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Geometrical Optics Theory_e

thinkiit lecture notes iit physics

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  VK\SLCS jnglskdujnrpkyslcs.lg  > BEAJEXPL OAVXL S LGXPAHUCXLAG= @oueondes,ackreheserts,breegiarest,nghjuotlcaoarehrnlg`awscng`eegmayeh`yngyagewkaknseyeswltkwklcktaseetkej.@ut`ystuhylgbtke`rngckai pkyslcscnooeh aptlcs ,wklckhenos wltktke`eknvlaur aiolbktnghatkereoectrajnbgetlcwnves,wecngrencknheepernppreclntlagaitkevlsl`oewaroh.Ndgawoehbeai tke prapertles ai olbkt nooaws us ta ugherstngh tke `oue caoar ai tke sdyngh tke heslbg ai aptlcno hevlcessuck ns teoescapes, jlcrascapes, cnjerns, eyebonsses, ngh tke kujng eyes. Xke snje `nslc prlgclpoesai aptlcs nosa ole nt tke kenrt ai jaherg heveoapjegts suck ns tke onser, aptlcno il`ers, kaoabrnjs, aptlcnocajputers,nghgewteckglques lgjehlcnoljnblgb. >.CAGHLXLAGIAPPECXLOLGENPVPAVNBNXLAGAIOLBKX (Agoy iar lgiarjntlag gat lg LLX-MEE syoon`us) Saje pnrt ai tke aptlcs cng `e ugherstaah li we nssuje tknt olbkt trnveos lg n strnlbkt olge ngh lt`eghs n`ruptoy wkeg lt suiiers reioectlag ar reirnctlag.Xke nssujptlag tknt tke olbkt trnveos lg n strnlbkt olge ls carrect li (l) tke jehluj ls lsatraplc, l.e. lts `eknvlaur  ls snje lg noohlrectlags ngh (ll) tke a`stncoe pnst wklck tke olbkt javes ar tkeapeglgb tkraubk wklck tke olbkt javes ls gat very sjnoo.Cagslher n solt ai wlhtk ‛n“ tkraubk wklck jagackrajntlc olbktrnys pnss ngh strlde n screeg, ponceh nt n hlstngce H ns skawg.Lt ls iaugh tknt tke olbkt strldes lg n `ngh ai wlhtk ‛`“ jare tkng ‛n“. Xkls `eghlgb ls cnooeh hliirnctlag .Olbkt `eghs `y (`-n)/0 ag enck slhe ai tke cegtrno olge .Lt cng `e skawg `y wnve tkeary ai olbkt tkntslg   :n  .......(N),wkere    ls skawg lg ilbure.Xkls iarjuon lghlcntes tknt tke  `eghlgb ls cagslhern`oe agoy wkeg n ~   . Hliirnctlag ls jarepragaugceh lg saugh `ecnuse lts wnveoegbtk ls juck jare tkng tknt ai olbkt ngh lt ls ai tke arher ai tke slze ai a`stncoes ar npertures. Iarjuon (N) blvesnH0n`   .Lt ls coenr tknt tke `eghlgb ls gebolbl`oe li  Hnn   ar   n H    .Li tkls caghltlag ls iuoilooeh , olbkt lssnlh ta jave rectlolgenroy. Lg jast ai tke sltuntlags lgcouhlgb beajetrlcno aptlcs tke caghltlags nresuck tknt we cng snieoy nssuje tknt olbkt javes lg strnlbkt olge ngh `eghs agoy wkeg lt betsreioecteh ar reirncteh.Xkus beajetrlcno aptlcs ls ng nppraxljnte trentjegt lg wklck tke olbkt wnves cng `e represegteh`y strnlbkt olges wklck nre cnooeh rnys. N  rny  ai olbkt ls tke strnlbkt olge pntk ai trngsier ai olbktegerby. Nrraw represegts tke hlrectlag ai prapnbntlag ai olbkt.Ilbure skaws n rny wklck lghlcntes olbkt ls javlgb iraj N ta @.  VK\SLCS jnglskdujnrpkyslcs.lg  0 0.VPAVEPXLESAIOLBKX (l) Speeh ai olbkt lg vncuuj, hegateh `y c, ls equno ta 3 Ò >6 ; j/s nppraxljnteoy.(ll) Olbkt ls eoectrajnbgetlc wnve (prapaseh `y Jnxweoo). Ltcagslsts ai vnrylgb eoectrlc ileoh ngh jnbgetlc ileoh.(lll) Olbkt cnrrles egerby ngh jajegtuj.(lv) Xke iarjuon v : i    ls nppolcn`oe ta olbkt.(v) Rkeg olbkt bets reioecteh lg snje jehluj, lt suiiers ga ckngbe lg irequegcy, speeh nghwnveoegbtk.(vl) Irequegcy ai olbkt rejnlgs ugckngbehwkeg lt bets reioecteh ar reirncteh. 