Physics (CBSE 2009) General Instructions. Time: 3 hours Max. Marks: 70

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1 Physics (CSE 9) Tim: 3 hus Mx Mks: 7 Gnl nstuctins ll qustins cmulsy Th 3 qustins in ttl Qustins t 8 cy n mk ch, qustins 9 t 8 cy tw mks ch, qustins 9 t 7 cy th mks ch nd qustins 8 t 3 cy fi mks ch 3 Th is n ll chic Hw, n intnl chic hs bn idd in n qustin f tw mks, n qustin f th mks nd ll th qustins f fi mks ch u h t ttmt nly n f th gin chics in such qustins 4 Us f clcults is nt mittd 5 u my us th fllwing lus f hysicl cnstnt wh ncssy: c = 3 8 ms h = Js = 6 9 C m = 4 7 T m 9 9 = Nm C 4πε Mss f lctn m = 9 3 kg Mss f nutn m n = kg ltzmnn s cnstnt k = 38 3 JK gd s numb N = 6 3 ml dius f th = 64 km Wht is sky w gtin? [] n th fquncy ng fm fw MHz u t 3 4 MHz, lng distnc cmmunictin cn b chid by inshic flctin f di ws bck twd th th This md f gtin f lctmgntic ws is clld sky w gtin, nd it is usd in shtw di cmmunictin Wit th fllwing ditins in scnding d in sct f thi fquncis : X-ys, micws, U ys nd di ws [] di ws, micws, U ys nd X-ys 3 Mgntic fild lins cn b ntily cnfind within th c f tid, but nt within stight slnid Why? [] f fild lins w ntily cnfind btwn tw nds f stight slnid, th flux thugh th css-sctin t ch nd wuld b nn-z ut th flux f fild thugh ny clsd sufc must lwys b z F tid, this difficulty is bsnt bcus it hs n nds [] 4 u gin fllwing th lnss Which tw lnss will yu us s n yic nd s n bjcti t cnstuct n stnmicl tlsc? [] Objcti: L, bcus th lns L hs lg tu cmd t th lnss nd th sling w nd light gthing dictly dnd n th tu dimt Eyic: Th mgnifictin w f n stnmicl tlsc is dictly tinl t th w f yic, thf th lns L 3 is chsn s this yic Lnss Pw (P) tu () L 3 D 8 cm L 6 D cm L 3 D cm 5 f th ngl btwn th ss xis f liz nd th nlyz is 45, wit th ti f th intnsitis f iginl light nd th tnsmittd light ft ssing thugh th nlyz [] Th intnsity f th light ft ssing thugh th liz is = cs, wh ngl q i is th ngl btwn th initil liztin nd th xis f liz θ i Physics Scil mkt k _9 CSEindd // :7:3 PM

2 Physics (CSE 9) Lt b th intnsity f th incidnt light, which ft ssing thugh th liz bcms = cs 45 ft ssing thugh th nlyz, it bcms = cs 45 = = 4 Thf, th intnsity f th light bcms n qut f th initil intnsity ft ssing th nlyz 6 Th figu shws lt f th cus, b, c shwing th itin f htcunt s cllct lt tntil f th diffnt intnsitis, nd 3 hing fquncis u, u nd u 3, sctily, incidnt n htsnsiti sufc Pint ut th tw cus f which th incidnt ditins h sm fquncy but diffnt intnsitis [] Phtlctic cunt c b Cllct lt tntil Th sting tntil f mtil dnds nly n th fquncy nd wk functin f th mtil t is indndnt f intnsity Sinc bth cus nd b h th sm sting tntil, th fquncy f ditin which cus cus nd b th sm 7 Tw nucli h mss numbs in th ti : Wht is th ti f thi nucl dnsitis? [] dius f th nuclus is gin by = / 3 wh is th tmic mss m m ρ = = π π 3 3 ( ) = / 3 3m 4π S, th nucl dnsity is cnstnt 8 Wht ty f wfnt will mg fm : () int suc nd (b) distnt light suc? int suc ducs shicl wfnt nd distnt light suc ducs ln wfnt 9 cll f mf E nd intnl sistnc is cnnctd css ibl sist Plt gh shwing th itin f tminl tntil with sistnc [] Pdict f th gh th cnditin und which bcms qul t E Th tminl tntil = E wh is th tminl tntil, E is th mf f th cll nd is intnl sistnc f th cll ( + ) = E = E E E = + + Th tminl tntil chs th mf whn th xtnl sistncs ch infinity O quilntly, th tminl tntil bcms qul t th mf if th cicuit is n () Cn tw quitntil sufcs intsct ch th? Gi sns [] (b) Tw chgs q nd +q lctd t ints (,, ) nd (,, +), sctily Hw much wk is dn in ming tst chg fm int P (7,, ) t Q ( 3,, )? (i) f tw quitntil sufcs intsct, t th int f intsctin, th tntil will h tw distinct lus (ii) W = Q ( ( Q) ( P)) kq kq ( P ) = + = Thf P P kq kq kq kq ( Q) = + =lt W Q Q = Q = J = lt Z wk is ndd t m chg fm P (7,, ) t Q ( 3,, ) y wht cntg will th tnsmissin ng f T tw b ffctd whn th hight f th tw is incsd by %? [] Th tnsmissin ng f T tw is gin by d= h wh d is th ng, is dius f th nd h, is hight f th tw Th nw hight h = h+ h= h( ) Thf, nw tnsmissin ng d = h( ) = d Physics Scil mkt k _9 CSEindd // :7:6 PM

