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# lecture25 - Physics 2102 Gabriela Gonzlez Interference...

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Interference Physics 2102 Gabriela González

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Light is a wave When two beams of light combine, we can have constructive or destructive “interference.” http://www.colorado.edu/physics/2000/applets/fourier.html
Reflection and refraction laws hc hc 2 2 sin , sin λ θ = = 1 1 2 1 2 2 sin sin v v = = 1 1 1 2 2 sin sin n n = 1 The light travels more slowly in more dense media: v=c/n ( n = index of refraction) Since the period T is the same, the wavelength has to change (v= λ /T) Snell’s law! 2 1 2 v v = 1 n c v n n = = f c n n c v f n n n = = = = / / Wavelength: Frequency:

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Interference: example A red light beam with wavelength λ =0.625 μ m travels through glass (n=1.46) a distance of 1mm. A second beam, parallel to the first one and originally in phase with it, travels the same distance through sapphire (n=1.77). How many wavelengths are there of each beam inside the material? In glass, λ g=0.625 μ m/1.46= 0.428 μ m and Ng=L/ λ g=2336.45 In sapphire, λ s=0.625 μ m/1.77= 0.353 μ m (UV!) and Ns=L/ λ s=2832.86 What is the phase difference in the beams when they come out? The difference in wavelengths is Ns-Ng=496.41. Each wavelength is 360o, so N=496.41 means ∆φ = Nx360o=0.41x360o=148o How thick should the glass be so that the beams are exactly out of phase at the exit? (destructive interference!) N=L/ λ s - L/ λ g= (L/ λ )(n2-n1)=0.31 (L/ λ )=m+1/2 A thickness L=(m+0.5) 2.02 μ m would make the waves OUT of phase. For example, 1.009 mm = 499.5 x 2.02 μ m makes them come OUT of phase, and 1.010 mm = 500.0 x 2.02 μ m makes them IN phase.
Thin film interference: The patterns of colors that one sees in oil slicks on water or in bubbles is produced by interference of the light bouncing off the two sides of the film. To understand this we

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## This note was uploaded on 11/18/2011 for the course PHYSICS 2102 taught by Professor Dowling during the Fall '10 term at LSU.

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lecture25 - Physics 2102 Gabriela Gonzlez Interference...

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