3.PEIOECXLAGAIOLBKX Rkeg olbkt rnys strlde tke `aughnry ai twa jehln suck ns nlr ngh bonss, n pnrt ai olbkt ls turgeh`ncd lgta tke snje jehluj. Xkls ls cnooeh  Peioectlag ai Olbkt. (n) Pebuonr Peioectlag= Rkeg tke reioectlag tndes ponce iraj n periect ponge surincelt ls cnooeh  Pebuonr Peioectlag . Lg tkls cnse tke reioecteholbkt kns onrbe lgtegslty lg age hlrectlag ngh gebolbl`oy sjnoolgtegslty lg atker hlrectlags. (`) Hliiuseh Peioectlag Rkeg tke surince ls raubk, we ha gat bet n rebuonr  `eknvlaur  ai olbkt. Notkaubk nt enck palgtolbkt rny bets reioecteh lrrespectlve ai tke avernoo gnture ai surince, hliieregce ls a`serveh`ecnuse eveg lg n gnrraw `enj ai olbkt tkere nre jngy rnys wklck nre reioecteh iraj hliieregtpalgts ai surince ngh lt ls qulte passl`oe tknt tkese rnys jny jave lg hliieregt hlrectlags hueta lrrebuonrlty ai tke surince . Xkls pracess egn`oes us ta see ng a`mect iraj ngy pasltlag.Suck n reioectlag ls cnooeh ns  hliiuseh reioectlag . Iar exnjpoe  reioectlag iraj n wnoo, iraj n gews pnper etc.Xkls ls wky yau cng gat see yaur ince lg gews pnper ngh lgtke wnoo. 3.>OnwsaiPeioectlag (n)  Xke lgclhegt rny, tke reioecteh rny ngh tke garjno nt tke palgt ai lgclhegce ole lg tkesnje ponge. Xkls ponge ls cnooeh tke  ponge ai lgclhegce (ar ponge ai reioectlag) .Xkls caghltlag cng `e expresseh jntkejntlcnooy ns P  . (    Ò  G  ) :  G  . (    Ò  P  ) :  VK\SLCS jnglskdujnrpkyslcs.lg  3   . ( G  Ò  P  ) : 6 wkere    ,  G  ngh  P  nre vectars ai ngy jnbgltuhe noagb lgclhegtrny, tke garjno ngh tke reioecteh rny respectlveoy. (`)  Xke ngboe ai lgclhegce (tke ngboe `etweeg garjnongh tke lgclhegt rny) ngh tke ngboe ai reioectlag (tkengboe `etweeg tke reioecteh rny ngh tke garjno) nreequno, l.e.    l :   r  SpeclnoCnses= Garjno Lgclhegce =  Lg cnse olbkt ls lgclhegt garjnooy,l : r : 6   : >;6½ Gate =  Re sny tknt tke rny kns retrnceh lts pntk. Brnzlgb Lgclhegce =  Lg cnse olbkt strldes tke reioectlgb surince tngbegtlnooy,l : r : <6hevlntlag,   : 6½ ar 396½ Gate =  Lg cnse ai reioectlag speeh (jnbgltuhe ai veoaclty) ai olbkt rejnlgs ugckngbeh `ut lg brnzlgblgclhegce veoaclty rejnlgs ugckngbeh. Exnjpoe - > Skaw tknt iar n olbkt rny lgclhegt nt ng ngboe ‛l“ ag bettlgb reioecteh tke ngboe ai hevlntlag ls  :     0l ar      0l. Saoutlag Iraj ilbure (`) lt ls coenr tknt olbkt rny `eghs eltker `y   >  ngtlcoacdwlse ar `y   0  (: 0   –   > )coacdwlse.Iraj ilbure (n)   >  :    – 0l .   0  :    + 0l . 3.0A`mectnghLjnbe (n) A`mect (A) = A`mect  ls heilgeh ns palgt ai lgtersectlag ai   lgclhegt  rnys.  VK\SLCS jnglskdujnrpkyslcs.lg  8 A A Oet us cnoo tke slhe lg wklck lgclhegt rnys nre presegt ns lgclhegt slhe ngh tke slhe lg wklckreioecteh ( reirncteh) rnys nre presegt, ns reioecteh (reirncteh) slhe. Gate =  Ng a`mect ls cnooeh  reno  li lt oles ag lgclhegt slhe atkerwlse lt ls cnooeh  vlrtuno . (`) Ljnbe (  ) = Ljnbe  ls heilgeh ns palgt ai lgtersectlag ai   reioecteh  rnys (lg cnse ai reioectlag) ar   reirncteh  rnys (lg cnse ai reirnctlag).  Gate =  Ng ljnbe ls cnooeh  reno  li lt oles ag reioecteh ar reirncteh slhe atkerwlse lt ls cnooeh  vlrtuno. 8.VONGEJLPPAP Vonge jlrrar ls iarjeh `y paolsklgb age surince ai n ponge tklg bonss ponte .Lt ls nosa snlh ta `eslovereh ag age slhe. N `enj ai pnrnooeo rnys ai olbkt, lgclhegt ag n ponge jlrrar wloo bet reioecteh ns n `enj ai pnrnooeoreioecteh rnys. Exnjpoe - 0 Iar n ilxeh lgclhegt olbkt rny, li tke jlrrar `eratnteh tkraubk ng ngboe    (n`aut ng nxls wklck oleslg tke ponge ai jlrrar ngh perpeghlcuonr ta tke pongeai lgclhegce), skaw tknt tke reioecteh rny turgs tkraubkng ngboe 0  lg snje segse.   Saoutlag  See ilbure J > , G >  ngh P >  lghlcnte tke lgltlno pasltlag ai jlrrar, lgltlno garjno ngh lgltlno hlrectlagai reioecteh olbkt rny respectlveoy. J 0 , G 0  ngh P 0  lghlcnte tke ilgno pasltlag ai jlrrar, ilgnogarjno ngh ilgno hlrectlag ai reioecteh olbkt rny respectlveoy. Iraj ilbure lt ls coenr tknt    N@C      : 0   +    ) ar     : 0  . Gate = Deeplgb tke jlrrar ilxeh li tke lgclhegt rny ls ratnteh `y ngboe   n`aut tke garjno tkegreioecteh rny ratntes `y snje ngboe lg tke snje hlrectlag ai ratntlag