Chapter 25: Interference and Diffraction
Chapter 25: Interference and Diffraction
Chapter 25: Interference and Diffraction
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<strong>Chapter</strong> <strong>25</strong>: <strong>Interference</strong> <strong>and</strong><strong>Diffraction</strong><strong>25</strong>.1 <strong>Interference</strong> of two waves<strong>25</strong>.3 Thin films<strong>25</strong>.4 Young’s double slit<strong>25</strong>.5 Gratings
<strong>Interference</strong>Constructive:Blue + Green = redThe Blue <strong>and</strong> GreenWaves are in phaseDestructive:Blue + Green = redThe Blue <strong>and</strong> GreenWaves are 180°Out of phase
Why Phase differences?• Different paths• Phase shifts onreflection
Example: different paths Michelson InterferometerλM1L1Path difference is ΔL=2(L2-L1)M2L2If ΔL=mλ (m=0,1,2,3,…) we have constructive interferenceAnd we see a bright spotIf ΔL=(m+1/2)λ (m=0,1,2,3,…) we have destructiveinterference <strong>and</strong> we see a dark spot
Example <strong>25</strong>.2• Suppose a transparent vessel 30.0 cm long is placein one arm of a Michelson interferometer. Thevessel initially contains air at 0°C <strong>and</strong> 1 atm. Withlight of vacuum wavelength 633nm, the mirrors arearranged so that a bright sot appears at the centerof the screen. As air is gradually pumped out of thevessel, the central region of the screen changesfrom bright to dark <strong>and</strong> back to bright 274 times.Calculate the index of refraction of air.
Problem 6• A Michelson Interferometer is adjustedso that there is a bright fringe on thescreen. As one mirror is moved <strong>25</strong>.8µm, 92 bright fringes are counted onthe screen. What is the wavelength ofthe light used?
Young’s Double slit
Max <strong>and</strong> minDouble-slit maximad sin" = m#m=0,+/-1,+/-2!Double-slit minima#d sin" = m + 1 &% ()$ 2'm=0,+/-1,+/-2!
Double slit example <strong>25</strong>.4• A laser (λ=690.0nm) is used toilluminate two parallel slits. On ascreen that is 3.30 m away from theslits, interference fringes are observed.The distance between adjacent brightfringes in the center of the pattern is1.80 cm. what is the distance betweenthe slits?
Gratings• Like having lots <strong>and</strong> lots of slits• For two slits, there is a gradual changefrom maximum to minimum. For lots ofslits, the maxima are narrow <strong>and</strong> theintensity everywhere else is tiny.Maxima are given byWhere m= 0, +/-1,+/-2,…d sin" = m#!
Spectroscopy
Thin Films
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