3 O th tnsmissin ng will incs by d d = 458% d Di n xssin f dift lcity f f lctns in cnduct in tms f lxtin tim [] Whn tw nds f th cnduct cnnctd t th btty, n lctic fild E is gntd insid th cnduct Thf, fc cting n th lctn is F = m = E () N fild x Physics (CSE 9) 3 Mgntic fild Elctn wh is th chg f th lctn, nd m is mss f lctn Thf ccltin is E = m Thf th g lcity f th lctn which is clld dift lcity is = E d τ = m τ wh t is th g tim btwn tw succssi cllisins nd is clld dift lcity 3 Hw ds chg q scillting t ctin fquncy duc lctmgntic ws? [] Sktch schmtic digm dicting lctic nd mgntic filds f n lctmgntic w gting lng th z-dictin chg q which scillts ducs tim-ying mgntic fild in th nighbhd which in tun ducs tim-ying lctic fild in th nighbhd This css cntinus sinc bth tim-ying lctic nd mgntic filds ct s sucs t ch th; thus th lctmgntic w is gntd y x E 4 chg q ming lng th x-xis with lcity is subjctd t unifm mgntic fild cting lng th z-xis s it csss th igin O [] q O z - xis y z Dictin f mgntic fild is in t th g (b) Mgntic fc ds nt chng kintic ngy f ticl, bcus this fc is lwys ndicul t lcity 5 Th fllwing figu shws th inut wfms (, ) nd th utut wfm () f gt dntify th gt, wit its tuth tbl nd dw its lgic symbl [] Th tuth tbl f th gin digm is Thf th gt usd in th cicuit is NND gt 6 Stt it St lw cunt flws in cnduct lcd ndicul t th ln f th ndict th dictin f th mgntic fild du t smll lmnt dl t int P situtd t distnc fm th lmnt s shwn in th figu z y ασ x () Tc its tjcty (b) Ds th chg gin kintic ngy s it nts th mgntic fild? Justify yu nsw x d O P y Physics Scil mkt k _9 CSEindd 3 // :7:9 PM

4 4 Physics (CSE 9) () ccding t th it St s lw, th mgnitud f th mgntic fild d t ny int P lctd t sitin ct with sct t cunt lmnt dl cying cunt is () Ptinl t th cunt, (b) Ptinl t th lngth lmnt dl f th cunt ci, (c) Ptinl t sin q, wh q is th ngl btwn nd dl i d ( l ) d 3 () Fm it St s lw th mgntic fild t P is lng th x dictin 7 Why high-fquncy ci ws usd f tnsmissin? [] O Wht is mnt by th tm mdultin? Dw blck digm f siml mdult f btining n M signl High-fquncy ci ws usd in cmmunictin du t th fllwing sns : () Siz f th ntnn F fficint tnsmissin nd ctin, th tnsmitting nd ciing ntnns must h lngth qul t n by futh f th wlngth f th udi signl t is nt cticl t us hug ntnn f tnsmissin nd ctin (b) Effcti w ditd by th ntnn Th w ditd by th lin ntnn f lngth l is gin by w ditd l Thf f high λ wlngths th w ditd by th ntnn dcss (c) Mixing u f th signls f mny tnsmitts tnsmitting th bs bnd infmtin signls simultnusly, ths signls will gt mixd u nd th is n wy t distinguish btwn thm This cn b idd by using high fquncy tnsmissin nd thn lltting bnd f fquncis O Th css f suimsing th infmtin signl n t high-fquncy ci w is clld mdultin Th blck digm f th M mdult is gin blw m(t) x(t) Squ y(t) + lw dic m sinw m t (Mdulting signl) c(t) c sinw c t (ci) x(t)+cx(t) ndss filt cntd t w c M w 8 dicti nuclus undgs sis f dcys ccding t th fllwing schm: [] γ 3 4 β Th mss numb nd tmic numb f 8 nd 7, sctily Wht ths numbs f 4? Emissin f n -ditin dcss th mss numb f th tm by 4 nd tmic numb by tw Thf, gin Emissin f gmm ditin ducs th ngy f th nuclus Thf, 68 7 = 4 68 Thf, tmic numb f 4 is 68 nd mss numb is 7 9 thin cnducting shicl shll f dius hs chg Q sd unifmly its sufc Using Guss s lw, di n xssin f n lctic fild t int utsid th shll Dw gh f lctic fild E() with distnc fm th cnt f th shll f [3] ccding t th Guss s lw, E i d = Q nc ε Thf f chgd shicl shll, th lctic fild utsid th shll Q Ei4π = ε E = Q πε 4 Elctic fild f int insid th shll Thf E = E O E = Ei4π = E = 4πε Th idnticl ccits C, C nd C 3 f ccitnc 6 mf ch cnnctd t btty s shwn Q Physics Scil mkt k _9 CSEindd 4 // :7: PM

