Lzi'ri\ Q'

r,t-rlotictltNz€k 3

Two 9ourc€ lnterreren.e (e.s. vounsrs Do!bl€ S!it Experimenrl

Palhdfle.ene/i lnlerferefce

1

2

l

5 31. - 2.5I=0.5t

E:3!!ple2Wtlr referen@ to Exampte 1, the h{o colrerent sou.@s are now generating waves out olphase Detem ne wheth€r constructve or desttuclve interferen€ occuB ai each oo nt

Exampie 3Two microwaves solrces A and B are n phase wrh one anolher. They emt waves orwavelength 40 0 mm The ampllrde ofthewavefom source B s 3 times thal ot solrce A Adeleclor s pla@d at po nl P where it is 1.00 m irom A 6nd 1.19 m i.om B as shown berow

Conditlons iorobsetuable. steadv interterence panerns (irinoes)

(i) The sources mlsl be cohereni (ioplyng sources rrave same rrequency afd

(i) They have roughLy ih€ sahe amplillde {1o achlev€ mmpete wave cznceLalionand good cont.asl belween maxima and miniha or nlensly)

(i) For lrais@6e wav€s they mlsl be eilhe. unpolarlsed or polarized in rh6 sameplane (rortknsveFewaves)

Constructivs oesirucrivelX =nr. _ =r" jnwhere,=0.1 2. wrerer=o j,z.

^o = 2nr Ed A,l = {2n lrr €d

wher€n=01 2

^x -nL o" =1a l1i

wherer=0,'l 2 wh€re.=o 1 2

Expainwhvthe intensity detected at pont P s a m nma

Path dlilerencG BP - AP;1 18'1,00 =0,13 h = 4,51, Since the sources Aand B arein phas€, dgstruclive inlerference occuE at P.nd intensityat P is minlmum.

What s the facl on ofth€ nlenslyatPcomparedlorhe nlenstyatO

Amplituds at P = 34-A= 2AAmpliluds at O -3A+ A= 44

since r.,a:. ! = /arll'?= %

As the deteclor s moved from P lo O. a serles ofminma and ha,maw€.€ obsetuedExpla n lh s phenomenon and staie how many mi.imum and ma{mum po nts w I beencouflercd alons lhe way to o (ncus ve ol P and o)

As the d6tecto. moves to Oj the intenslty alt6rnates dueto rhe changing pathdifierence. There willbe 5 minlma {lncruding P)and 5 maxima (inctuding O)

State lhe type ol fl€rfe@nce al P when solre B is changed to be anl,phase wlh

Conslructive interf erenco-

$E.AEIA{L!qIE.lfth€ bro coheBnt sources ha\e a ohase ditrerence aln /ad.

the conditions for constructive and d€structive interlerence are lnterchanded.

EI3lplel-rhe d agram below shows n{o coherenl sour@s ge.eratino wave n phase Tlre dashed lnes

denote the wave lroughs soid ines denole lrre wsve cresls Th€ tvo waves nterfere ln theshaded.eglon Delemine whelher conslructve ordeskuctve l.lerierence occuis ateaclr po nl

(i)

(i)

(iD

(iv)

Ya!-o-s5-D.a!.bl9sl!!s-q-a!.s!

Lighl sou.ce olwavelen9th r.

I

J

h,^",,t,w,,w,r'v",.rrr,wlI ,,.,.

Delermine how the sDacnq belween lhe tlnges on th€ screen woud be ,fieded if thelo low ng changes were made separatey

O lhe screen Ls brought nearerlo lhe sits by0 5 m

Slnc6 r cD, il D decreases by 0.5 m, x willdocrease too.

(i) the sits are separaled turlh€rapad by 0.5 mm

Since x d 1/a, ifa is increased, x willdecrease,

(i) a red lght oiwaveLength 7 O x 1o r

m is used

Sinc€ x d l, if l increases, x lncreases too.

