Lecture 20 (Ch 27.4-27.7)

# Lecture 20 (Ch 27.4-27.7) - Lecture 20 Wave Optics Ch 27...

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Lecture 20 Wave Optics Ch 27

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Interference Fringes o The light and dark regions produced by interference of light are called “fringes” o Bright regions are produced where waves from the two slits interfere constructively o Dark regions are where the two waves interfere destructively
Constructive & Destructive Interference o At points where the waves arrive “in phase”, the E vectors are the same and I total = (E 1 +E 2 ) 2 = 4E 2 o At points where the waves arrive out of phase, the E vectors are opposite and I total = (E 1 -E 2 ) 2 = 0 o The separation between bright fringes corresponds to a difference of one wavelength in light travel distance

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Double-slit Constructive interference o The path difference to each point y i on the viewing screen depends on the angle to it θ i. o δ i = r 2 – r 1 d sin θ i
Double-Slit Experiment o Due to interference between light from the two slits, a pattern of light and dark regions is produced on a screen at different heights y. y L

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“Order” of Fringes o The central maximum of intensity (at θ =0) is called the 0 th order fringe (m = 0) o Each subsequent fringe is counted outward from the central one (m= ± 1, ± 2, etc) o Dark fringes halfway between bright ones: d sin θ = (m+ ½ ) λ 0 +1 +2 -1 -2 Bright areas Dark areas λ /2 - λ /2 Bright and dark spacing Δ (d sin θ ) = λ /2
Interference in thin films Light traveling from a medium with index of refraction n 1 towards a medium with n 2 ==> undergoes a 180 degree phase change on reflection if n 1 <n 2 . ==> undergoes no phase change if n 1 >n 2

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Waves at a “Hard” Boundary o Waves are reflected when they hit a “hard” boundary they can’t displace Reflected wave is inverted 180° ( π radians) phase shift Wave exerts force on barrier Barrier exerts equal but opposite force Force on wall Force on string
Waves at a “Soft” Boundary o When waves hit a “soft” boundary they can freely displace, they are also reflected Reflected wave is not inverted Phase remains the same Boundary is displaced in one direction and then the other by the wave Same as if it had been moved up and down by hand

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Transmission and Reflection o When a wave encounters a boundary that can move, but not freely, the wave is partially reflected and partially transmitted Reflection from boundary with denser medium is inverted Reflection from boundary with less dense medium is not inverted o If media have same density, there is no reflection and the wave is completely transmitted.
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