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Interference Chapter 35Chapter 35
February 2, 2012Chapter 35Chapter 35
February 2, 2012 Physics 221 1
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
February 2, 2012 Physics 221 2
Interference and coherent sources
February 2, 2012 Physics 221 3
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)
February 2, 2012 Physics 221 4
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
February 2, 2012 Physics 221 5
phase change due to the difference in optical paths of the two rays…
Phase changes upon reflection
From Maxwell’s Equations:
iba
bar E
nnnnE
+−
=
February 2, 2012 Physics 221 6
Phase changes upon reflection
Phase change of reflected ray by π when n2 > n1
No phase change for the reflected ray when n2 < n1
February 2, 2012 Physics 221 7
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 ( )
February 2, 2012 Physics 221 8
Newton’s Rings….
Interference is used to measure the radius ofcurvature of a spherical mirror…..
hlens
rhair
lens
February 2, 2012 Physics 221 9
Examples of air wedges….
Flat pieces of glasspattern of regular fringes
Not so flat pieces of glassfringes more ragged..
February 2, 2012 Physics 221 10
Soap Film Interference Pattern
Soap film approximately uniform in thicknessPhase shift of π approximately uniform in thicknessPhase shift of π
No phase shift
February 2, 2012 Physics 221 11
Anti-reflection Coatings on glasses
Phase shift π
Phase shift π when n of coating is smaller than n of glass
February 2, 2012 Physics 221 12
g
Michelson Interferometer….
This device uses interference to makeprecise measurements of distances
February 2, 2012 Physics 221 13
Other uses of an interferometer
Can use these devices to measuredifferences in “optical path lengths” too!differences in “optical path lengths” too!
February 2, 2012 Physics 221 14
Measuring indices of refraction
February 2, 2012 Physics 221 15