This document discusses electromagnetic waves and interference patterns of light. It introduces Maxwell's equations, which describe electromagnetic wave behavior. It also covers topics like reflection, refraction, thin film interference, and the Michelson interferometer. The key goals are to study interference from multiple coherent light sources and to determine intensity patterns from interference effects.

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To do an overview of Maxwell's equations and
d'haptn'32 electromagnetic waves
To study sinusoidal electromagnetic waves
To consider the passage of electromagnetic waves
I: lcci t'qrn ril l:t t('l ic. r'ittics through matter
To determine the energy and momentum of
electromagnetic waves
POWe,PClni t-ac|.....s f :
To observe u'ave addition. the formation of a
Untve rc ;ly P hvs i cs IFet.&lr Frill.rf ,
stand in g electrom agnetic rvave
- llrNh l) l'),'r,tt) i 4. , . 1 ! 'at 111:.i'l
I r.r'il,'' r l,'tt(. l,J,,rn
c rrlc rr*Foir&i.-rr.Fbhi;rir!,n..i {.b141.u r,4 , ,,+frffi,.&B
I rt { r'ollrrtl ilrr i{it xrr el I's cr1 rral iorr:
. Ifan electric field vector propagates, it After Ampere and Faraday came James Clark Maxwell. FIe pennecl
generates a nragnetic field vector. Or, a set offour equations that draw Gauss, Ampere, and Faraday's
is it the other way? laws together in a comprehensive description of the behavior of
. The "chicken and the egg" argument
electromagnetic waves.
ofwhich disturbance causes the other
aside, this is often a favorite portion of (29.r8)
a first course in physics.
O=0 (Crauss'r taw for magnerism) (29.19)
Electromagnetic waves, at least in the fU.
fonn of light, are common to many of
{u.n = r"(r. " "'j"),-, (Am*re,s raw) (29.20)
our daily experiences. Even i.vithout
vision, you can stand in the sun {n'ot
: -o!,' (Faaday,sraw) (2e.21)
wearing a dark shirt and perceive
electronragnetic waves.
,!ildelri &rrci^onridrer-,r". arrm;.-r-.""iulJiil,
l'.lcc{ lrtrtut grtr'l it rr :! 1 r. ;t t"{., rr !ri11 1; I llrrn Ii lt'c I lrtrrre grrcl ir * ilvrs { re{: rr r. {n,t: t. ir n.irlc t.an gc
. If you tried to cite all ' Where -rrlr-.tlgrg1t; j"tJiu:grJl-rq.Uilr,1{:lJr,slnnll,
the places you notice ' The range extends from low energy and frequency (radio and
electromagnetic waves television) to high energy and small wavelength (gamma rays)
in your classroom, you -
l1tvelengths in nr
rir ro i riri; irj-;;i'iol' ir) i, i; ii I
would conclude in a /j ---Xriy(--- _ ----i--'--*-
TV ts_Micr,$arc€
few minutes that they ullmvnrld > {__ oarmra rnvs**j
are everywhere.
(nrrilh(r ?rurcrFonrdtr.d,-r. a*run""*r."""iiri-^.n,
__-
(l$nchl{
c* xf c
- 3.0 x 108 mls
}n3lc:Fonldrcdn{lir.ntrttihii!iltclGoi ddi6-d[

2. l' l',rpa gl I io n o I' elcc( rorn:lgn cl ir: rvn r es | |
T'he wave front moves at spccd c. eqLral lo -1.0 . 108 m;s
t- - .'*---*-
l_E_: !:S$ygnetic wave in vacuum)
,,,u,,,, *",,
:B_ - ..t|
1.
,:l o"l
3.0 x 108 m/s
nnl l: = (l
rt=0
L+ ll c
l. l = --_--, (sIEd of eleuomagnetic
B.l ..--- 1y'KK-Yrnpn /KK^ wava in a diclectric)
E:t t
l;
I tt :
index of
l
- refraction
r6ni.. sfc:.rG t.rn,
l ht' * ar c cr;ulrliorr
The wave
BQ,t) = jE ocos( kx - ot)
rtQ,t) = i8.,,cos (*x - t,;t)
rI
I
,,| Electromagnetic rvave
ii
..1. traveling in the +x direction
'l -r--'/'., 'J
t:
tr.t| I
I
''
,l
,i
B
(.tr_ndr{ lfittrrron t:duqrin tE
(on;3ir ? rlnff rli^oDr dil.rrr*."*,rn-s-u-^."iao^*
The wave
o . A coating of oil on water or a
delicate glass prism can create a
rainbow. A rainstorm among open
T: l.6s patches ofdaylight can cast a
conventional rainbow. Both effects
are beautiful and arise from the
horizontal axis - time axis wavelength dependence of refraction
1l angles.