(v) one olthe doube s ts s cove@d

Th6 interference fringes will disappear,

the d slan@ betleen lhe doub e slls and slng e sLit s edlced

Ths rring. sopa€tion is unaffected, lntensliy ol brighlfringes is increased.

lhe spae between the doube sll and sceen slledwlhal.ansoarentm€diumoJreiracl ve index lrigher than thal for air orvac!um

Th€ rringes produced on the sc@en wlrl b6 narrowor. This is becauso thowavel6n9th I is smaller in medium where the refracttve index is higher than

where x s lhe dlstan@ benve€f tuo adia@nl brqhl fnnqes {or two dark ir.ges)a s the distan@ behreen the doLbre sils (sitsepamton)D s lhe distan@ irom the sltslo the sc€eni is the wavelenglh orllre ighl

Exampl€ 4lnaYouiqsdoubLesllexpe nent a tulrerent honochromallc bue llghl ol waveength 4 0 x10' m I lum nales two naFow para Ie s its s€paraled by 0 50 mm A wh le screen s p a@d 2 !m aqay irom lhe slls as shown below:

=g=l=B

(b)

Descib€ whal caf be seen on thescreen.

Evonly spaced and approxlnately equally brighltringos of blu€ llghiwill be fomed

Calculalethe separaton beh{een the fringeson lhe screen

1c)

1.,Ils.

I

I

Iio,I.lerBrorsflrnseI+ enlG brgrrLrrnge

I. rElDrsnrrrnse

tI

(v)

I

(v)

(vi)

'-)

one of the doubie sits iscovered by a thin g ass sh€et

The opticaL path ls increased and the tringe sysbm is shilted

AD

Examolo 5

Fg 5.1 below shows nol lo see a. expermenta arangemenl ior srldynS the tEnsmtsston

. ro't. io,. )6 .o,

v 'o

60frP

l4onochromatic lghl from a aser fa]ls norma yontwo narrow coseyspa@dparae sits.The inl€fsily olLght transmtted is sludied by movng a sma ighl sensor a ong the inepe,at2 perpe.d cu ar d stane of 6 0 m froh llre s its Fg 5 2 shows how the iqhl ntenstv vartesr I'or r" f )'oi e ad por'O.

OQ

-6.0 -4.r1 0

Fig. 5,2

O Wial s the phase d li€rence. in rad ans. befiveen lhe waves atrving at po nl S?

phase diite6nce atS = 2r x fl =znx/2 .3nad

(c) The spaclng ol the s s in the expenmenl was 020.0nr. use lhs tolerher wlhnirrmation kom th€ d aqrams.lo ca cltate rhe wave enarh oi the toht

F.om Fig, 5,2, fringe separatlon y = 1,8 x 1ot m

Youns s Doubls s irs Equarroni). = !l

=6.0r 10i m

(d) Descrbeandexpranchanges(itany) nFi!.5.2 I the I ne pQ is I led wirh p ctoser to

From O ro Qj the intonsity peaks wi become sma erand the separation betweenrhe peaks (frrng€ separatioh)wideras e ts now turtheriion theatirs.

+o"OtoP the nr€nsity peahs wittbe(ome tdrgerand rhe soparaton berw.en thepea(s wil become "a ro6or .s P is now nearerro rho stirs

Exaholo 6

Fg.6 beow shows n{o speakers. S, and S,, confected to a stgfatlenerator The wav€s

so€ed ofi.'rn.l'q rrn (

(0

Fiq.6

Whal woud a person standng at point p h€ar a oud or soit sound tntensty?

Path diftereace = 1 m = 2(0.5) = A, ie. n A, duftipte ot wavetensthsinc. sources arc in phase, cohsttuctive inteiercnce takes ptace atpThetelore,.taud saund wilt be heard atpointp.

?.0 ,10 6.0

lExplalnwhyllre Nvo lghl waves from the stG prodLe a min mum intensity at R

As the two wav6s are oul of phase on aniva at R, destructive interfe@nce takes

Ih6 superposed wav€ is a minimum and thus intensity (that is proporUo.at tosqlate of €surtanr ampritudel is atso a minimum,

(i) Point o s equid slanl fron the sirs sial€ . re.ns oithe wavee.gth I rhe parhd fferen@ belween the waves arriv.q atS

Since il ls the second order mtmim!m arS, the path difierence = {1 + %)L

{ii) Ih€ person stzds lo move away rrom p towards O Ca cu ate rhe d slance that he has rocoversuch thal he wt frst reaclr a pointthalgiv€s mnimum sound inlensity?

a='l(1f14-5n)D Ai.t2

Hencehe haslo nave0,6 n ftom p.

