Interference-1 PDF

oteo Palarigod ion/Intestecence -I 0. Introductorn " (i) tictoxicsl Account (Fom Gaep mehical to Physical otptics) Light an an aid ló our visibi lily o Metual objecks has been weil studid sinee lhe dawn o ciilizatfon oilk one ot 1le tirst Ihcorelieal underslandings due lo Euclid (3...

oteo Palarigod ion/Intestecence -I 0. Introductorn " (i) tictoxicsl Account (Fom Gaep mehical to Physical otptics) Light an an aid ló our visibi lily o Metual objecks has been weil studid sinee lhe dawn o ciilizatfon oilk one ot 1le tirst Ihcorelieal underslandings due lo Euclid (30o B.c.)a þropo exþlavatiM at lke Jau_ o bropagatior -nent st recilinea ight ray and geowcrhc reflectioy teromena vellecton and refrachtom have been widely Pplied o Conshuet vatiowO splicol insuen}a ranginz lens la telescobe down he agcs. The -skanding refaction exbeiwental wnder N: Snell and 1hat ot total intcma veflection by 3. Kéble jee finally demonoshated in theoreica terms ee wilk ha andinci ple o lecat time y P. deintroduetion 'obtical bal Fewat (160i- 1GcSAb) 1ight wmotiom ´st mediem þropagation ght involting lka as invokec ar thio leewton Lo a lhin r a i and Hocke corpusculae lhory ot ight. TLbHooke's cbservation and qualitative Rblanoation te remained il| nderstood especially in lha contxt ot intoference and dirachion. st was StuygenS/sieally Matwe ot light te was þrobaby one atached oobserve o 1h ivit 4igurs le source. þolariged lightin oa doubly re achn calcitelõ yclal, tuygen s wave wGs qite less þopulariged fn sbite ot i6initial succes[, The vebilh of Huygens habbened el lhe haid ot Those Young sthY Ihcory hatpeine tue essence o estailished lhe Auygens' exþlaining lhe intt«frre nctpiciple in phsici oyiico cohevent patern due in sþite ofsourecs. A llis þoint it is lo be lhe success of tuygns' vicriuve thi observation rewlaire ill- Lnders tiud lheoy esbiallyiomar þropaqotion occws The exþexinients ovne by fres nl,thrgh an anisohepie cyskl Ike efect of bolkrigction Young anol Arago'on inteatenvc eventualy led lo Young's suggertion tia he real ibratton miht have beenhanese. The,ransvr se ntwe ot lightwave wa furlthered by Farady's exbe vinnts on polanation indie ting þossible assoiaton o' igh iave and elechoaqnctie 1kzovy. Fnally, k þrcpaetii e light wave as bern 1heorised 13ik lhc Maxuwe's (G uatiom) on clechoy wanic Vectoxs  i) Waves and Wave- fvonl, like lhi Foy ouY oreset bucose We a WaVe einito21: A planc hoamonic wave frepagoting aloug tYve x-diyecion s defined by a unciom -A os (k*-ot) evzarki 1. The (oord plane is justi fied be cause fact hat at any þaticula vaue of t he tunction,t o Constant over lhe blanc X= (onst. called |he wave font. 2. hc fuoctioga in 4] nd ve to facilitate lhe caleulatio1. are lhe sotions o so called classical ave quotion: =0 and t) M called lhe wave function. Iy view f eguaton - ) c is tound 3 and k being Constant and c is called lie þhae velo city o lki toave. uce Nee ssay Diag tams x Diagram -1 Diagrom-2. Eqwation - J can bebe intaprehed in lhë Iight of the atoove diaram  represe nls vibration n sin wt, diag rc tine a basficle at =0 ovexY a (simble harmoni wotion) < ibvatio. period 2yo Asinkx, diagram-2 repvesents at t o b. tors l=0, vibratioys at all lhe aticles snab- shots o< -xis. Fo too pa shicles se þaroted byef Gmanged aleng are idential a diance 2k lhe vaes of t for all t. for exmple, Y,t=0, =X| (venfa) lke fregueny and w Called lhe Jetiniton-21 The quantily |kE constanl lenglh atlet wave, IK being The cwaVe vector, lha fact tial i we Lemark:!. Diasram-2 vebvesenls Ike consider 4Shite wenmber of points aloug lhe x-axis 1kan in view of he junctioy , l lha oibrate þoints vibrate simble, harmonically tut not all at a ne. They are lhdrefore sibraiag in dierent þheaes depents ubon lheir displacemenla rom lhe origi. Ts expla - ation sunyo p to lh fact Hat a wave is pospaaating clong lhe positive X-divection tsfile lhã nediim pastilgs ate oscill ating noral to lhe probasation directio. Equation phyjsical consideratiom-1(21) veprc oilk such tyþe t sents a tanseverse loave. The i anoltix kind s wave called louaituina wave 1shue 1he wedium þaticles vibrae lhz ropaçation direchon, lkãngh lhay ainial þarallel lo invelved vequire iore 2. TH s to be noted ltt 1he wave þroile af t=o. diagram-2 vepresenh 3. To unerstandwtict is ectually mDD0M ili lhe wave, let wo tix a a Nae o vale st = This weans isblacewent and hence tixing lhe trom lhc X-axis xis (diaqram- ) (+). hi weans as he quanithy k- at called oilk time le vaue wave mavea move Ika phase. Hene = - to ’d = dt  lhà vectocity c(= 2)ilk shich lha bhase This meays 1he said to be moving i of any þasticalar eeated bhane veboity moving aong lhey- diechion. 