' Eyeglasses or contact lenses both use
refraction to correct imperfections in
the eyeball's focus on tire retina and
allow vision correction.
horizontal axis - position axis r--
. 4rnprr I I'r'R fc,-,n I an.r,.{ tR . nilFin! il I.qf.," .,J rm ^,r
(bpn!fir r 2$xlk,non lih,lnnn tR.ruitnhii!
i fciF.n.dd!6,bft

3. r'llt'r'lintr :trtrl r'1'lj ;r1 t i,r1r r * ill r(ln:ii(lf t. slxrcrrlur l"clleclions
The figure below illuslrates both rellection and refraction at
once. fhe A real surface will scatter and reflect light. Diffuse reflection is the
storefront windorv both slros5 ths passersbl their reflections
and allows thent rule. not the ex.ception, We will use spe;ular reflection as we used
lo see inside.
rne rav approxtmatton, to Inake a very difficult problem
manaseable.
.....
t
.>{--
'. )<---.
.
-_--
c
n: U
><LA-r.ll
.Ttn*!. yr*ryr
l.;trrs r'rl' rt'llt'r'liorr iurrl r r.lr.:rr.liou Yh'r,shoultl lhc ruk:r al)[)ritt. lo ltc bcnl.l
. Angle ofincidence = angle ofreflection
The difference in index ofrefraction for air and water causes your eye
ffi
0,: 0" (lawofreflection) be deceived. Your brain follows rays back to the originthey would
to
have
had ifnot bent.
" Snell's Law of Refraction considers the
slorving of ltght in a medium other than
acuum . .. the inder of refraction
nosinOo : nrsinO, (law ofrefraction) (b) vhr rlc n,lt rnrur I'err
()'. r, 7
r',,,r,,,.- i,' "
" T---.. , rL.,L.l
,, ,.,-,1itr-
t
i ,i-i{r'ril: l.jr '
Itr,r.;.t,, i tt"r",i,,r ltll"f"''t"i
rr"3'
l'' i, '
I
,,,,i,n '- ri'r'l
r',,i':,i-.+ ,"1:
lrrrrrirl.r | lrrrrirt /,
!''ll"r"'l i Il''ir'rc'l
(hDiqhr+ rrhr - '-
*irilr. u"r,rn;. * w-...;:,
'c,Fin '*. "-^_
I:tbulxtr:rl iudcrlr of rt'Ir.:rr.1inrr
Quiz'/u sheet of paper
'L Witc
down the relationship of frequency and lhe wavelength of light in a vacuum.
2. lf an EM wave or light enters a dielectric, ii .: t |,rq,lrr 1r:y rrjrna i1s thr
safrle. As il enters
the malerial, the electrons in lhe material vibrate with a driving frequency
equal to that
of the EM wave but ils wavelenglh would differ.
' The speed of light in vacuum is c = 3.0 x 10s m/s, what wourd be irs speed
in water if its
index of refraciion is .1.33?
3. r'Urite down the law of reflection andiefraction (Snell,s law)
l)r.|t,j4rtj( t!1,
'
As index ofrefraction increases, velocity of 4. Knowing Snell's law ani the theory of index of refaction, rank the
speed of light through
each medium from l.easl lo greatest.
light in the mediurn decreases
iil[ ]l i(lll r!lli
:rr '
I I l):
I r, ! r,rr,{
(i 1,,' r1 r!.
ti.riL,.
{ ll: |'1.' 1l'1. l i
roplns6rs r,xrsft:noi fd'c!i* r... ru"rl-, *L""".iim;u
{r,Dn!frrrY)Nt,c'nonrihrcnnhtnc ntrhrnhinsrrsF$.ddn6_{atdr

4. Quiz (by pair) >:)
?8. r' : r'.. ....rs r I rt it nrc ,: tr I rm
l-,.r. ' -. ': , 'r, r d,r ,r.1. . f , lt.0 flr, I
I
ibi:rr - -- r n ,,, r ,._.1 -r,. sb,c
.il.d fi:. , , ' r;, r.lJLiur rN ui('j ti4.