5 Physics (CSE 9) 5 C C + Find () chg n ch ccit (b) quilnt ccitnc f th ntwk (c) ngy std in th ntwk f ccits () Chg n ccit C = C = 36 C; Chg n ccit C 3 = = 7 C (b) C q = 3 F + 6 F = 9 F (c) W = 648 W () Th ngy lls f n tm s shwn blw Which f thm will sult in th tnsitin f htn f wlngth 75 nm? [3] C D C 3 45 (b) Which tnsitin csnds t missin f ditin f mximum wlngth? () Th diffnc btwn th ngy lls = ngy f th htn mittd hc E E λ = ut it is gin tht th wlngth is 75 nm Thf 4 nm E E = = nm Thf th tnsitin mits ditin f wlngth 75nm (b) Th ditin f mximum wlngth is mittd whn th chng in ngy is minimum Tnsitin hs th minimum chng f ngy thf tnsitin mits th mximum wlngth tn nd n lh ticl ccltd thugh th sm tntil Which n f th tw hs () gt lu f d gli wlngth sscitd with it nd (b) lss kintic ngy? Justify yu nsws [3] Th ngy f ticl cclting in tntil diffnc is E = Q Sinc th chg n th lh ticl is twic tht f th tn KE = KE Thf, th kintic ngy f th tn is lss thn tht f th lh ticl W h Thf, KE = P m P m P P P = m m = m Th d-gli wlngth is insly tinl t th mmntum f th ticl Thf tn hs th lng wlngth n singl slit diffctin ximnt, whn tiny cicul bstcl is lcd in th th f light fm distnt suc, bight st is sn t th cnt f th shdw f th bstcl Exlin why? [3] Stt tw ints f diffnc btwn th intfnc ttns btind in ung s dubl slit ximnt nd th diffctin ttn du t singl slit Th bight st s in th middl f th shdw bcus f th diffctin f light t th dgs f th tiny bjct Diffnc btwn intfnc nd diffctin : () Th intfnc ttn hs numb f bight nd dk fings f qul intnsity Th diffctin ttn hs cntl bight fing f mximum intnsity nd intnsity flls s w g wy fm th cnt (b) ntfnc is du t th susitin f tw ws cming fm tw chnt sucs, whs diffctin is th susitin f scndy wlts cming fm diffnt ts f sm wfnt 4 () Dfin slf inductnc Wit its S units (b) Di n xssin f slf inductnc f lng slnid f lngth l, css-sctinl hing N numb f tuns [3] () Th ffct in which chnging cunt in cicuit inducs n mf in th sm cicuit is clld slf inductin ccding t Lnz s lw, slf-inductin lwys ss ny chng in th cunt in th cicuit nd is gnlly tmd s bck mf Th ttl flux linkd t th cicuit du t cunt in th cicuit is gin by Φ=L wh L is th tinlity cnstnt clld slf inductnc L = Φ (b) Lt lngth f th slnid b, css-sctinl b nd numb f tuns unit lngth b n f is th cunt in th winding, th mgntic fild insid th slnid hs th lu = n Physics Scil mkt k _9 CSEindd 5 // :7:4 PM

