes from– Phase shift fromreflection (top)– Phase shift from extrapath length• Extra path length fornormal incidence = 2tair: n=1n>1180˚ phase shiftfrom reflectiontλλvac/nExtra pathlength=2t! "# + 2#2t$vac/ n( ) =Phase difference =Reflectionphase shift# wavelengths inextra path length! 2m"constructive! 2m "1( )#destruct iveMonday, Jan. 28 Phy208 Lecture 216Constructive interference• Q: red light (700 nm) is observed in a section of soap film(n=1.33). What is the local thickness? ! 2t = m +12" # $ % & ' (n (m = 0,1,2K)constructive interference ! 2t = m"n (m = 0,1,2K)destructive interferenceMonday, Jan. 28 Phy208 Lecture 217Biological iridescence• Some organisms seem to reflect incredibly vivid colors. Thisis not by pigmentation, but interference!Monday, Jan. 28 Phy208 Lecture 218‘Morpho’ family butterfly scales• Spacing ~ 170 nm4Monday, Jan. 28 Phy208 Lecture 219! 2"2t1#o/n+ 2"2t2#o= 2"m#o=2mnt1+ t2( )#o= 2(1.5 $ 64nm + 217nm ) = 446nmThin-film like interference, multiple layers, multiple
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