interference chapter 35chapter 35 - physics and...
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Interference Chapter 35Chapter 35
February 2, 2012Chapter 35Chapter 35
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Interference and coherent sources
Reminder of the form of E&M WavesE(x t) = E0 j sin(kx - ωt + ϕ) withE(x,t) E0 j sin(kx ωt + ϕ) , with k = 2π/λ and ω = 2πf
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Interference and coherent sources
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Constructive and Destructive Interference
Constructiver2 – r1 = m λ (m = +/- integer values)r2 r1 m λ (m +/ integer values)
Destructive r r (m + ½) λ (m +/ integerr2 – r1 = (m + ½) λ (m = +/- integer
values)
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How does light bounce off these thin films?????
Light will bounce off boththe top and bottom surfaces f thi fil
Phase change of πnair < noil
of a thin film…
No phase change
There will be two differentphase changes at these interfacessince the indices of refraction change
noil > nwater
There will be an additionalh h d t th
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phase change due to the difference in optical paths of the two rays…
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Phase changes upon reflection
From Maxwell’s Equations:
iba
bar E
nnnnE
+−
=
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Phase changes upon reflection
Phase change of reflected ray by π when n2 > n1
No phase change for the reflected ray when n2 < n1
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Wedge of Air between parallel plates of glass….
Phase change at reflectionfrom top plate is 0 but phase change at the reflectionphase change at the reflectionfrom the bottom plate (π)plus the difference in optical paths in air wedge (2t)..p p g ( )
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Newton’s Rings….
Interference is used to measure the radius ofcurvature of a spherical mirror…..
hlens
rhair
lens
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Examples of air wedges….
Flat pieces of glasspattern of regular fringes
Not so flat pieces of glassfringes more ragged..
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Soap Film Interference Pattern
Soap film approximately uniform in thicknessPhase shift of π approximately uniform in thicknessPhase shift of π
No phase shift
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Anti-reflection Coatings on glasses
Phase shift π
Phase shift π when n of coating is smaller than n of glass
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g
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Michelson Interferometer….
This device uses interference to makeprecise measurements of distances
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Other uses of an interferometer
Can use these devices to measuredifferences in “optical path lengths” too!differences in “optical path lengths” too!
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Measuring indices of refraction
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