6 6 Physics (CSE 9) Thn th slf inductnc is L = Φ nl ( nl)( nl)( ) L = = Tht is, Slf inductnc f th slnid is 6 Di th xssin f fc unit lngth btwn tw lng stight lll cunt-cying cnducts Hnc dfin n m [3] O Exlin th incil nd wking f cycltn with th hl f schmtic digm Wit th xssin f cycltn fquncy [3] L= n l 5 d X G F b b D C Th figu shws ximntl stu f mt bidg Whn th tw unknwn sistncs X nd instd, th null int D is btind 4 cm fm th nd Whn sistnc f Ω is cnnctd in sis with X, th null int shifts by cm Find th sitin f th null int whn th Ω sistnc is instd cnnctd in sis with sistnc Dtmin th lus f th sistncs X nd [3] Th blncing cnditin t is gin tht l = 4 m Thf, l X l = 3 = X = 3 X () f th sistnc Ω cnnctd in sis t X, thn th nw blncing cnditin is Fm () nd () Thf, X + = = X + () X = Ω nd = 3 Ω X = + Thf th nw null int is 3333 cm wy fm th int b Lt tw stight lll cnducts nd b b std by distnc d ccding t m s cicuitl lw th mgntic fild xincd by th cnduct b du t th cunt in is = π d lng th dictin ndicul t wi b Thf, th mgntic fc cting n th wi t wi sgmnt f lngth L is S, F F = dl b L = L b L = π d b b Similly th fc n du t b cn b fund Fm cnsidtins simil t b w cn find th fc F b, n sgmnt f Lngth L f du t th cunt in b t is qul in mgnitud t F b, nd dictd twds b Thus, F = F b Thf, tw cunt cying cnducts ttct ch th if th cunt is flwing in th sm dictin Th fc unit lngth F b b = b π d Th m is th lu f tht stdy cunt which, whn mintind in ch f th tw y lng, stight, lll cnducts f ngligibl css-sctin, nd lcd n mt t in cuum, wuld duc n ch f ths cnducts fc qul t 7 nwtns mt f lngth Physics Scil mkt k _9 CSEindd 6 // :7:8 PM

7 Physics (CSE 9) 7 njctin f in T iw Outut bm f high lcity in Sid iw N S N S Unifm mgntic fild gin Elctic cclting fild btwn th mgntic fild gins n th fist fc C f th ism ll th ys incidnt nmlly Thf, th ys g unditd n th fc C f th ism ll th ys incidnt t ngl f 45 Th ngl f fctin f th blu y is n sin45 = sin sin = 47 = 3944 Thf th blu y undgs ttl intnl flctin Th ngl f fctin f th gn y is n G sin45 = sin G D Cycltn is mchin inntd by EO Lwnc which is usd f cclting chgd ticls, such s tns nd nutns t high ngis Th bsic wking incil is tht chgd ticl undgs cicul mtin with fquncy indndnt f its sd if th lcity f th ticl nd th dictin f mgntic fild dictly ndicul t ch th, whs n lctic fild will cclt it Th cycltn cnsists f chmb in which th tw smicicul hllw mtl D-shd bxs, D, D clld ds insultd fm ch th Th chmb is lcd btwn th ls f y stng lctmgnt s tht th mgntic fild sss css th ds ndicul t th th f th in n lctic scillt stblishs n cclting tntil diffnc css th g btwn th ds Th fc cting n th ciculting chg is q = m Thf th fquncy f th ticl is sin G = 44 = 88 Thf, th gn y ls undgs ttl intnl flctin Th ngl f fctin f th d ys is G n sin45 = sin sin = 39 = 988 = ω = q m ω q f = = π πm 7 Th light ys d (), gn (G) nd blu () incidnt n ight ngld ism bc t fc b Th fcti indics f th mtil f th ism f d, gn nd blu wlngths 39, 44 nd 47 sctily Out f ths which cl y will mg ut f fc c? Justify yu nsw Tc th th f ths ys ft ssing thugh fc c [3] G b 45 c 8 () Di n xssin f th g w cnsumd in sis LC cicuit cnnctd t c suc in which th hs diffnc btwn th ltg nd th cunt in th cicuit is f [5] (b) Dfin th qulity fct in n c cicuit Why shuld th qulity fct h high lu in ciing cicuits? Nm th fcts n which it dnds O () Di th ltinshi btwn th k nd th ms lus f cunt in n c cicuit (b) Dscib bifly, with th hl f lbld digm, wking f st-u tnsfm st-u tnsfm cnts lw ltg int high ltg Ds it nt ilt th incil f cnstin f ngy? Exlin Physics Scil mkt k _9 CSEindd 7 // :7:3 PM