I
r. -., i,- j.t.r'rrd :p:shr or in I
-
t f.lrapfer"35
i I trlrr(trtrt qhs Fr .:il
"ih iFr inArc O -
nutrcn an8lc or in, ,Lj,.. ,j ti,r qtth
fm.Bc rr.il il,. !,Jr(r ridc:
.
Irr1u'l'crurcc
t
I
I
--J "FlSarnoin t' L eiure j jrr
Uhivereity phvsics. iltetfth Ediilon
.
- tlu;h tt | ,'.,,-."nj R,,-;; 4.r,14.g,,1,,,
f*rtura b] ta'lres e".," '., .
".46. - * r!-*,*. g"*.iror.***,,
r*m
( ioals lor.( hupltr-"l5
I rr I rorlucl ion
' To consider interference and coherent . Rainbows in the skv: been
sources there, seen that. A t-hin-film
. soap bubble: why should that
To study two-source interference of light create a rainbow effbct?
" To determine intensity in interference " This thin filrn is dispersing
patterns white light and revealine i
r.o.y.g. b.i.v. spectrum oicolor.
. To consider interference ill thin
films
. To study the Michelson interferometer
;h.mil;rm;;6,,uffi;
c.ri!h! { 7(n3 t{iFoi |dtr.dhi ln! pullrhins n tjdnoi lddRon.st{
Wlll. I'r"onls l)rrrrr :l rlirlrrrfrl:rn.r,
'lhink back
"srra;rslroI"
to our first slide on
rvave motion rvhen the father The "snapshot" of sinusoidal waves spreading
out from two
thre, an object into the pool and coherent sources.
the boy watched the ripples
proceed outward from the
disturbance. We can begin our
discussion of interference from
.lust such a scenario, a coherent a.- *tt
source and the waves from it that
can add (constructively or.
destructi ve ly,).
I
1
''u tl
,i ll
(;r$sir I ld,src.roi r:dkilr,-r""
n,,riu*,-^i'iu***.
;;;;;;ilffi ffi ;;;r.h;ffi ;;',*N.-

5. ittlcrl'crcrtr:c ol' lighl
" The "snapshot" of sinusoidai war,es spreading out from two
We consider
coherent sources.
(i)],,.,J' ..,i I I rl'i
l:ll11rlr: !1 r rr111 1;iq'
Single wavelength
Best example is laser
(..:olrer eitl
.?' ,,)
'1 '
I
tr,r.. ,t Same frequency
I -.-..'' ,",,, Definite constant phase relationship (not necessarily in
. phase)
",,;,
i{.:i;
',
. ,. ,,",i:q, ^
' 't,
i .Trrsr , rnr rr,n"i I hn!. k*-;*;
^ "**""r.
l)ou hlc slit iltIcrf'cr'*-.ncr nf' IiIh1 l)oublc slif i rr lcrl'crurcc ol' liglrt
" Trvo rvaves interfering constructively and destructively, ' Two waves interfering constructively and destructively
. Young did a sinrilar experinrent 'ith light . Young did a sinrilar experiment with light.
( tlrnilrir:rl lJ,rrl: lrorrr ri,,.lil
r,i. lrirnl. i (b) ;ctLNl $r.ort'tn, {c( 0 lrln} thr. .i(|f;) (c) Af If,iitnirlc gc(nnctry
{rnn lllrnrirl i(
if i,1{&**;
'I i/ rirr d
lir:h(
- -/ t .l
I
!'i
=
-
T
*
-*r
i orrnrhr 1 l0,r ltrF4 t Jtrrrih tk. rlFlthrr n t,cr^( i !t.r!i $r, (nfn9hrl]i)ili.i^onrh'!niitn..ntr6tnhii!ntciAoi JdL6.brc
s the ll'tr1cs inlcrlcrr:" trtrlur 1lr rrrlut'r. li.ing.es As thc 1'aves intcrl'crr, tlrcl' produce li.ingcs
4i
I
.hr.i
lrhr
'- I
. ni
H
:
I
'*[-
I
,4
I
*i
.=l "0t1 ,i.
