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