8 8 Physics (CSE 9) Lt th ltg in th cicuit b = sin( ω t) nd th cunt = sin( ω t + ϕ ) wh ϕ is hs diffnc btwn th ltg nd cunt = = Z + ( X X ) C Thf th w in th cicuit is P= = sinωtsin( ωt+ ϕ) Z Th g w is P = ms csϕ Z ( (sin ωtsin( ωt+ ϕ) = csϕ cs( ωt + ϕ) = csϕ) Th qulity fct Q f th cicuit is dfind by hw sh th snnc is f th cicuit is m sh, it bcms m slcti Mthmticlly L Q = ω wh ω is th ntul fquncy f th cicuit, L is th inductnc, nd th sistnc in th cicuit O () Th ms lu f th cunt is dfind s ms = sin ωt T wh is th k cunt T (b) Tnsfm is dic which wks n th incil f mutul inductin tnsfm cnsists f tw sts f cils, insultd fm ch th On f th cils clld th imy cil hs N tuns Th th cil is clld th scndy cil; it hs N s tuns /C suc / = M tuns, high ltg Cunt ssing thugh th imy cil inducs mgntic fild und thm sinc bth th imy nd th scndy wund n sm in c Th flux du t th cunt in th imy sss thugh th scndy cil S if n ltnting cunt is ssing thugh th imy, it ducs n ltnting mgntic flux which links th scndy cil nd inducs n mf in it Th inducd mf in th scndy cil ε s = N d Φ s dt Th sm mgntic flux Φ inducs bck mf in th imy ls ε = N d Φ dt f th sistnc f th tnsfm is y lw, ε = nd if nly littl cunt tkn fm th scndy it is n cicuitd, thn Thn ε s = N d Φ = s dt nd N d Φ = dt s Ns = N st u tnsfm is usd t incs th ltg Thf, it hs m numb f tuns in th scndy nd th utut ltg is N s s = N st u tnsfm cnts lw ltg t high ltg withut ilting th cnstin f ngy Duing th cnsin, th cunt in th cicuit gs dwn s tht th w which is th duct f cunt nd ltg mins cnstnt 9 () Dw cicuit digm t study th inut nd utut chctistics f n n--n tnsist in its cmmn mitt cnfigutin Dw th tyicl inut nd utut chctistics [5] (b) Exlin, with th hl f cicuit digm, th wking f n--n tnsist s cmmn mitt mlifi O () Hw is zn did fbictd s s t mk it scil us did? Dw - chctistics f zn did nd xlin th significnc f bkdwn ltg (b) Exlin bifly, with th hl f cicuit digm, hw -n junctin did wks s hlf w ctifi + m C + + E CE CC E E C nut chctistics Physics Scil mkt k _9 CSEindd 8 // :7:3 PM

9 Physics (CSE 9) 9 / CE = ltg ( z ) f th Zn did, th is lg chng in th cunt Nt tht ft th bkdwn ltg z, lg chng in th cunt cn b ducd by n lmst insignificnt chng in th s bis ltg n th wds, Zn ltg mins cnstnt, n thugh cunt thugh th Zn did is wid ng This ty f th Zn did is usd f gulting suly ltgs s tht thy cnstnt (m) Cllct cunt ( C ) in m (c) CE mlifi i Outut chctistics s cunt ( ) E / Cllct t mitt ltg ( CE ) in lts C E E C C CC 6 m 5 m 4 m 3 m m m s bis z (m) (b) Fwd bis () - chctistics Whn th s bis ltg = z, thn th lctic fild stngth is high nugh t ull lnc lctns fm th hst tms n th -sid which ccltd t n-sid Ths lctns ccunt f high cunt bsd t th bkdwn Th missin f lctns fm th hst tms du t th high lctic fild is knwn s intnl fild missin fild iniztin Th lctic fild quid f fild iniztin is f th d f 6 /m Did s ctifi Pimy Tnsfm Α Scndy X L Th cllct ltg is CC = CE + CL nd in th inut cicuit, = E + whn smll ltg i is ddd t th inut ltg nd th utut cunt is + = + +Δ ( + ) i E =Δ ( + ) i Δ = β C O Zn did is fbictd by hily ding bth - nd n-sids f th junctin Du t this, dltin gin fmd is y thin (< 6 m) nd th lctic fild f th junctin is xtmly high (~5 6 /m) n f smll s bis ltg f but 5 t is sn tht whn th lid s bis ltg () chs th bkdwn did llws cunt t ss nly whn it is fwd bisd S if n ltnting ltg is lid css did th cunt flws nly in tht t f th cycl whn th did is fwd bisd This ty is usd t ctify ltnting ltgs nd th cicuit usd f this us is clld ctifi Duing th siti hlf cycl f th c, th did cnducts nd cunt flws thugh th ld sistnc fm X t Duing th ngti hlf cycl f th c, th did ds nt cnduct Thf, th cunt flws thugh th did in nly n dictin ltg css L ltg t () nut c Outut ltg t t Physics Scil mkt k _9 CSEindd 9 // :7:3 PM