,,
fi.,...-i: -ol I
l
-,H I
:
I
J
$ ftsins krcn
dsi,n0 : m^ Consftuctive Interference
dsin7: (m + l)r Destructive nterference
I
m is called the order number
'ornshr a 2fir3 Pd^o. fdnciin tN. roht(i;! r fo6oi,!kr,!D.!_r$
co'+n,r2mrpsftoi*r,cri-r*.1,nrn'n3-"*.^..ii[iilil

6. Irt(u'fi'l'cuce li'orrr Iwo slils ol Irvo l'arlio sle{iolrs
L,' '. l:r l',rsition of rn,ir lrright band ' In a trvo-slit interference experiment. the slits are 0.200 mm aDart
fi
E
and the screen is at a distance of 1.00 m. The third bright lringb
.q ' (not counting the central bright fringe straight ahead from the slits)
to,rt),,,: !Jn, lL is found to be displaced 9.49 mm from the central frinse. Find the
: .$1 .,, ttl rr avelerrgth of light used.
i U,,:^t
$fi
lrrtr s1t;t.. r1t{ir.s ll:r4,,, : .s1r14,,,
&s1''
,l
lt' brrL r1 sin.O,, : ry,),
3
2
m,A
tan0-.,
= .sin]m - d,
I
ton?r,,: llruf L
trt). _,. /T
$,.,,,.:
Um/t'
'l - k_n =
r--'-- -,- *it Screen
.rt nr . rrr
As=..!:
ar^o f do.r,6
-fl
f 1ru. N[L.hins il td^on dJnq.(!..,
l rrlcl'lcrtrtr"tt' lrr:lrr llri ntr,r' ll:ut ir.:r l l lr,l l l * :t,l t'c Thin Film Interfererrce
I 80o phere No phase
change changc
{c) I r. ,r,f,rri..rr nr. n{:.. l.
r --:. A
.: - r,,rh..rnt,.l.nLr'1(l
l1 2
n.
Air
Constructive Interference
;.- A
|Im i I 2nr= (nL+ t)I n= 0,1,2,
1f
il t
I
Destructive Interference
2nt'- mA rr = 0, '|,2.
{ onlnthr r ?orr h,roi I dr.nnn Inc. nnHnhiir il I'qlMo;ddnoi..Bkv
'l'ltin lilrrrs n ill irrlt:r'li'r,.'
Quiz. U nclerstanding interference
(a) llrlcrlerfD.. hctvcfil r0y n.'lr.rr,l 1n,!r if(
r$ o !r' x.ci,t x thir llhl l. A lascr bc:ln (I = {i32,ll nrn) is in(:i(l(:nt ()n tw() slill
l',,, fr,r.111,,,,,'r|.,i.t,,r i, 1 ., i 1).2()0 rrrrrr apart. I lorv far apirrt arc thr bright intcrfer-
. )r ,1., . ',: 1f- JrlIr i L, r.., tr,r ''lrr'r r'. !l crrr:e fringcs on a screcn 5.00 rn asal tiorn thc slits?
/ ,'rl t, r'!r:I ... ,t.rl. fr.
'3.1 lxrr rarlio rrrrcnr)as trcpiratcd l)1 3()() n as slrorvn in
t'igirrrr l'37.3 sintultancorrslr br oadcast idcirical signal!
at ih(: if,rnc $au:lcngtl) A rndi0 ir) r (rl trir(.li'tg (luc
(b) lhc nifhd{ lriil!c, ol xr oil li(k oil srrcr north rcccilca thc signalr. (r) Il drc caf i! nr rhc posi"
tion ol thr: sccond nruiorrrm, r,hlrt is thr: r,rrclcngrh ol
thc signalsi (b) I lor mnch fartbcr nrusr rhc car rnrrcl
lo cn(o(ultcr thc ncxt rninimunr in rcccptio0? (.'olr' l)o
not usc thc small,lnglc approximation in thi. problcn).)
3u,n
i.it'oungs d{)ublc-stil cxfcimcnr is pcr{brmecl wirh
58$nm light an(l a sliLrGcrcen disbnce ol 2.00 m. lhe
lcntll iDtcrfcrcncc ninimum is obsctlcd 7.26 mnr front
thc ccDtrnl tr)axirnum. I)crenlinc thc spacing of dtc alib

7. ('lltls J()
. Fresnel and Fraunhofer diffraction
Chapter 36 . Single-slit diffraction
. Diffiaction gratings
I)iIll'lrrtiorr
PORs'tr:i.' 9:.i,-.:i--
Unl!'er-cig, Pitlsirs. Ilreliii €rJarorr
- i/rrs.r lt l.,u,ri ..! R,,., .t t..(,,11tt,t
lcrlr,* l,r .l'rxr' l'rlun
c.r*. Fr b'!i r&ji6 lR. FNnhiis i lrFoi l,Uion_6!.