ExamFle 7

Two oudspeake6 L, and L, drven rrom a @nmon osci taror a@ ara.ged as showf be ow Addd-o'r dd co! D ea - , o rpos.ratoi gred_atr .cd.eoioa,-0! to,000.1/rt-oele.Fo ord pd.sF. 1.o.q' o F,60o

Ca cu ate the frequency al whch the second m n hum is obsetoed q ven that the speed ot

---patn aifierencs = rzo- Lro= ./40t;!i - qo = r m

f10Since thesound waves orlglnating tron both sp€akeF are tf phase, the sound wavesariving at D are tr rad ou!-of"phase and a minimum ts obsewed when t= t70 Hz.

As tinc€ases, A oisound waves decreases,

When Ax;l, a maxlmum is obseNed and when Ax = 3/2l, a htnimum is obseru€d

Ihe second nln mum occurswh€n

!19 = 5 ro H.I

Diitraction qratinq eouatlon

Th€ sou.ces are at in phaseAtthe biglrt spots @nstructive interieren@ occurs,lhus path dlferen@ = ni.

1.",1..-"..'),."..' ,"1,:t',, ... where n s an nteger. the order ot diffraction

I rs the waverength ol tghtd is the 9ratng spacng3i is the anqte ofdifiracl on

dnedon oi the nlh order brqrrt ine and theAnge oi d lrraction s the angte beh!€ef thestra ghtlhro!gh d.ectior

Example 8 (N95/l /3)

You ae asked 1o nnd ttie wavelefOth otmonochromatic red tght emred by a taserThe appdrarus s Iustral€d n the n9!re

The dillEclon gratng has 5.gt105 ines permelre and s set so that irs plane is fomatiothe incident ight and is situated 1 50 m froha arg€ screen Bright spols are obserued at055 m and I44 m from lhe @nlE bnght

0 Ca cu ate lhe wave ength ofthe taser tghr ofthe nrst ord€r dfiracted tqht

1=dnn, =r 82\Loir-fll=625,,il5r+o 5t(i) suqs€st o.e advanrage and one dsadvantaqe oi obtaining lhe wav€tengrh by usng

obseryations olthe secand,orderdifiracred ighl ratherlhan thef6rode.d fiiacte; i!ht.'

oisadvantago: 2"d ord6r tmage is t6ss shalp and tess brlqhl determinarion of th6oostrroa ol ,? is toss accu€!6i tess accuacy in ca c-tdred vatue ot i.,Aold-rage: 2 d oro€r image has targe, d) compae ro r. lrom 1! oder rmdge.Largervarue of A? g&€s towet percenkge uncedaj.ty itr tho measurem6nt ofr? a;dcal.ulated value of i.,

d =1/5.5x10' = 1,82x10' m,

Using I andforn-1

Example 9

Adiifraction gEting wlh 500 .espermm susedtoexamine ilhl toh a gtow ng gas lisloundthatlhelrslordervioelfrngeefrergedalangtell.5 lromthe st.atghllhro!gh positior

0 Show that llr€ wave enqth ofthe votet lghr ts 3 99 x tO r

m

d =O.OO1/5OO-2x10{ m,€ = 11.5, n=1d sino = nl

2 x 1Oi Xsin11,5l = (1)Al - 399nm

(i) Lt s obseNed lrral the 3'd order red fiinge overaps wilh the 4ri order vio el irnoeDeterfrine the wave ength oithe red tght

Since theirlnq6s ovedap, the difractlon angle,0, isrhe same isin 0= n,Ir/d = n!4,/d

h€nce, n..\. : n! A!3I. :4(399x10!)