10 Physics (CSE 9) 3 Tc th ys f light shwing th fmtin f n img du t int bjct lcd n th xis f shicl sufc sting th tw mdi f fcti indics n nd n Estblish th ltin btwn th distncs f th bjct, th img nd th dius f cutu fm th cntl int f th shicl sufc Hnc di th xssin f th lns mk s fmul [5] O Dw th lbld y digm f th fmtin f img by cmund micsc Di th xssin f th ttl mgnifictin f cmund micsc Exlin why bth th bjcti nd th yic f cmund micsc must h sht fcl lngths y substituting () nd () in this qutin, n n n n = OM M MC ut OM = u, M = nd MC = Thf, n Lns mk s fmul O m n n = u n m m C P C P C X O n u i M N Th gin figu shws th gmty f fmtin f img f n bjct O n th incil xis f shicl sufc with cnt f cutu C, nd dius f cutu Th ys incidnt fm mdium f fcti indx n, t nth f fcti indx n s bf, w tk th tu ( th ltl siz) f th sufc t b smll cmd t th distncs inld, s tht smll ngl ximtin cn b md n ticul, NM will b tkn t b nly qul t th lngth f th ndicul fm th int N n th incil xis tn NOM = MN OM tn NCM = MN MC tn NM = MN M Fm ΔNOC, i = NOM + NCM Similly ut fm Snll s lw i = MN OM + MN MC = NCM NM C n () = MN MN () MC M ni= n OP u Cnsid cnx lns ( cnc lns) f bslut fcti indx m t b lcd in mdium f bslut fcti indx m Cnsiding th fctin f int bjct n th sufc XP, th img is fmd t t distnc f C = P = (s th lns is thin) CC = P C = CO = P O = u t fllws fm th fctin du t cnx shicl sufc XP tht u + = Th fctd y fm suffs scnd fctin n th sufc XP nd mgs lng Thf is th finl l img f O H th bjct distnc is u= Cl Pl= Lt Cl Pl = P (Nt P P is y smll) (Finl img distnc) Lt b dius f cutu f scnd sufc f th lns t fllws fm fctin du t cnc shicl sufc fm dns t mdium tht dding () & () () + = = () + = ( ) u u = ( ) Physics Scil mkt k _9 CSEindd // :7:3 PM

11 Physics (CSE 9) ut = nd u f = = = ( ) f O Th ngul mgnifictin mgnifying w f cmund micsc is dfind s th ti f th ngl b subtndd by th finl img t th y t th ngl subtndd by th bjct sn dictly, whn bth lcd t th lst distnc f distinct isin Thf, ngul mgnifictin, M = β/α F f u f F L F D b E Ey Sinc th ngls smll, tn nd b tn b Thf, Nw, nd M = tn b tn tnb = D "" tn = = D D Substituting th lus f tn nd tn b in th xssin f M, w gt M = D = D M = Thus, th mgnifictin ducd by th cmund micsc is th duct f th mgnifictins ducd by th yic nd th bjcti; tht is, M= M M, () Wh M nd M th mgnifying ws f th yic nd th bjcti sctily Th lin mgnifictin f th l, intd img ducd by th yic is / Lin mgnifictin is gin by D M = +, () wh f is th fcl lngth f th yic nd / is th lin mgnifictin f th bjct ducd by th bjcti ls, Fm Eqs (), () nd (3), w h f M = u (3) M D = + u f W knw tht = u f Multilying bth sids by w gt u u = u f = + f = f Substituting this lu in th xssin f M, w h D M = f + f Fm th b xssin it cn b cncludd tht f high mgnifictin M th fcl lngth f bjcti nd yic shuld b smll s bth th fcl lngths insly tinl t mgnifictin M Physics Scil mkt k _9 CSEindd // :7:3 PM