0n any 4. tor a blaue tocve in geweral mquing fixed direchion detemintd by lli10ave vecor k Kx ika wave-function = (t)= Asin (K,7-wt) The bhaae" tem k.7-t (at any baticulat instan) i! kept -fxed K.7-t,= Const a t to (onst -4] Thio plane infinik mang indicoteas þoins each|la characteed fact tat thkreby are in brncibk a tiplet {,Y, x whih e in Sae þhase and on lhe same hlane uation Siane o called -4]: Jhe blane a wave moveS ae t vane, he font DefinitoxA ontains all lhe p lane (or a surface in geweral) Itat called a þoints which are In same phae w wave -fon. i) Too Pivctl Issuga in Physica Ohes huyggnsBinciple : et 2, be lla wave front at any 4ime ihstant t and ' be lhe same at t'(>). Jhen some lter instant þossibly deteminea hom Iha kyuledge (), Sere envelo pe tondany Se wavelets and ye comeS wavelets. o lheac (tii) Thc ind fregue nseconday wave lets have same he þaimory wavelel. velocib Se coyndoy Wavelet evelcbe enelake  TCmak : 1, In Huyges' binccble i} atio assumed that The, Ihe boint ohere H hao hoo chect cxccpt Seconday Wave hao touchis \hã envelope. 2. I is also assu med Hat onty lke forwar ming envelobe n lo be consicered n ass uvapton very ften in one and Harec dimenion & o so obowe Valid two diMan sion (ylindical wave). extension 3. Huygens' bincilole avd ts subseguent can suecessfly xblain Ilc phenoCna st refeclion, gMeral. ve haction, intfcrne and difraction o Polariation and Trans verse watune at ligkt wave Y and A(inie wave Replacing Ike seolazs resbeclivel fune tion o cgm 0) by vecto end E gc aE land hencc E) in Gny veclos in Y-z blane Satistyies lhe classical Jave Can be writen cO quction (egn- io).En (s! Foy it Ez )sin Sin(kx--ot) i t Eoz Sin (ka-ot) Eoy toy and Ez aYe constants. How at t=0 we gel he follousing svab-shot af such or yecor wave funchon. (love of bretion) diecton. X bopogation) Y-z kicne (tia. o bolavigation)  lhe fact Hat if one Diagram- 3 vebvesent along lhe x-is Momark :. points bolhetical vectoys(harmoicalty) Considexs a sefo h ing þositions, lhe finC VaryI r relative caable lo brocuce e magnitudea deped Em a vector tshose o rt. Iha fundton, veþrts ibon' ke bosiHon ot Iki þoint lhe, Hþ o maqmitde dehends hore to). And wave time t, 1he res þective orin (at any' þaaheulan connected gives wo lhe þroþaaion all sucn vectors shen vector E s noral to þrofile. This Aiectiox. Thc wave thanse/er Se E(in eqn (si) -in elechie feld, JhE 2. when weclor Hhat thre due lo iMaxwel| assessit and resides clechowagnahic hao to be a maqnehe tield ass ociated oilk is nomal t(Y-z þlane) and 1ha lat o E. Anmong heoc E E ields it one n knowm, ottr caN equotioys. So it be determinad by Mawell'slke'vech. always suffiient lo coyside only. We call iá be lhe it Iight vecor. Tne quaraity E implieo he inteusity olia field (hee zlas tte thlavie potariatioh ihe plane detcmi nee b lke vector an ha probasion dìc igt vecor) 1he plane o on(here x-axis) o Calle ibration. manMex iu called a ne ave nderstood is such a holoarized Wave, Cemposihon 4. Lquation -- 6 can Se viewed yo a supesposhien tao simle haoic osallations atiug ot each oHrc ayd lhey cZe in Sae b n apeskeniuloa t la osillations have non-iial phaae difference lhe plane nibration stots roBaling ovehi ptne at lo vaiawo inter estig eatuzcs. botorizotig nse 5. The Z ualfecdiagram ivndicates a cowblee descption of wave, þocpareling along Y-dieeion X  Mote: Inter tore nec P-1 "I Swper position c} Naveo (i) Ele de The Moivre's formla follooing tuo vesultor il freguenty be used iy ouY subsequenl disca discussion: b. el6)" plne Cosno t isin n Kemank : i. These vesulis ac valid foraNdall nwill andbe0, rel 5ut for present þuspose intege " () Supe þosilion a too wave. Jetiaton-: By sube chosihiom, a< too elechomagmeie iaveo given y lka light veclors ; maan lia realanl etov given by [21 sohtiogs