l, : 532 nm o.5.32 x lot h

d "dqed*ri o

slnce sio 3: n,l,/ d <1,n, <d/4,

< (2t 10-6)/(5.32 x 101=3.3Thereforc maximum order ls 3

FromsnS=n,4./d 5 s = sini(3)(s.32x 1oJ)/(2 x 1011

(v) comment on how the irnge palteh and co rasr oirhe fringeswolld chafqe ifa gratngor'1000 ines p€rmm sLsed.stead Assumetlre stiwidrh is corslanl

When numberolslits pe.mm is doubled, spacing between brightriinges ircrease,totalnumberoi brightlringes reduced, Fringes b€come brighrerand sharperj orcontrast is improved (not bn9ht34.

ddsa. o-aar.gr'r/50 .pdro I o..oido bl Fl0r'

^ s! eF.ola Fd200.n b.yolor.Fo.h 9les o L6 adge! rda-.i-o c..-,dIpos ons on a scale o.lhe s.r€en as showf n F. 4 2

Example 10

(i)

(D

(i)

Use the lrst orderspectrum to dedu@ a va!e forthe waveenlth ofih€ btu€ ighl

, -.tEna' .226, =ra1.3

dsin9,=h^

r'-l! =ro.ro". and ."i =! ard n = 1

r=4ra=14 !. o.,la,=4rr, o .

Howwourd the panem obl:ined be diflerenl itred tghtwere used n p a@ of blle lght?You are nol elpected lo make any €tcuatonswhen answering ths parl oithe queston.

Red light has a rongerwavetongrh than that of the bhe tiqht. Fron the equatjon, - o , we erpsct the orderspecrums ro be sodcod runhe,apaar;or oae

anot'oron thesc.een slnco is largerto d tong"rsave,elgr".

Whatprobemwolld arse rtheexperimenr;ere rep€aledw h jnrra.ed.adia|on?Suggesl how lh s prob em cou d be overcome.

The 6ain problom i3 that lrfra{ed radiation is invisibt€, hence no image can b€seen on th€ sceen. Any dovice which can b€ used to d6t€cr heat auch as athernopilo may be used to de16ct regions oinaxima,

200s Jczts2Fhyscs SlpeFoston

E&splc]lLighl waves ollrequency 7 5 x 10! Hz is used 10 oblan a pallern of high and ow intens ly on a

S. a " 2 -"p" "t" soJ es

{,)

(D

Siale and explain the princlp e wh ch causeslhe patlem iofom on th€ screef

Principle of Superposition,Wh6n 2 or moro waves me6t in tne same space a.d time, the Esultant ot the wavesls the vector sum ot the indivldual waves and 6ach wavo procoods as tholgh no

Skte 2 condliofs thal musibe F.esentin orderlo oblaln obsetoabe interlerene panems.

The sources mustbe coheent AND

2. The waves mlsleither be unpolartzed or b. polarlzed ln tho san€ plan€3,Ihe waves dlsl be or the safre tpo,4. Th€ wav€s mustbo of simlla. am plitud€$

A deiecior. whose inlia posillon is O, s moved along the screen inlhe d recllon ofPnlelJa 'roJ d ar P srdlig noa o o-o erorg dl P d roe or 6

aa.rr.r I e.!psa'edFrA.ed Tl'"d6ra ceD s I0ihl.'eoDbb0r r0'{. f'1dlhe dslan@ betwe€n the 2 sources

(Dirqfn / Annhine 10 $h@ lhal OP 's

?., rims the d stare b€lwd 2 @'rsu1ileharimlm iit.nr ly 3p.L)

7 5x=6.0x 103 m hen@ x=8Ox1OrmI.lo'!

^tou.n..=19 o= ?5 10" 5^ro '-

(v) Sial6 one assumpUon in your *lcuallons in part {iii).

D ) a OR Amaximsm int€nsity lstoond alO.

(') The above expe mentis repealed bltwith a tew modiicalons1 LishlorwavelenglhS0xl0i misused2. A dlfi.acton gratinA wth 1000 inespermo susedlvhe lhe deEcro. c plsFo dl P, a xal o.de fa, r L- 5where this maxihum is delecled.

d=-=ta/ta.1000

using d sin€ : nI, n: 1

(ii)

.-'+i++-i++.-i+..-.?-|+'i.++.-]L