LECTURE8 Interference(1)

7/24/2019 LECTURE8 Interference(1)

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Physics 2C: Fluids, Waves,

Thermodynamics and Optics

Lecture 6: Interference

I have never let my schooling interfere with my education.- Mark Twain


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nterference and Coherence

nterference and Coherence

Interference is the result of linear superposition of the wave solutions.

Interferenceis a demonstration of the wave nature of light.Particles do not demonstrate this same behavior.

In order to create sustainedinterference you need two sourceswith identical wavelengths that arecoherent. What is coherence?

Coherence! "uantifies the #hasedifference between many $M wavesfrom a source.

Incoherent light Sunlight, light bulbs, fire

Coherent light LASERS


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Path length difference

ath length difference

%onsider in-#hase light from a single source that travels two different #aths to a

detector&

source

!etector

"onochro#atic $ in phase

What #ust the path length !ifference be in or!er to getconstructive%!estructive interference at the !etector?

&estructive interference'

m is an odd integer 'odd number ofhalf wavelengths(

Constructive interference'

m is any integer 'integer numbersof wavelengths(


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Clicker Question

licker Question

)hat ha##ens when two light #ath 'am#litude *( lengths differ by

a distance other than a half or full wavelength+

*.( There is no interference.

,.( The resulting am#litude is is somewherebetween and *.

%.( The am#litude is *.

.( The resulting am#litude is somewhere between

and /*.

$.( )e don0t have enough information to tell.


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%onsider two light #aths through air that are out of #hase by a half

wavelength 'so destructively interfere(. * thin #ane of trans#arentglass 'n 1 2.3( is introduced along one #ath. )hat ha##ens to theinterference at the end+

*.( The interference is still totally destructive.

,.( The interference becomes com#letely constructive.

%.( The interference is now #artially destructive.

.( )e need to know the thickness of the glass todetermine the interference.

$.( The conce#t of interference no longer a##lies.

Clicker Question

licker Question


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)hat ha##ens when two light #ath lengths differ by a half-

wavelength but the waves have different am#litudes+

*.( The resulting wave destructively interferes and theresulting am#litude is 4ero.

,.( The resulting am#litude is the average of the twooriginal am#litudes.

%.( The resulting am#litude de#ends on the directionthe #ath took.

.( The resulting am#litude de#ends on the fre"uency.

$.( The resulting am#litude is the difference betweenthe two original am#litudes.

Clicker Question

licker Question


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Huygens Principle

uygens Principle

Wavefront

Huygens principle describes how a

wavefront propagates.

ivide the wavefront 'same#hase( into a series ofinfinitesimal #oint sources.

$ach #oint source emits as#herical wave that0s in #hasewith all the other #oint sources.

(he wavefront at so#eti#elater is the superposition of allthese point sources.


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Huygens Principle

uygens Principle

5uygens #rinci#le a##lies to wavefronts of all sha#es. 5ere you

can see it can also be used to describe a s#herical wave as well.


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Coherence

oherence

Coherence is a propert) of waves which *uantifies the phase!ifference between waves both in space an! ti#e.

$M waves are said to be spatially coherent'transversecoherence( if the #hase is constant along a direction #er#endicularto the direction of #ro#agation.

$M waves are said to betemporally coherent'longitudinal

coherence( if the #hase difference between crests is constant in time.

In other wor!s, waves are sai! to be coherent if the) #aintainsa constant phase with respect to each other both in ti#e an!space.

Let+s loo at this pictoriall).

6et0s say we have lots of $M waves coming from the same source

'lots of #hotons 7 $M waves(.


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Temporal Coherence (Longitudinal)

emporal Coherence (Longitudinal)

)e define coherence time as the length of time over which the wavemaintains constant #hase between com#onents of different fre"uencies.

8or monochromatic waves'one fre"uency(&

8or waves of differentwavelengths 'two fre"uencies(&

Appears as a ti#e!epen!ent phase If'

(hen coherence

ti#e is large


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Temporal Coherence (Longitudinal)

emporal Coherence (Longitudinal)

*nother e9am#le& 5ere are a series of fre"uencies. )hen added together

they #roduce awave packet- an wave of finite e9tent in time.

(he length of ti#e of this pacet IS the coherence ti#e

Traveling light waves move at

s#eed c define the longitudinal'along the wave #ath( coherencelength as&

:ay the #ulse lasts for


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Spatial Coherence (Transverse)

patial Coherence (Transverse)

*s we0ve seen wavefronts can e9tend across multi#le dimensions and

most of those we0ve seen have #ro#agated isotro#ically but not allwaves have wavefronts that are isotro#ic.

Spatial coherence!escribes the length between an)two points over which the wave #aintains a

constant phase.

It0s determined by correlating the #hase ofthe wave at two #oints in s#ace over alltime. The #hase between these two must beconstant.