I lt l rorlucl iorr Ij l'es rttl a nrl Ii'ra u n h o Icr ll i,{l'ra r:i ion
, It's intuitive that sound can diffract According to geometric optics, a light source shining on an object
(and travel around corners). Light
in front of a screen will cast a sharp shadow. Surprisingly, this
doesn't "shor.v its poker hand" so
does not occur.
easily.
(lconrclfic optics l)rcdicts that rhis sjtuation
. Ifyou shine light fronr a point shtrtrkl frrllrtr: il i){rp bonndtrrv hets$)t
source to a ruler and look at the illurrination antl
shado,uv, you'11 see the edges are ... solid sltarl,
'rv i DOCST{'T
',veli ... not sharp. A close 'Ihat s NO'I $,hat HAPPTI'I
inspection ofthe indistinct edge rcrrlly hrpp.rrr!
rvill reveal fringes.
. This phenomenon may not sound
Point
source
useful yet but stay r.vith us until the
end ofChapter 36. This line of
thinking has shorvn the way fbr
advances in DVD technology and
applications in holographl,. Straighledge
rbPflghr r ld)[itr.on ltrtrn{ lr I 4^nph,
' )m | !Ja,.r |,ii,.rr i tr. rurtnhrs.! I,uFr- drr n.ct
l)if'filr'1inn l)il'fi'aeliorr l'rorn a sirrglc slil
Ifthe source and the screen are close to the edge causing the diffraction. the
effect is called "near-field" or Fresnel diflraction. Ifthese objects are far
o) wAri€atrY f,aPPlnr:
apart, so as to allow parallel-ray rnodeling. the diffraction is called ..far-
lffi' m
field diffraction" or Fraunhofer diffraction.
Fffi PxiilkLnry .r)n(1v('mric
li8hl
.opnrnr. nrihrcon lilLrNrr'i Inc rahtniii! n p$rrn dd;on.!td

8. lrt
/rllr'h ll ltlll(' ilt ilt:llr.ili{ rlrll,.r, r,,,11
I"l csrrcl ol' li'l-aunholt'1.':'
' The figure illustrates Fresnel and Frarrnholer oritconles
.
J,r !{r. {a), x. r L ,n trr, lfr. Differentiating Fresnel and Fraunhofer
ll, l
',' 'll *ril l
I ll
""''trl*:t
' .i .,fI.--- - _----
-:::=_lr
:-
I
i.rr! !
rholc riir. r,r /, relrt,.{,nlr;i rtrrl liir!r
i.l l..,ihrilitrr ftrLlr nrfiriili.i (d) lfr.'rrrs I r.(,nh..f.r rhtr.,: rr .n
(b) Enlargcd vicrv ot lhc h)p lrrlf ol thc srrr
. rr " , .,r,rll .r, ,...j| Lr.- rrlr
'
. , r rl: .,,. .,,r t1 t,,,, a
" i r.t tj
r! ., !r": . 1 ,r, .t.,!1. t.j.(' i.
(nrrsr . pr Rr^F r ar:{ir rr. n$tnhh! n tdroi etr,n ELr
I"l'ir rr n hol'c r rf i f'li.;tt't ic,r ra
F rr n lrol'cl. tli l'li.aciion
divide source into two eqLlal oa(s
f,r,,o=f destructive interference
il,*, bFqi
: ll . - i divide source into four equal parts
j.si.n, 0
-l
: !
r'lf"
Inconring
Vl.''u=?ll
l.l
I ano so on
v
(nnn8hr.z$eP.r^inFduc,ri6ts. .ruh[.r ier!t,o^oi djn,i !r il
Iil'lr u rr lrof'c r. rli l'l'r.ir,-.1 itrr I;r'aunhof'cr rlilli-acliolr rrnrl arr cxalnplc of analvsis
. A photograph ofa Fraunhofer pattern from a single slit.
|]
li
II 4
ll sn9 ' 211,,
. i r< r3
" n!2. sin0 - A/ a
,'A ,2
I 4 sirrd= o
" a/2.
sin9 - -7/ t
a. /
ll' ,i'', snr9 = -27/ t
-_ ll 'i
U-
k-- /i- /r0nt
I sin0=aI n-11,12,13,
l---.--' I .ru,iirdiu" I
conclition ror
lintgrlgl*l9q _ *J
lottrghrt 2rr[lc,Fonr:a'cirirtx.nhtrh;!iit,E^r [fn,n.trsts
16 i8h r' lm3 h'Bon lin,cir im I nc _ puilnfrin8 ,! lcrG.n ddr6_ b L!