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PHY122_L17_forPostingBeforeLecture

PHY122_L17_forPostingBeforeLecture - PHY122 Physics for the...

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PHY122 – Physics for the Life Sciences II Lecture 17 After a bit more about Interference Diffraction Note: Clicker Channel 21 11/03/2011 Lecture 17 1

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11/03/2011 Lecture 17 2 Too many missed this last time. The EM wave electric amplitude can be negative! Here it’s twice the “single-slit” (negative value), so it must be constructive interference: bright band!
Some indices of refraction: important in optics 11/01/2011 Lecture 16 3 at fixed wavelength Dispersion: n = n( λ ) n varies with wavelength

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The Behavior of Light in Dielectrics We know the speed of EM waves in a dielectric is reduced compared to the speed in vacuum: 11/01/2011 Lecture 16 4 dielectric c v κ = phase change 180° = path length increase by λ /2 n c = “index of refraction”
Why does this happen? 11/01/2011 Lecture 16 5

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n oil = 1.45 Lecture 16 6 Interference in Thin Transparent Films Reflection of normal incidence light off a thin layer of oil ( n= 1.45 ) on water ( n= 1.33 ): – ray A, under reflection off a material of larger index of refraction, undergoes a phase shift Δ φ = π • otherwise Δ φ = 0 identical to a wave on a rope that meets a more massive piece of the rope or a fixed end: the reflected wave is inverted (i.e. a phaseshift of π ) the electric field in particular: Refracted waves have zero phase shift… Q: dominant color of the reflected light? maxima for: Δ φ AB = (2 π / λ oil )(2 t ) + π = m 2 π barb4right λ air ,m = n oil λ oil = 4 n oil t /(2 m +1), m= 0,1,2,… barb4right λ air , 0 = 2204 nm (infrared; not visible) λ air , 1 = 735 nm (near infrared; not visible) λ air , 2 = 441 nm (violet-blue; visible) λ air , 3 = 315 nm (near UV; not visible) refl, inc, a b a a a b n n E E n n - = + n water =1.33 A B n air =1.00 t = 380 nm at larger angles, larger- λ colors dominate … 11/01/2011 from reflection of ray A – Only thin layers reflect colors selectively; thick layers reflect all colors (many maxima)
11/01/2011 Lecture 16 7 Summary: thin film interference Speed inside a dielectric: v dielectric =c / n barb4right λ dielectric = λ vacuum / n Extra phase change of 180° = π if n inc =n 1 <n 2 =n refract remember: pulse on a rope meeting a fixed end or a “loose” end … Constructive interference if: plus an EVEN number of phase changes ( 180° = π ) from reflection … ELSE: plus an ODD number of phase changes ( 180° = π ) from reflection … 2 0,1,2, t m m n λ = = L ( ) 1 2 2 0,1,2, t m m n λ = + = L

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Review: when waves meet an “obstacle” … parallel (water) wave fronts meeting a small (size ~ λ ) opening and a large (size >> λ ) opening in a barrier waves approach from the top of the picture … 11/03/2011
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