)aves can be s#atially coherent tem#orally coherent or both...or neither.

%onstant #hase over infinite e9tent #erfect s#atial coherence


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Coherence (pictorially)

oherence (pictorially)

Perfectly coherent's#atially andtem#orally(

;aried wavefrontbut still with#erfect coherence

8inite s#atialand tem#oralcoherence.


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aking the incoherent coherent!!!

aking the incoherent coherent!!!

There is a way of making incoherent light 'both

s#atial and tem#oral( into coherent light.

-irst pass the incoherent source through a s#all hole s#aller than thatspatial coherence length/ light is now spatiall) coherent.

Secon! pass the light through a wavelength filter, #aing it #onochro#atic

single fre*uenc)/ light is now spatiall) A0& te#porall) coherent.


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ichelson nterferometer


*n interferometer is a device for measuring changes in length tohigh degrees of #recision by utili4ing the interference of light.

2.( * beam of light is s#lit/.( It is directed along two different #aths


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The light is s#lit using ahalf-silvered mirror.

%onsider light coming from the

same monochromaticandcoherentsource.

6ight travels there and back ontwo #aths 62and 6/.

L3is s#oothl) varie!b) #oving "3

Constructive interference'

&estructive interference'

m is any integer inde9es the

fringes

Procedure&>radually move M2 and count n number offringes the wavelength can then be calculated&


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"ouTu#e $ideo Time%

ouTu#e $ideo Time%

Interfero#eter !e#onstration'

https'%%www.)outube.co#%watch?v456u7IEgc(i8


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?ow consider apartiallycoherent lightsource 'one with multi#le wavelengths(

with a coherence time

The light is s#lit in the same fashion.

If'

@ecombining leads to a time delaybetween the finite #ulses from thetwo arms.

As

Then the #ulses will start overla##ing and

interfering.*s they do fringes will a##earAThis allows us to measure the longitudinalcoherence length based on how far we moveM2.

9ver whichfringes arevisible




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Thin&'ilm nterference

hin&'ilm nterference

*n im#ortant factor to recall from beforeis that wavelength de#ends on inde9 ofrefraction.

Thin film interferenceoccurs when

light reflects off both the to# andbottom surface of a thin layer

The thickness and inde9 of

refraction of the layer determinewhat wavelengths of light will beconstructively or destructivelyinterfered

Ra) 3'Reflects of top surface

Ra) :'Refracts through topsurface, reflects off botto# surfacean! then refracts bac into first

#e!iu#.


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Thin&'ilm nterference phase shift

hin&'ilm nterference phase shift

@ecall the reflection of the wave #ulse off the fi9ed and free boundary&

8i9ed end 1 #hase shift 8ree end 1 no #hase shift

* wave #ulse #assing from onemedium to another will e9#erience

a #hase shift if medium / is moredense than medium 2...and viceversa.

With light waves it !epen!s on thein!e; of refraction instea! of

!ensit).


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Air n43/

Air

1:9 n43.7/ t



Fast-Slow-Fast media

Increasingthicness


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=lass n43.>/

=lass n43.>/

Air n43/ t

Slow-Fast-Slow media

0o phase shift


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Clicker Question

licker Question

air n43/

water n43.7/

oil n43.>/

)hat would be the total reflection #hase shift for the thin film

interference from a thin layer of water between air and oil+

*.(

,.(

%.(

.(

$.( It de#ends on the thickness of the

water.


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)hy is the to# #ortion of this film black+ )hy is it there there is

no reflected light+

*.( The film doesn0t e9tend u#that far.

,.( The film is too thin to

constructively interfere visiblelight.

%.( The light from that #ortion isat ,rewster0s angle and is gettingfiltered out.

.( )ho knows - it could be forlots of reasons.

-il# is so thin that there is essentiall) no path length!ifference, 2@( there is still a 3B !egree phase shift.So light of all wavelengths !estructivel) interfere.

Clicker Question

licker Question


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(o solve a thin fil# interference proble# )ou have to now how #an)

reflection phase shifts there are.

(hat+s how )ou now which e*uation to use'

3 phase shift B or : phase shifts

constructive

!estructive

!estructive

constructive

e*uation




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eneral rules for thin films

eneral rules for thin films

In phase reflections'

9ut of phase reflections'


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Thin 'ilm nterference approach

hin 'ilm nterference approach

Solving strateg)'

3./ I!entif) the thin fil# causing the interference.

:./ &eter#ine the in!ices of refraction of the fil# an! #e!ia on either

si!e.

7./ &eter#ine nu#ber of reflection phase shifts.

./ &eter#ine if )ou have constructive or !estructive interference an!

use appropriate relationship.


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*hat to do #efore ne+t class,

@eading& Princi#les of Physics :ections

LECTURE8 Interference(1)

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